<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.1 20151215//EN" "JATS-archivearticle1.dtd"> <article xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.1"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn pub-type="epub" publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">43154</article-id><article-id pub-id-type="doi">10.7554/eLife.43154</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Short Report</subject></subj-group><subj-group subj-group-type="heading"><subject>Epidemiology and Global Health</subject></subj-group></article-categories><title-group><article-title>Collider bias and the apparent protective effect of glucose-6-phosphate dehydrogenase deficiency on cerebral malaria</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes" equal-contrib="yes" id="author-63402"><name><surname>Watson</surname><given-names>James A</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">http://orcid.org/0000-0001-5524-0325</contrib-id><email>jwatowatson@gmail.com</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="other" rid="fund1"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" equal-contrib="yes" id="author-114823"><name><surname>Leopold</surname><given-names>Stije J</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0002-0482-5689</contrib-id><email>stije@tropmedres.ac</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-97658"><name><surname>Simpson</surname><given-names>Julie A</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">http://orcid.org/0000-0002-2660-2013</contrib-id><xref ref-type="aff" rid="aff3">3</xref><xref ref-type="other" rid="fund2"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-35005"><name><surname>Day</surname><given-names>Nicholas PJ</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="other" rid="fund1"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-35008"><name><surname>Dondorp</surname><given-names>Arjen M</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">http://orcid.org/0000-0001-5190-2395</contrib-id><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="other" rid="fund1"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-35051"><name><surname>White</surname><given-names>Nicholas J</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">http://orcid.org/0000-0002-1897-1978</contrib-id><email>nickw@tropmedres.ac</email><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="other" rid="fund1"/><xref ref-type="fn" rid="con6"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><label>1</label><institution content-type="dept">Mahidol Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine</institution><institution>Mahidol University</institution><addr-line><named-content content-type="city">Bangkok</named-content></addr-line><country>Thailand</country></aff><aff id="aff2"><label>2</label><institution content-type="dept">Nuffield Department of Medicine, Centre for Tropical Medicine and Global Health</institution><institution>University of Oxford</institution><addr-line><named-content content-type="city">Oxford</named-content></addr-line><country>United Kingdom</country></aff><aff id="aff3"><label>3</label><institution content-type="dept">Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health</institution><institution>The University of Melbourne</institution><addr-line><named-content content-type="city">Melbourne</named-content></addr-line><country>Australia</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Lipsitch</surname><given-names>Marc</given-names></name><role>Reviewing Editor</role><aff><institution>Harvard TH Chan School of Public Health</institution><country>United States</country></aff></contrib><contrib contrib-type="senior_editor"><name><surname>Ferguson</surname><given-names>Neil M</given-names></name><role>Senior Editor</role><aff><institution>Imperial College London</institution><country>United Kingdom</country></aff></contrib></contrib-group><author-notes><fn fn-type="con" id="equal-contrib1"><label>†</label><p>These authors contributed equally to this work</p></fn></author-notes><pub-date date-type="publication" publication-format="electronic"><day>28</day><month>01</month><year>2019</year></pub-date><pub-date pub-type="collection"><year>2019</year></pub-date><volume>8</volume><elocation-id>e43154</elocation-id><history><date date-type="received" iso-8601-date="2018-10-26"><day>26</day><month>10</month><year>2018</year></date><date date-type="accepted" iso-8601-date="2019-01-22"><day>22</day><month>01</month><year>2019</year></date></history><permissions><copyright-statement>© 2019, Watson et al</copyright-statement><copyright-year>2019</copyright-year><copyright-holder>Watson et al</copyright-holder><ali:free_to_read/><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref>http://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife-43154-v2.pdf"/><abstract><object-id pub-id-type="doi">10.7554/eLife.43154.001</object-id><p>Case fatality rates in severe falciparum malaria depend on the pattern and degree of vital organ dysfunction. Recent large-scale case-control analyses of pooled severe malaria data reported that glucose-6-phosphate dehydrogenase deficiency (G6PDd) was protective against cerebral malaria but increased the risk of severe malarial anaemia. A novel formulation of the balancing selection hypothesis was proposed as an explanation for these findings, whereby the selective advantage is driven by the competing risks of death from cerebral malaria and death from severe malarial anaemia. We re-analysed these claims using causal diagrams and showed that they are subject to collider bias. A simulation based sensitivity analysis, varying the strength of the known effect of G6PDd on anaemia, showed that this bias is sufficient to explain all of the observed association. Future genetic epidemiology studies in severe malaria would benefit from the use of causal reasoning.</p></abstract><kwd-group kwd-group-type="author-keywords"><kwd>causal inference</kwd><kwd>severe malaria</kwd><kwd>collider bias</kwd><kwd>glucose-6-phosphate dehydrogenase deficiency</kwd><kwd><italic>Plasmodium falciparum</italic></kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd><italic>P. falciparum</italic></kwd></kwd-group><funding-group><award-group id="fund1"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100004440</institution-id><institution>Wellcome Trust</institution></institution-wrap></funding-source><principal-award-recipient><name><surname>Watson</surname><given-names>James A</given-names></name><name><surname>Day</surname><given-names>Nicholas PJ</given-names></name><name><surname>Dondorp</surname><given-names>Arjen M</given-names></name></principal-award-recipient></award-group><award-group id="fund2"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/501100000925</institution-id><institution>National Health and Medical Research Council</institution></institution-wrap></funding-source><award-id>Senior Research Fellowship 1104975</award-id><principal-award-recipient><name><surname>Simpson</surname><given-names>Julie A</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Selection bias, also known as collider bias, likely explains the apparent protective effect of G6PD deficiency against cerebral falciparum malaria.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Severe falciparum malaria is defined by one or more criteria indicating vital organ dysfunction in the presence of microscopy confirmed asexual blood stages of <italic>Plasmodium falciparum</italic> in the peripheral blood film (<xref ref-type="bibr" rid="bib15">WHO, 2015</xref>). Multiple vital organ dysfunction is associated with increased mortality (<xref ref-type="bibr" rid="bib14">WHO, 2014</xref>). Common major clinical manifestations of severe malaria include coma, acidosis, renal failure and anaemia. Of these manifestations, anaemia is an inevitable consequence of symptomatic malaria (<xref ref-type="bibr" rid="bib13">White et al., 2014</xref>). However, anaemia in individuals at risk of <italic>Plasmodium falciparum</italic> infection can also be the consequence of red cell genetic polymorphisms frequent in the populations at risk, such as glucose-6-phosphate dehydrogenase deficiency (G6PDd) or haemoglobinopathies.</p><p>There is considerable interest in understanding the mechanisms conferring protective effects against severe falciparum malaria of the genetic polymorphisms which are common in malaria endemic areas (<xref ref-type="bibr" rid="bib12">Weatherall, 2008</xref>). For some, such as the sickle cell trait, several different mechanisms have been proposed. These include reduced parasite erythrocyte invasion, enhanced parasitised red cell phagocytosis and a reduced propensity of infected red cells to sequester in the microvasculature (<xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al., 2014</xref>; <xref ref-type="bibr" rid="bib1">Band et al., 2015</xref>; <xref ref-type="bibr" rid="bib2">Cholera et al., 2008</xref>; <xref ref-type="bibr" rid="bib16">Williams, 2016</xref>). The mechanism underlying protection from severe falciparum malaria is less clear for others such as glucose-6-phosphate dehydrogenase deficiency (G6PDd). This X-linked genetic polymorphism results in the most common human enzymopathy. Nearly 200 different genetic variants have been reported (<xref ref-type="bibr" rid="bib5">Howes et al., 2012</xref>; <xref ref-type="bibr" rid="bib6">Luzzatto and Arese, 2018</xref>). The mechanism whereby G6PD deficiency protects against malaria, and the natural selection forces which have resulted in the different genotypes are still debated. Prospective observational hospital or clinic based patient studies have provided the major component of the evidence base. Estimating causal effects from observational studies in severe malaria patients is difficult due to both confounding and selection bias. This work focuses on collider bias introduced by inappropriate data filtering (<xref ref-type="bibr" rid="bib9">Snoep et al., 2014</xref>; <xref ref-type="bibr" rid="bib8">Pearce and Richiardi, 2014</xref>).</p><p>It has been suggested that G6PDd both increases the risk of severe malarial anaemia (SMA) and decreases the risk of cerebral malaria (CM) (<xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al., 2014</xref>; <xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>). These conclusions were based on a pooled analysis of observational data from over 11,000 patients with severe malaria studied in Africa and Asia, and relevant population controls. Based on these genetic association studies, a new formulation of the balancing-selection hypothesis was proposed in which G6PD polymorphisms are maintained in human populations, at least in part, by an evolutionary trade-off between different adverse outcomes of <italic>P. falciparum</italic> infection (<xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>). Collider bias probably explains this negative association between G6PDd and CM, suggesting that causal interpretations of this association and the novel formulation of balancing selection in G6PDd are invalid.</p></sec><sec id="s2" sec-type="results"><title>Results</title><p>Two published analyses of pooled data from observational studies of patients with severe falciparum malaria used severe malarial anaemia (SMA) and cerebral malaria (CM) as the main endpoints (outcomes) of interest (<xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al., 2014</xref>; <xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>). Both these published analyses defined cases of CM as the presence of coma but without concomitant SMA, and cases of SMA as patients with severe anaemia but who were conscious. Therefore, these case definitions excluded patients who had both SMA and CM. All other presentations of severe malaria were also excluded (pulmonary oedema, shock, etc.). Population controls were recruited at each site to match the ethnic composition of cases, and in some instances cord blood samples were used as controls. The consequence of these case definitions is to create an artificial dependency between SMA and CM: if a patient has SMA then they cannot have CM. G6PDd is known to influence haemoglobin concentrations directly by causing haemolysis of older erythrocytes in acute malaria. Therefore it is to be expected that SMA is positively correlated with G6PDd, thus creating a negative correlation between CM and G6PDd. In probabilistic terms, this conditional dependence is written as <inline-formula><mml:math id="inf1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">C</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>≠</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mstyle></mml:math></inline-formula>. Indeed, when all the G6PDd mutations were mapped onto the WHO severity classification score (<xref ref-type="bibr" rid="bib17">Yoshida et al., 1971</xref>), it was observed that "The mean G6PDd score was 13.5% in controls, 13% in cerebral malaria cases and 16.9% in severe malarial anaemia cases [..]." (page 8, <xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>). This pattern remained consistent (6, 5.6, and 7.1%, respectively) after exclusion of the G6PD c.202C > T mutation (one of the ‘A-’ mutations and the most prevalent in the pooled data).</p><p>By excluding patients with both SMA and CM (approximately 12% of those with either SMA or CM in the pooled data), the number of G6PDd patients in the CM category is artificially reduced and we would expect there to be fewer G6PDd patients than in the control group. <xref ref-type="fig" rid="fig1">Figure 1</xref> proposes a simple causal diagram which posits plausible inter-dependencies limited to the variables of interest. A simple simulation study based on the assumptions shown in <xref ref-type="fig" rid="fig1">Figure 1</xref> can be used to estimate the relationship between G6PDd and SMA which would result in the observed odds ratio for G6PDd in CM cases versus controls reported in <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref>. We assessed the null model in which there is no direct causal link between G6PDd and CM in severe falciparum malaria (i.e. no arrow from G6PD deficiency to CM). We also assume that there is no direct link between SMA and CM. We calibrated the model with the marginal probabilities of SMA and CM reported in <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref> and only varied the odds ratio of G6PDd in SMA cases versus controls from 1 (assuming no effect of G6PDd on SMA) to 2 (twice as likely to be G6PDd in the SMA cases than in the controls). For simplicity (avoiding assumptions concerning gene dose effects) we restricted the analysis to males and only compare the simulation results with the reported associations in males.</p><fig id="fig1" position="float"><object-id pub-id-type="doi">10.7554/eLife.43154.002</object-id><label>Figure 1.</label><caption><title>Causal diagram highlighting collider bias in <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref> and <xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al. (2014)</xref>.</title><p>G6PD deficiency is the exposure of interest (green) and cerebral malaria (CM) is the outcome of interest (red). By defining the CM cases as those who had coma but no severe anaemia, collider bias operates on the effect of G6PDd on CM.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="article.xml.media/fig1.jpg"/></fig><p><xref ref-type="fig" rid="fig2">Figure 2</xref> shows that if the odds ratio for G6PDd in SMA cases versus controls is strictly greater than 1, the estimated odds ratio for G6PDd in CM cases versus controls is biased (the thick red line is below the true simulated value of 1). The magnitude of this bias increases monotonically as the odds ratio for G6PDd in SMA cases versus controls increases. As can be seen from the causal diagram in <xref ref-type="fig" rid="fig1">Figure 1</xref>, there is no bias in the estimated odds ratio for G6PDd in SMA cases versus controls (in <xref ref-type="fig" rid="fig2">Figure 2</xref> the thick blue line approximates the identity line). This simple simulation model, restricted to males, shows that for any value of the odds ratio for G6PDd in SMA cases versus controls taken inside the reported 95% confidence interval (CI) [1.2–1.8] from <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref>, will result in a biased odds ratio for G6PDd in CM cases versus controls inside the interval [0.69–0.98], the reported 95% CI for G6PDd in CM cases versus controls (<xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>). Moreover, if we use their reported point estimate of 1.48, restricted to males, for the odds ratio of G6PDd in SMA cases versus controls, the simulation model estimates that the observed (biased) odds ratio for G6PDd in CM cases versus controls is 0.87, qualitatively very close to their estimate of 0.82. We note that the effect of G6PDd on severe anaemia in homozygous G6PDd girls and hemizygous G6PDd boys reported in <xref ref-type="bibr" rid="bib10">Uyoga et al. (2015)</xref>, an odds ratio of 1.71 (95% CI: 1.34–2.18) for G6PDd in SMA cases versus controls, is also consistent with these results. Therefore collider bias could be sufficient to explain all the observed association.</p><fig id="fig2" position="float"><object-id pub-id-type="doi">10.7554/eLife.43154.003</object-id><label>Figure 2.</label><caption><title>Results of the simulation based sensitivity analysis showing how collider bias can explain all the reported association between CM and G6PDd.</title><p>The simulation assumes that CM is independent of G6PD status but that SMA is dependent on G6PDd status (<xref ref-type="fig" rid="fig1">Figure 1</xref>). Case definitions of CM and SMA exclude patients with both. The left panel shows the observed simulation based estimate of the odds ratio (OR) for G6PDd in SMA cases versus controls (y-axis) as a function of the true simulated value (x-axis). No bias arises (the observed and true values lie on the line of identity). The right panel shows the observed simulation based estimate of the OR for G6PDd in CM cases versus controls (y-axis), again as a function of the true simulated value of the OR for G6PDd in SMA cases versus controls (x-axis). This estimate suffers from collider bias since the true value of the OR for G6PDd in SMA cases versus controls was set to 1). The faint blue shaded areas show the 95% CI [1.22–1.8] for the odds ratio of G6PDd in SMA cases versus controls, restricted to males (<xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>). The point estimate (1.48) is shown by the dashed blue line. The faint red shaded area shows the 95% CI [0.69–0.98] for G6PDd in CM cases versus controls, also restricted to males, with the point estimate (0.82) shown by the dashed red line. CI: confidence interval.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="article.xml.media/fig2.jpg"/></fig></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>This re-analysis of recent reports that G6PDd reduced the risk of CM directly (<xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al., 2014</xref>; <xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref>) suggests that the observations could have resulted entirely from collider bias. This highlights the difficulty of inferring causal relationships between baseline patient covariates (in this case G6PDd) and covariates which define inclusion criteria. The necessary causal odds ratios for G6PDd in SMA cases versus controls which would give rise to the biased observed association between G6PD status and CM fit with the recent estimate of 1.71 in homozygous girls and hemizygous boys (<xref ref-type="bibr" rid="bib10">Uyoga et al., 2015</xref>). This is not to say that the risk of CM is unaffected by G6PDd, but that the observations reported could have arisen purely as a result of the implicit collider bias induced by the selection of patients by the severe malaria criteria.</p><p>The example reported here highlights a major difficulty when attempting to estimate causal contributions when factors of interest define inclusion into the clinical study and the subsequent data analysis. All prospective observational severe malaria studies suffer from two major issues. First, case definitions are subjective and change over time (even though standard guidelines exist, see <xref ref-type="bibr" rid="bib15">WHO (2015)</xref>) and mortality is strongly dependent on the case definition. Second, enrolment into studies can only be done at the hospital or clinic level and neither duration of illness nor treatment seeking behaviour can be accounted for adequately.</p><p>The notion and definition of ‘severe malaria’ has two operational purposes. First it is a clinical tool for appropriate triage of malaria patients at high risk of death. Second it is a research tool for the evaluation of novel interventions seeking to reduce mortality. Interventions aimed at reducing mortality need to be trialled in the most severely ill patients in order to demonstrate intervention efficacy in this important subgroup. Pooled analyses of severe malaria studies need to take into account the variability of study inclusion and exclusion criteria. Researchers must appreciate that severe malaria is not an objective category but a subjective case definition subset from a spectrum of severity. Moreover, restricting analyses to specific patient subgroups, especially in the analysis of large pooled datasets, can have a considerable impact on the final result (<xref ref-type="bibr" rid="bib4">Gelman and Loken, 2013</xref>). With increased emphasis on providing open access data so that analyses can be evaluated and best use made of clinical research it would be very helpful if investigators could publish reproducible code alongside their analyses. Future genetic epidemiological studies could benefit from use of causal diagrams and would be more readily evaluable by provision of accompanying code.</p></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Data analysis in <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref> and <xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al. (2014)</xref></title><p>The odds ratios for G6PDd in cases versus controls are given in Table 3 of <xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al. (2014)</xref> (page 1201). The results, restricted to males, are 0.81 (95% CI: 0.68–0.96) for CM and 1.49 (95% CI: 1.24–1.79) for SMA. The case phenotype definitions are denoted ‘Cerebral malaria only’ for CM and ‘Severe malarial anaemia’ only for SMA. These case definitions, whereby patients with both SMA and CM are excluded, are also given in their Table 1. A total of 6283 cases had cerebral malaria or severe malarial anaemia, broken down as 3345 had cerebral malaria only; 2196 had severe malarial anaemia only; 742 had both cerebral malaria and severe malarial anaemia. The reported odds ratios were computed using logistic regression models with the main adjustment of interest being sickle haemoglobin genotype (HbS). We only consider the reported results restricted to males. The relevant section from the paper is: "<italic>Single-SNP tests, adjusted for HbS genotype, sex and ancestry, for association with severe malaria and the severe malaria subtypes cerebral malaria only and severe malarial anemia only were performed for the 55 SNPs with a known association with severe malaria. Standard logistic regression models were used for tests of association at each autosomal SNP (Supplementary Table 25). Primary analyses comprised tests of association between each SNP and severe malaria phenotypes across all individuals combined as well as separately by sex (X-chromosome SNPs only) and study site: genotypic, additive, dominant, recessive and heterozygote advantage genetic models of inheritance were considered.</italic>" (online Methods, Statistical analysis, (<xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al., 2014</xref>)).</p></sec><sec id="s4-2"><title><xref ref-type="bibr" rid="bib3">Clarke et al., 2017</xref></title><p>The odds ratios for G6PDd in cases versus controls are given in Table 3 of <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref> (page 6). In this publication, the results, restricted to males, are 0.82 (95% CI: 0.69–0.98) for CM and 1.48 (95% CI: 1.22–1.8) for SMA (their Table 3). The reason for the slight discrepancy between the two publications does not appear to be stated. They included a total of 6284 patients with cerebral malaria or severe malarial anaemia, broken down as: 3359 individuals had cerebral malaria only; 2184 had severe malarial anaemia only; 741 had both cerebral malaria and severe malarial anaemia. Table 1 and 6 of <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref> show the case definitions for CM and SMA, highlighting that those who have both clinical presentations are excluded from the respective case definitions. This is further confirmed on page 18 where the authors state: "<italic>For reasons of sample size, we did not conduct a detailed analysis of other sub-types of severe malaria, or of those individuals who had both cerebral malaria and severe malarial anaemia’.</italic> Standard logistic regression models were also used to obtain the odds ratios: <italic>‘In primary analyses, standard fixed effects logistic regression methods were used for tests of association with severe malaria and sub-types at each SNP under additive, dominant, recessive and heterozygous models. [..] Results were adjusted for sickle hemoglobin (HbS), gender and ethnicity.</italic>" (bottom of page 18).</p></sec><sec id="s4-3"><title>Sensitivity analysis</title><p>In order to characterise the proportion of the reported association explained by collider bias we constructed a simple simulation study based on the analytical procedures in <xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al. (2014)</xref>; <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref>. We restrict our simulation to males, and calibrate and test the model using only the results reported in males in both publications (identical up to one decimal point). For simplicity, the simulation ignores the effect of HbS which is a confounder between SMA and CM, and generates data where the two presentations occur independently, which is equivalent to adjusting for HbS in the regression model. The procedure generates simulated data dependent on a parameter characterising the effect of G6PDd on severe malarial anaemia. As no adjustment is necessary, we then compute the non-parametric odds ratio for G6PDd in CM cases versus controls, excluding from the CM case definition all those who have SMA. This simulated ‘observed’ odds ratio estimated from the 2 x 2 table (cases and controls versus G6PDd and G6PD normals) is thereby directly comparable to the reported odds ratios (obtained from logistic regression with the appropriate adjustments) in <xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al. (2014)</xref>; <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref>, if we assume that only sex, ethnicity and <italic>HbS</italic> are the true confounders (i.e. all necessary adjustments were made in both publications).</p><p>The hypothetical data were simulated based on the following assumptions:</p><list id="I1" list-type="order"><list-item><p>G6PD deficiency increases the risk of SMA in acute symptomatic malaria (the size of the effect is the only free parameter in the model and varies from 1 to 2 as defined by the odds ratio for G6PDd in SMA cases versus controls). In reality this would be expected to be a function of genotype and gene dose (i.e. hemizygotes and homozygotes would have a greater risk than heterozygotes).</p></list-item><list-item><p>CM is independent of G6PD status.</p></list-item><list-item><p>A population of males only (i.e. no heterozygote women, so no partial effects) with homogeneous background frequency of G6PDd.</p></list-item><list-item><p>CM and SMA occur independently.</p></list-item></list><p>From the data in <xref ref-type="bibr" rid="bib3">Clarke et al. (2017)</xref> and <xref ref-type="bibr" rid="bib7">Malaria Genomic Epidemiology Network et al. (2014)</xref>, we can estimate the marginal probability of CM as 0.34, independent of G6PD status (assumption 2). We can also estimate the marginal probability of SMA as 0.24. The probability of G6PDd in males was 0.15.</p><p>If we denote <inline-formula><mml:math id="inf2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>π</mml:mi><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>≥</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>0.24</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mstyle></mml:math></inline-formula> then by the law of total probability:<disp-formula id="equ1"><mml:math id="m1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">n</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mfrac><mml:mrow><mml:mn>0.24</mml:mn><mml:mspace width="thinmathspace"/><mml:mo>−</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>0.15</mml:mn><mml:mi>π</mml:mi></mml:mrow><mml:mn>0.85</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></disp-formula>where G6PDd denotes G6PD deficient and G6PDn denotes G6PD normal.</p><p>The true proportion of G6PDd in the controls is known and fixed as <inline-formula><mml:math id="inf3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mstyle></mml:math></inline-formula>, with the proportion of G6PDn in the controls is given by <inline-formula><mml:math id="inf4"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mstyle></mml:math></inline-formula>, therefore the odds of G6PDd in the control group is given by <inline-formula><mml:math id="inf5"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></inline-formula>.</p><p>We then simulate cases as follows. For each value of <inline-formula><mml:math id="inf6"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>π</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mn>0.24</mml:mn><mml:mo>,</mml:mo><mml:mn>0.5</mml:mn><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mstyle></mml:math></inline-formula>:</p><p><bold>Step 1</bold>. Simulate 1 million patients such that:</p><p><inline-formula><mml:math id="inf7"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">C</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>0.34</mml:mn></mml:mrow></mml:mstyle></mml:math></inline-formula>,</p><p><inline-formula><mml:math id="inf8"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>0.15</mml:mn></mml:mrow></mml:mstyle></mml:math></inline-formula>.</p><p><inline-formula><mml:math id="inf9"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace"/><mml:mo>=</mml:mo><mml:mspace width="thinmathspace"/><mml:mi>π</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula>.</p><p><bold>Step 2</bold>. Select only the patients who have either just CM, or just SMA, filtering out those with concomitant SMA and CM.</p><p><bold>Step 3</bold>. In the remaining data compute <inline-formula><mml:math id="inf10"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle></mml:math></inline-formula> (number of G6PDd with SMA); <inline-formula><mml:math id="inf11"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">n</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle></mml:math></inline-formula> (number of G6PDn patients with SMA); <inline-formula><mml:math id="inf12"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">C</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle></mml:math></inline-formula> (number of G6PDd patients with CM); <inline-formula><mml:math id="inf13"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">n</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">C</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle></mml:math></inline-formula> (number of G6PDn patients with CM). The simulated odds ratio for G6PDd in SMA cases versus controls is <inline-formula><mml:math id="inf14"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">n</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">S</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mspace width="thinmathspace"/><mml:mo>−</mml:mo><mml:mspace width="thinmathspace"/><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></inline-formula>, and the simulated odds ratio for G6PDd in CM cases versus controls is <inline-formula><mml:math id="inf15"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">C</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">n</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">C</mml:mi><mml:mi mathvariant="sans-serif">M</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mspace width="thinmathspace"/><mml:mo>−</mml:mo><mml:mspace width="thinmathspace"/><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="sans-serif">G</mml:mi><mml:mn mathvariant="sans-serif">6</mml:mn><mml:mi mathvariant="sans-serif">P</mml:mi><mml:mi mathvariant="sans-serif">D</mml:mi><mml:mi mathvariant="sans-serif">d</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></inline-formula>.</p><p>The causal diagram which corresponds to exclusion operating in Step two is shown in <xref ref-type="fig" rid="fig1">Figure 1</xref>. Selection bias can be seen via the role of the vertex <italic>Case definition</italic> which is a collider between <italic> G6PD deficiency</italic> and <italic>Cerebral malaria (CM)</italic>. Implementation of the simulation model in R can be found at: <ext-link ext-link-type="uri" xlink:href="https://github.com/Stije/SevereMalariaAnalysis/SelectionBiasSimulation.Rmd">https://github.com/Stije/SevereMalariaAnalysis/SelectionBiasSimulation.Rmd</ext-link> (<xref ref-type="bibr" rid="bib11">Watson and Leopold, 2019</xref>; copy archived at <ext-link ext-link-type="uri" xlink:href="https://github.com/elifesciences-publications/SevereMalariaAnalysis">https://github.com/elifesciences-publications/SevereMalariaAnalysis</ext-link>).</p></sec></sec></body><back><sec id="s6" sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="COI-statement" id="conf1"><p>No competing interests declared</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>Conceptualization, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing</p></fn><fn fn-type="con" id="con2"><p>Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing</p></fn><fn fn-type="con" id="con3"><p>Supervision, Methodology, Writing—review and editing</p></fn><fn fn-type="con" id="con4"><p>Resources, Funding acquisition, Validation, Writing—review and editing</p></fn><fn fn-type="con" id="con5"><p>Resources, Supervision, Validation, Writing—review and editing</p></fn><fn fn-type="con" id="con6"><p>Conceptualization, Resources, Supervision, Funding acquisition, Validation, Writing—review and editing</p></fn></fn-group></sec><sec id="s5" sec-type="supplementary-material"><title>Additional files</title><supplementary-material id="transrepform"><object-id pub-id-type="doi">10.7554/eLife.43154.004</object-id><label>Transparent reporting form</label><media mime-subtype="docx" mimetype="application" xlink:href="elife-43154-transrepform-v2.docx"/></supplementary-material><sec id="s7" sec-type="data-availability"><title>Data availability</title><p>This manuscript is a methodology paper; no new data were generated. 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person-group-type="author"><name><surname>Yoshida</surname> <given-names>A</given-names></name><name><surname>Beutler</surname> <given-names>E</given-names></name><name><surname>Motulsky</surname> <given-names>AG</given-names></name></person-group><year iso-8601-date="1971">1971</year><article-title>Human glucose-6-phosphate dehydrogenase variants</article-title><source>Bulletin of the World Health Organization</source><volume>45</volume><fpage>243</fpage><lpage>253</lpage><pub-id pub-id-type="pmid">5316621</pub-id></element-citation></ref></ref-list></back><sub-article article-type="decision-letter" id="SA1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.43154.006</article-id><title-group><article-title>Decision letter</article-title></title-group><contrib-group><contrib contrib-type="editor"><name><surname>Lipsitch</surname><given-names>Marc</given-names></name><role>Reviewing Editor</role><aff><institution>Harvard TH Chan School of Public Health</institution><country>United States</country></aff></contrib><contrib contrib-type="reviewer"><name><surname>Murray</surname><given-names>Ellie</given-names> </name><role>Reviewer</role><aff><institution>Harvard Chan School of Public Health</institution><country>United States</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.</p></boxed-text><p>[Editors’ note: this article was originally rejected after discussions between the reviewers, but the authors were invited to resubmit after an appeal against the decision.]</p><p>Thank you for submitting your work entitled "Causal pathways in severe falciparum malaria" for consideration by <italic>eLife</italic>. Your article has been reviewed by two peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by a Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Ellie Murray (Reviewer #2).</p><p>Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in <italic>eLife</italic>.</p><p>This is a very interesting and thoughtful effort to bring causal reasoning to the extremely complex world of malaria clinical outcomes. Such approaches will be important to generating hypotheses for how to improve clinical care in this field, as the authors note, and I am glad to see these efforts. Toward that end, however, we have substantial concerns about the way it has been applied.</p><p>However for reasons stated below, both reviewers have major concerns with the analysis. As a result, this paper cannot be published in something like its current form. The first Case Study is not appropriate because it doesn't ask well-posed causal questions, and the second Case Study is essentially a critique of another paper that I can't verify includes a correct description of what the other paper did. If it is a correct description, it is a very important point that should be made as a letter or some other way, and the simulation is superfluous except to provide an illustration to those outside the epidemiology field.</p><p>Normally when <italic>eLife</italic> declines a paper the reviews are appended verbatim to the review, while only revise and resubmit decisions have a combined letter detailing required changes. In this instance, the reviewers had considerable dialogue post review and pre-decision, so we have written a combined letter that contains our key points from the original reviews, revised after discussion.</p><p>Major comments:</p><p>1) In Case Study I, most of the exposures studied are health states, rather than interventions. As has been discussed in the context of obesity (a health state), the causal question "what is the effect of (a particular health state) on (a particular outcome)" is incoherent, or at best incomplete; causal questions imply a specified (hypothetical) intervention that could be applied in a hypothetical randomized trial to change the health state in a particular way. If the intervention is not specified, then two hypothetical trials employing different interventions to achieve the same change in a patient's health state would potentially get different (even different signs of) results.</p><p>The most important implications of a lack of well-defined interventions are (1) that confounding can be hard to define when the way in which a variable is changed is unknown; (2) the practical utility of the estimate is limited since we do not know how to act upon it; and (3) when there are methods of changing the variable that have effects in different directions we are estimating a weighted average and may make the wrong conclusion. For an example of this 3rd issue, consider the exposure weight loss. Some individuals lose weight by diet and/or exercise and this is expected to improve their health status, but other individuals lose weight by developing cancer and this is expected to worsen their health status. If we don't know the relative frequency of these interventions then we might find that losing weight is harmful to overall health even though intentional weight loss via diet and exercise would be beneficial.</p><p>To take a key example for this paper, anemia on admission could be changed by (1) moving up the date of admission, presumably to an earlier time in the disease course – e.g. by active case finding and referral; (2) administering blood transfusions on admission; (3) administering drugs to stimulate red cell production on admission; (4) iron dietary supplements at the population level (pre-admission). Even if these were calibrated to achieve exactly the same mean change in hematocrit, (1) could be beneficial; (2) could be slightly harmful (as suggested by the slight increase in mortality in this study); (3) and (4) might go either way, depending on whether they protect the host more or enhance parasite replication more. Similarly, almost any of the other harmful states could be changed on admission by either earlier admission or changing treatment at admission, with potentially different effects. As a result, even if all confounding pathways were blocked, the interpretation of the resulting estimate would be as a weighted average of the effects of 1-4 (and any other possible methods of changing anemia) with unknown weights, making the answer uninterpretable for clinical or public health decision-making.</p><p>By this logic, the effects in Figure 4, with the exception of the treatment effect, are not the answers to well-posed causal questions and should be removed.</p><p>We note that both reviewers, who are knowledgeable about causal inference, acknowledge that the view taken here – that well-defined interventions are required for a well-posed causal question – is not universal in the field. Some have defended the use, for example, of race or sex as causes of disease outcomes, without a well-defined notion of how an intervention could change these. However, we make a distinction between effectively "unalterable" states (such as sex and race), about which controversy exists as to whether they can be considered in causal analyses, and readily alterable states (such as hematocrit) in which very straightforward alterations (transfusion, nutrition, earlier presentation) plausibly have opposite signs of effect. Here, using the machinery of causal inference to isolate the "causal" effect of hematocrit does not helpfully inform interventions, because the interventions might have the same or the opposite effect as suggested by the analysis. Besides this there were other concerns about the causal reasoning in Case Study I.</p><p>2) It was not clear that the DAG in Figure 3 supports the authors conclusions about the identifiability of a causal effect of parasitemia as drawn – in the fifth paragraph of the subsection Case study 1: factors determining survival in "severe malaria", this is described as biased through an open path at immunity, while in the subsection "Simulation study for case study 2" as through an open path at anaemia. But, assuming that all the blue and green nodes represented measured covariates which can be adjusted for, there are no open backdoor paths from parasitemia to death through either immunity (the path becomes blocked again at anaemia) or anaemia itself (the open collider path is blocked at age). However, it is certainly reasonable that there exist other unmeasured common causes of anaemia or immunity (for example, the gene from case study 2 is not included in this DAG, nor are diet or other co-infections), and if those were included (or if some of the green or blue nodes especially age or AKI were not measured) there would indeed be an open backdoor path. Most common biases in real data analyses occur because of paths that involve unmeasured variables, so including unmeasured variables such as genes, diet, or coinfections as unknowns in your figure would also be useful for didactic purposes. Furthermore, it's not clear that it would be appropriate to condition on all the blue and green variables for exactly this reason – they are likely to be colliders and therefore conditioning can induce bias; and conditioning on them would remove some of the effect of parasitemia.</p><p>3) If this paper is intended to be a tutorial for readers who have not had prior exposure to causal inference or directed acyclic graphs, the description of the assumptions required for these methods and their comparison to other approaches is insufficient. A simpler example would be more useful and the paper should probably include more detail on how to read the DAG to determine potential for bias. In general, a separate DAG should be drawn for each causal question – the DAG in Figure 3 contains many more variables than are necessary to estimate an effect of parasitemia (presuming we could define one sufficiently well), but does not include sufficient variables to estimate the effect of anti-malarial drugs except from a randomized controlled trial (and in that case has too many variables). Finally, it seems likely that a number of these variables have a cyclic / feedback relationship, in which case there may be time-varying exposure-confounder feedback which could exacerbate the problems of a lack of well-defined interventions.</p><p>4) For Case Study II, it is hard to understand what was done in Clarke et al., the paper in <italic>eLife</italic> that they criticize. We can't tell on a brief look at that paper whether the comparison was between:</p><p>a) Severe malaria anemia (SMA) (+- cerebral malaria CM) vs. population controls, and separately CM+-SMA vs. population controls, for G6PD status (which would not suffer from the problem the authors posit);</p><p>b) SMA only vs. population controls, and CM only vs. population controls (in which the CM only group would be depleted of those with SMA, and thus a risk factor for SMA would falsely look protective against CM only);</p><p>c) SMA vs. CM among severe malaria (which appears to be the case for the DAG presented in Figure 7, though I'm not sure), which seems to be what the R code posted on GitHub assumes.</p><p>This needs to be clarified further before it can be evaluated.</p><p>[Editors’ note: what now follows is the decision letter after the authors submitted an appeal.]</p><p>I and the reviewers have read and considered your letter of appeal, which makes a number of thoughtful points. After discussion among the reviewers, our view is as follows:</p><p>1) The first half of the paper could be a focused effort to assess the evidence for the effectiveness of rapid transfusion in preventing malaria mortality, with causal machinery used to improve the credibility of this inference compared to more informal methods. Such a study would avoid attributing causal effects to state variables such as hematocrit or temperature or the like, and would focus on a well-defined intervention. Without resolving the philosophical question of whether causal questions can ever be asked without a well-defined intervention, it seems that in the context of acute malaria mortality, with an explicit justification in the introduction that the authors seek to inspire clinical studies, this is a reasonable constraint. If you resubmit a version with this issue, please also attend to the other issues raised by the second reviewer.</p><p>2) The second half of the paper is really quite unrelated, except by the use of causal methodology, and while it seems to make a very important point, it does so in a way that is confusing in the sense that the back-story and evidence for what was done in previous studies is obscure. In my personal opinion, this seems to be a short paper of its own, where the history of prior studies needs to be presented in such a way that the reader can clearly tell what has been done, before the authors of the present manuscript explain why that is fallacious.</p><p>3) There is a third, implicit purpose of the paper, which is to introduce the malaria clinical epi community to causal reasoning. This is in our view not ideally done by the first half of the paper, which is extremely complex and raises the issue of what is a causal question as well as the rather complicated mechanics of how to control for various confounders. The second half may be better suited to this purpose as it is simpler.</p><p>We can think of a few different ways you might proceed; a focused paper on the second part (which would seem appropriate for <italic>eLife</italic> given the publication of the prior paper in the journal); a tutorial paper that uses the second part as an example but is more generally about causal reasoning; or perhaps the full paper (in which case we would suggest switching the order of the parts because the G6PD piece is easier to understand so could naturally come first). This last possibility seems unwieldy for the same reasons as the original paper.</p><p>You are free to take or leave any of these suggestions, but this is how we see the paper. If you do split it up, we would suggest that the G6PD part (with or without surrounding tutorial material) would be of greatest interest to <italic>eLife</italic> given the prior publication. The mortality prediction part is a large and complex approach to a focused clinical question that might by itself be a very good paper for a more specialized journal.</p><p>[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]</p><p>Thank you for submitting your article "Berkson's bias and the apparent protective effect of glucose-6-phosphate dehydrogenase deficiency on cerebral malaria" for consideration by <italic>eLife</italic>. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Neil Ferguson as the Senior Editor. The reviewers have opted to remain anonymous.</p><p>The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.</p><p>This paper attributes findings of a protective effect of G6PD deficiency against cerebral malaria to a statistical/causal artifact known as Berkson's bias (though maybe not the orthodox version thereof) or more generally selection or collider bias. It uses argumentation and simulation to suggest that the problem is:</p><p>1)G6PDd is a cause of increased risk of severe malarial anemia (SMA);</p><p>2) Two prior studies compared cases with various forms of severe malaria, specifically SMA and CM, to community controls for the prevalence of G6PDd, and found it was higher than controls in SMA and lower than controls for CM. They concluded a likely causal protective effect of G6PDd on CM;</p><p>3) The case definitions used were CM alone (i.e. no other severe malaria diagnosis) and SMA alone (i.e. no other severe malaria diagnosis. Under the assumption that CM and SMA risk are independent complications of malaria, and that G6PDd predisposes to SMA, this exclusion means that the CM cases in the analysis were SMA-free, thus less likely to have a predisposing allele to SMA. This would show up as a "protective" effect of the allele on CM because CM really means, in this study, CM and not SMA;</p><p>4) Simulation shows this could account for the full effect.</p><p>The reviewers and reviewing editor have discussed the manuscript and believe it can be made acceptable for publication after some crucial but relatively minor revisions:</p><p>1) Clarity about what was done. Reviewers had a hard time establishing precisely what was done in the two papers, and how that relates to the simulations. In particular, please:</p><p>a) State precisely the regression that was made in each paper [which we believe was Pr(CM and not SMA) vs. Pr (control), in logistic regression with G6PD genotype as predictor in a case-control format, and similarly for SMA and not CM) and quote the relevant passage in each paper that states the exclusion of dual cases.</p><p>b) State that this is the same comparison (with certain simplifications e.g. males only) in the simulation.</p><p>2) Address a reviewer concern that the statistical noise around the estimated OR looks large in your simulations given the use of 1 million people. This may be a false impression or may be due to the rarity of one cell in the odds ratio, but please explain.</p><p>3) Address a reviewer concern that producing a close quantitative match to the biased odds ratio for CM is not easily interpretable given the simplifying assumptions notably males only – would that not change the value substantially so that the agreement becomes qualitative rather than quantitative? A simulation including females would be simple to do.</p><p>4) Reviewers found point #1 confusing perhaps for several reasons, one of which is the use of Berkson's bias as the explanation here. Indeed, on first reading I had thought that the mistake was that the earlier papers had looked at predictors of SMA and CM among all severe malaria patients (without healthy controls). That would be classic Berkson's bias as taught in basic epidemiology classes. The bias you have identified is closely related, is still a form of collider bias, but is not exactly the same; it is that "CM" is really "CM and not SMA" and vice versa. The wording about Berkson's bias may just mislead people – maybe you want to say collider bias, and make clearer in the DAG how this works. Removing Berkson from the title could also clarify for those who only read the title!</p></body></sub-article><sub-article article-type="reply" id="SA2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.43154.007</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><p>[Editors’ note: the author responses to the first round of peer review follow.]</p><disp-quote content-type="editor-comment"><p>[…] However for reasons stated below, both reviewers have major concerns with the analysis. As a result, this paper cannot be published in something like its current form. The first Case Study is not appropriate because it doesn't ask well-posed causal questions, and the second Case Study is essentially a critique of another paper that I can't verify includes a correct description of what the other paper did. If it is a correct description, it is a very important point that should be made as a letter or some other way, and the simulation is superfluous except to provide an illustration to those outside the epidemiology field.</p></disp-quote><p>The summary letter clearly demonstrates that both the editors and the reviewers have spent considerable time delving into the paper and the accompanying code. We are very grateful. The synthesized criticisms are informed and constructive and this assessment and review is much appreciated and will ultimately lead to a substantially improved manuscript.</p><p>We would like to appeal against the decision to reject the paper.</p><p>The major concern (point 1) is that Case Study 1 does not ask well-posed causal questions because it does not discuss interventions. However, both reviewers acknowledge that this view is not universal in the field of causal inference and that this perspective is subject to some debate. We accept that consideration and presentation of this important aspect was lacking in the submitted version of the paper. However, contextual understanding of the medical aspects of severe malaria is needed for a correct interpretation of our results. Severe malaria is a medical emergency with high mortality, and a very rapid evolution. Most deaths occur in the first 24 hours following admission to hospital resulting from sudden onset of acute complications. The pathological process and therapeutic implications are more comparable to haemorrhage. There is a single well-defined and feasible intervention: blood transfusion. Indeed, severe malaria is the major reason for blood transfusion in children in sub-Saharan Africa. Severe malaria is the consequence of the malaria parasite invading a substantial proportion of circulating red blood cells, and these invaded red cells blocking the microcirculation – a process with a time course measured in hours. Anaemia results largely from obligatory haemolysis following schizogony, and sequestration of infected and uninfected red cells. To this extent, the primary way in which the variable haematocrit changes is clear. Furthermore, the degree of anaemia (measured as haematocrit) is certainly a determinant of patient outcome and has considerable practical utility. The counterfactual outcomes of interest are those that would be observed if it were possible to change the haematocrit on admission. Transfusion on admission is the only acute intervention to treat severe malaria in this emergency situation. The other interventions that are mentioned to treat anaemia are not relevant in this context. Patients would die before any drugs acting on the blood marrow took effect; active case detection cannot be done in remote rural areas where severe malaria kills most children; iron supplements at a population level are not a reasonable intervention providing no protection against acute haemolysis causing anaemia in falciparum malaria. Thus, in the case of haematocrit, the way in which this variable changes is known; there is practical utility in its measurement; and the only relevant intervention is transfusion. For these reasons we do not think that the measured causal effect can be explained as a weighted average of multiple factors. However, we agree with the reviewers, that this might not the case for each of the other variables.</p><p>The other critique is the dependence on the time of admission. Every study in severe malaria suffers from the selection bias of only considering patients who seek treatment at larger health centres. However, the problem addressed in our paper addresses the real-life situation on how to manage patients with severe falciparum malaria admitted to hospital. Whether or not to transfuse these patients on admission is a very important question and we believe causal reasoning is essential in the debate. We find that moderate anaemia is not harmful and could be even be beneficial in severe malaria. We are careful not to overstate the implications for blood transfusion due to the exploratory nature of the analysis. Our finding may explain why the very large FEAST study reported a six-fold higher mortality in patients who were above the recommended haematocrit transfusion threshold yet still received a blood transfusion. In summary, the causal question for haematocrit is well-posed and this work should help guide future analyses of transfusion-based intervention studies.</p><p>Well-defined interventions are also potentially available for raised blood urea nitrogen: the intervention is here is hemofiltration or dialysis; high parasitaemia: the intervention is the anti-parasitic drug; pulmonary oedema: the intervention is oxygen and positive pressure ventilation. For seizures, anticonvulsants can be given. For acidosis there are experimental treatments. For coma itself there are no direct interventions possible and we agree to remove this from Figure 4. However, we think anaemia, pulmonary oedema, seizures and blood urea nitrogen should stay in Figure 4. None of these variables are chronic unalterable health states but the result of the acute infection.</p><p>The second major concern (point 4) is that Case Study 2 is a critique of two recent major papers (notably one in eLife) and that the validity of this critique cannot be verified. Both Nature genetics and eLife only accept correspondence up to one year after publication (publication dates were 2014 and January 2017, respectively), and therefore this channel of communication is closed. The availability of open channels for balanced critiques of published research is essential for reproducible research. We are sure that eLife promotes this healthy scientific exchange. We have asked Professor Kwiatkowski (corresponding author for both papers) which of the possible analyses were done and it was confirmed to be scenario b (from your summary letter). When we subsequently sent our concerns along with a draft manuscript (in total two emails), no response was given. We have the email correspondence to verify these exchanges.</p><p>This highlights the problems of publishing data analytic results with no accompanying code. Even if their data were openly available, reproducing the analysis would require reverse engineering. We have gone to significant effort to support all our results with open, carefully annotated code and deidentified data.</p><p>As a final point, it is mentioned that the simulation study we present in Case Study 2 is superfluous. We respectfully disagree. This simple simulation shows that reasonable values of the effect of G6PD deficiency on anaemia (taken from previous published estimates) would suffice to explain the observed negative association between cerebral malaria and severe malarial anaemia. This `sensitivity’ analysis is an important building block in the argument: if larger, unreasonable effects were necessary to explain the observed results, a residual direct effect could still be posited.</p><p>Would eLife consider our appeal under the following set of conditions?</p><p>· We will add to the Methods section careful consideration of the counterfactual states underlying the exposure variables.</p><p>· We will remove coma as an exposure with an interpretable causal effect and add a point to this effect in the discussion.</p><p>· We will address the concerns in point 2. This highlights an error in the manuscript and this will be changed accordingly.</p><p>· We disagree with point 3. All variables considered are at the point of admission and therefore there are no feedback loops involved. The didactic aspect will also be addressed, but the DAG in Figure 3 is useful in that it shows the overall picture of expert knowledge in severe malaria using the key admission variables.</p><p>[Editors’ note: the author responses to the re-review follow.]</p><disp-quote content-type="editor-comment"><p>[…] We can think of a few different ways you might proceed; a focused paper on the second part (which would seem appropriate for eLife given the publication of the prior paper in the journal); a tutorial paper that uses the second part as an example but is more generally about causal reasoning; or perhaps the full paper (in which case we would suggest switching the order of the parts because the G6PD piece is easier to understand so could naturally come first). This last possibility seems unwieldy for the same reasons as the original paper.</p><p>You are free to take or leave any of these suggestions, but this is how we see the paper. If you do split it up, we would suggest that the G6PD part (with or without surrounding tutorial material) would be of greatest interest to eLife given the prior publication. The mortality prediction part is a large and complex approach to a focused clinical question that might by itself be a very good paper for a more specialized journal.</p></disp-quote><p>This is a re-submission of a previously rejected paper, entitled "Causal pathways in severe malaria". Following the recommendations of the senior editor (Prof. Neil Ferguson), after a successful appeal against the reject decision, we have made considerable changes to the manuscript. We have kept only the section which deals with Berksonian bias in two recent major publications (Malaria Gen Nature Genetics 2014, and Clarke et al., 2017) which report a protective effect of G6PD deficiency in severe cerebral falciparum malaria. Our re-submission focuses on highlighting how Berkson’s bias likely explains all of the observed association. This would invalidate the model of balancing selection for G6PD deficiency mutations proposed by Clarke et al.</p><p>The only relevant reviewer comment concerning this re-submission is now:</p><disp-quote content-type="editor-comment"><p>4) For Case Study II, it is hard to understand what was done in Clarke et al., the paper in eLife that they criticize. We can't tell on a brief look at that paper whether the comparison was between:</p><p>a) Severe malaria anemia (SMA) (+- cerebral malaria CM) vs. population controls, and separately CM+-SMA vs. population controls, for G6PD status (which would not suffer from the problem the authors posit);</p><p>b) SMA only vs. population controls, and CM only vs. population controls (in which the CM only group would be depleted of those with SMA, and thus a risk factor for SMA would falsely look protective against CM only);</p><p>c) SMA vs. CM among severe malaria (which appears to be the case for the DAG presented in Figure 7, though I'm not sure), which seems to be what the R code posted on GitHub assumes.</p><p>This needs to be clarified further before it can be evaluated.</p></disp-quote><p>The Materials and methods section of the paper now shows that scenario 3 is almost certainly the one used in Clarke et al.to demonstrate a protective effect of G6PD deficiency on cerebral malaria. Although it is not directly stated in the Clarke et al. Materials and methods section, we show that it can be deduced from tabular data presented in the paper.</p><p>We suggest that the article type of this re-submission is modified from `Research Article’ to `Short Report’ in light of its new brevity.</p><p>[Editors’ note: the author responses to the re-review follow.]</p><disp-quote content-type="editor-comment"><p>The reviewers and reviewing editor have discussed the manuscript and believe it can be made acceptable for publication after some crucial but relatively minor revisions:</p><p>1) Clarity about what was done. Reviewers had a hard time establishing precisely what was done in the two papers, and how that relates to the simulations. In particular, please:</p><p>a) State precisely the regression that was made in each paper [which we believe was Pr(CM and not SMA) vs Pr (control), in logistic regression with G6PD genotype as predictor in a case-control format, and similarly for SMA and not CM) and quote the relevant passage in each paper that states the exclusion of dual cases.</p><p>b) State that this is the same comparison (with certain simplifications e.g. males only) in the simulation.</p></disp-quote><p>We agree that the original presentation lacked clarity and we have substantially rewritten the Materials and methods section in light of this comment (subsection "Data analysis in Clarke et al., 2017, and MalariaGEN et al., 2014".</p><p>The rationale for why we believe our simulation mimics these reported results is then given in the subsection "Sensitivity analysis".</p><p>The bias stems directly from the selection distortion in the CM case definition. The adjustment for sickle cell in the logistic regressions in both MalariaGen, 2014, and Clarke et al., 2017, will not impact on the bias we are investigating in our simulation study. Sickle cell is a confounder between the two clinical presentations – as demonstrated in the causal diagram (<xref ref-type="fig" rid="respfig1">Author response image 1</xref>), an extension of Figure 1 in our paper to include a vertex for sickle cell status – and the authors are correct to adjust for it, therefore removing any biased association. Our simulation assumes that SMA and CM occur independently thereby reflecting the adjusted relationships in both papers (subsection "Sensitivity analysis").</p><fig id="respfig1"><label>Author response image 1.</label><caption><title>Role of sickle cell in case definitions of SMA and CM.</title><p>Sickle cell mutations will increase the likelihood of anaemia and are presumed protective against CM.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="article.xml.media/resp-fig1.jpg"/></fig><disp-quote content-type="editor-comment"><p>2) Address a reviewer concern that the statistical noise around the estimated OR looks large in your simulations given the use of 1 million people. This may be a false impression or may be due to the rarity of one cell in the odds ratio, but please explain.</p></disp-quote><p>This was a typo in the code – the original plot was not based on 10<sup>5</sup> rather than 10<sup>6</sup> individuals. We have corrected this and the noise in the plot (Figure 2) is greatly reduced. We thank the reviewer for pointing this out!</p><disp-quote content-type="editor-comment"><p>3) Address a reviewer concern that producing a close quantitative match to the biased odds ratio for CM is not easily interpretable given the simplifying assumptions notably males only – would that not change the value substantially so that the agreement becomes qualitative rather than quantitative? A simulation including females would be simple to do.</p></disp-quote><p>In fact, we contrast our simulated results against the reported results in males only. We get an almost perfect match for the reported results in males. This has been made clearer in the Results (second paragraph). Therefore, in our opinion, there are no major simplifying assumptions that should impact this simulation/sensitivity analysis.</p><p>Although it is simple to generate proportions of females and males with G6PDd under an assumption of Hardy-Weinberg equilibrium, a simulation involving females is in fact more complicated. It necessitates assumptions regarding the gene dose effect (female heterozygotes are mosaics of deficient and normal red blood cells). As the simulation is currently written, there is a unique free parameter and this facilitates interpretation. The gene dose effect would require one extra parameter for which there are little data on which to calibrate it.</p><disp-quote content-type="editor-comment"><p>4) Reviewers found point #1 confusing perhaps for several reasons, one of which is the use of Berkson's bias as the explanation here. Indeed, on first reading I had thought that the mistake was that the earlier papers had looked at predictors of SMA and CM among all severe malaria patients (without healthy controls). That would be classic Berkson's bias as taught in basic epidemiology classes. The bias you have identified is closely related, is still a form of collider bias, but is not exactly the same; it is that "CM" is really "CM and not SMA" and vice versa. The wording about Berkson's bias may just mislead people – maybe you want to say collider bias, and make clearer in the DAG how this works. Removing Berkson from the title could also clarify for those who only read the title!</p></disp-quote><p>We agree and thank you for this suggestion. The title has been changed to "collider bias" and we have changed all mentions in the main text to collider bias also.</p><p>In the DAG in Figure 1, we have changed the name of the collider variable from "Included in study" to "Case definition". This shows how the case definition is simultaneously dependent on both clinical presentations.</p></body></sub-article></article>