Author response: Improving statistical power in severe malaria genetic association studies by augmenting phenotypic precision

Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Appendix 7 Appendix 8 Appendix 9 Appendix 10 Appendix 11 Appendix 12 Appendix 13 Data availability References Decision letter Author response Article and author information Metrics Abstract Severe falciparum malaria has substantially affected human evolution. Genetic association studies of patients with clinically defined severe malaria and matched population controls have helped characterise human genetic susceptibility to severe malaria, but phenotypic imprecision compromises discovered associations. In areas of high malaria transmission, the diagnosis of severe malaria in young children and, in particular, the distinction from bacterial sepsis are imprecise. We developed a probabilistic diagnostic model of severe malaria using platelet and white count data. Under this model, we re-analysed clinical and genetic data from 2220 Kenyan children with clinically defined severe malaria and 3940 population controls, adjusting for phenotype mis-labelling. Our model, validated by the distribution of sickle trait, estimated that approximately one-third of cases did not have severe malaria. We propose a data-tilting approach for case-control studies with phenotype mis-labelling and show that this reduces false discovery rates and improves statistical power in genome-wide association studies. eLife digest In areas of sub-Saharan Africa where malaria is common, most people are frequently exposed to the bites of mosquitoes carrying malaria parasites, so they often have malaria parasites in their blood. Young children, who have not yet built up strong immunity against malaria, often fall ill with severe malaria, a life-threatening disease. It is unclear why some children develop severe malaria and die, while other children with high numbers of parasites in their blood do not develop any apparent symptoms. Genetic susceptibility studies are designed to uncover why such differences exist by comparing individuals with severe malaria (referred to as ‘cases’) with individuals drawn from the general population (known as ‘controls’). But severe malaria can be a challenge to diagnose. Since high numbers of malaria parasites can be found in healthy children, it is sometimes difficult to determine whether the parasites are making a child ill, or whether they are a coincidental finding. Consequently, some of the ‘cases’ recruited into these studies may actually have a different disease, such as bacterial sepsis. This ultimately affects how the studies are interpreted, and introduces error and inaccuracy into the data. Watson, Ndila et al. investigated whether measuring blood biomarkers in patients (derived from the complete blood count, including platelet counts and white blood cell counts) could improve the accuracy with which malaria is diagnosed. They developed a new mathematical model that incorporates platelet and white blood cell counts. This model estimates that in a large cohort of 2,220 Kenyan children diagnosed with severe malaria, around one third of enrolled children did not actually have this disease. Further analysis suggests that patients with severe malaria are highly unlikely to have platelet counts higher than 200,000 per microlitre. This defines a cut-off that researchers can use to avoid recruiting patients who do not have severe malaria in future studies. Additionally, the ability to diagnose severe malaria more accurately can make it easier to detect and treat other diseases with similar symptoms in children with high numbers of malaria parasites in their blood. Watson, Ndila et al.’s findings support the recommendation that all children with suspected malaria be given broad spectrum antibiotics, as many misdiagnosed children will likely have bacterial sepsis. It also suggests that using complete blood counts, which are cheap to obtain and increasingly available in low-resource settings, could improve diagnostic accuracy in future clinical studies of severe malaria. This could ultimately improve the ability of these studies to find new treatments for this life-threatening disease. Introduction Severe malaria caused by the parasite Plasmodium falciparum kills nearly half a million children each year, mostly in sub-Saharan Africa (World Health Organization, 2020). By causing death in children before they reach their reproductive age, P. falciparum has exerted a substantial selective evolutionary pressure on the human genome (Carter and Mendis, 2002; Kariuki and Williams, 2020). Recent advances in whole-genome sequencing and haplotype imputation (Teo et al., 2010), combined with data gathered prospectively from large patient cohorts, have improved our understanding of genetic susceptibility to P. falciparum infection and severe disease (Malaria Genomic Epidemiology Network et al., 2013; Malaria Genomic Epidemiology Network, 2014; Band et al., 2019; Malaria Genomic Epidemiology Network et al., 2017), but many questions remain unanswered (Kariuki and Williams, 2020). A major limitation of genetic association studies in severe malaria is that the diagnosis of severe falciparum malaria in children is imprecise (White et al., 2013; Taylor et al., 2004; Bejon et al., 2007). This imprecision increases with transmission intensity because of the low positive predictive value of a ‘positive blood film’ or rapid diagnostic test (RDT) in areas where the background prevalence of microscopy detectable parasitaemia in apparently healthy young children is high (often around 30%, Rodriguez-Barraquer et al., 2018, but can exceed 90%, Smith et al., 1994). Severe falciparum malaria has been defined by experts convened by the World Health Organization (WHO) as clinical or laboratory evidence of vital organ dysfunction in the presence of circulating asexual P. falciparum parasitaemia (World Health Organisation, 2014). The WHO definition of severe malaria is aimed primarily at clinicians and health care workers managing patients with malaria who appear severely ill. This appropriately prioritises sensitivity over specificity (Anstey and Price, 2007). An inclusive clinical definition ensures that cases are not missed and patients receive the best treatment. In contrast, genetic association studies require high specificity (Zondervan and Cardon, 2007). For a given sample size, their statistical power, false discovery rates (FDRs) and the validity of their interpretation are weakened by phenotypic inaccuracy. Specificity in the diagnosis of severe malaria depends in part on the prevalence of malaria parasitaemia. This reflects background transmission intensity. In areas of low or seasonal transmission (e.g. most of endemic Asia and the Americas), clinical and laboratory signs of severity accompanied by a positive blood film for P. falciparum are highly specific for severe malaria, which predominantly affects young adults. In contrast in high transmission areas in sub-Saharan Africa and in lowland areas of the island of New Guinea, where severe malaria is largely a disease of young children, the diagnostic criteria for defining severe malaria are less specific because of the high background prevalence of asymptomatic parasitaemia and the lower specificity of the clinical manifestations. Standard case definitions of severe malaria will therefore inevitably include both patients with non-malarial severe illness with concomitant parasitaemia and with concomitant non-severe malaria. Our goal was to develop a biomarker-based model that can differentiate probabilistically between ‘true severe malaria’ and severe illness not caused primarily by malaria, but with concomitant parasitaemia. We define ‘true severe malaria’ conceptually as a febrile illness caused by malaria parasites, with organ dysfunction, that can result in death whereby mortality is attributable directly to the malaria parasites. This attributable mortality can be given a formal causal definition by using a conceptual (albeit unethical) randomised experiment of delayed versus prompt antimalarial therapy. In a theoretical patient population with true severe malaria, delay in administration of an effective antimalarial would result in increased mortality (Warrell et al., 1982; Gomes et al., 2009) whereas in a population with severe illness not caused by malaria (‘not severe malaria’) there would not be a corresponding increase in mortality. We developed a probabilistic diagnostic model of severe malaria based on haematological biomarkers using data from 1704 adults and children mainly from low transmission settings whose diagnosis of severe malaria is considered to be highly specific. We used this model to demonstrate low phenotypic specificity in a cohort of 2220 Kenyan children who were diagnosed clinically with severe malaria. We validated the predictions using a natural experiment, the distribution of sickle cell trait (HbAS), the genetic polymorphism with the strongest known protective effect against all forms of clinical malaria (Malaria Genomic Epidemiology Network, 2014). Building on work on ‘data-tilting’ (Nie et al., 2013), we suggest a new method for testing genetic associations in the context of case-control studies in which cases are re-weighted by the probability that the severe malaria diagnosis is correct under the model. As proof of concept, we ran a genome-wide association study across 9.6 million imputed biallelic variants using the subset of cases with genome-wide genotype data (n = 1297) and population controls (n = 1614). Adjusting for case mis-classification decreased genome-wide FDRs (Storey, 2002) and increased effect sizes in three of the top regions of the human genome most strongly associated with protection from severe malaria in East Africa (HBB, ABO and FREM3, Band et al., 2019). A re-analysis of 120 directly typed polymorphisms in 70 candidate malaria-protective genes in the 2220 Kenyan cases and 3940 population controls, examining differential effects between correctly and incorrectly classified cases, suggests that the protective effect of glucose-6-phosphate dehydrogenase (G6PD) deficiency has been obscured in this population by case mis-classification. Our results show that adding full blood count metadata – routinely measured in most hospitals in sub-Saharan Africa – to severe malaria cohorts would lead to more accurate quantitative analyses in case-control studies and increased statistical power. Results Reference model of severe malaria We used the joint distribution of platelet counts and white blood cell counts (both on a logarithmic scale) to develop a simple biomarker-based reference model of severe malaria. To fit the reference model (i.e. P[Data | Severe malaria]), we used platelet and white count data from (i) severe malaria patient cohorts enrolled in low transmission areas where severe disease accompanied by a positive blood stage parasitaemia has a high positive predictive value for severe malaria (930 adults from Vietnam [Hien et al., 1996; Phu et al., 2010] and 653 adults and children from Thailand and Bangladesh); and (ii) severely ill African children with plasma PfHRP2 concentrations >1000 ng/mL and >1000 parasites per μL of blood (121 children from Uganda, Maitland et al., 2011). Severe illness accompanied by a high plasma PfHRP2 concentration makes the diagnosis of severe falciparum malaria highly specific (Hendriksen et al., 2012). The joint distribution of platelet and white blood cell counts in severe malaria was modelled as a bivariate t-distribution with both blood count variables on the log10 scale. Figure 1A shows the reference data (green triangles: patients with a highly specific diagnosis of severe malaria, summarised in Table 1) alongside data from a large Kenyan cohort of hospitalised children diagnosed with severe malaria, whose diagnosis had unknown specificity (pink squares). The median platelet count in the reference data was 57,000 per μL, and the median total white blood cell count was 8400 per μL. In contrast, the median platelet count in the Kenyan children was 120,000 per μL, and the median total white blood cell count was 13,000 per μL. Direct comparisons of white counts across these two datasets are confounded by geography and age. Total white blood cell counts are known to be age-dependent and vary across genetic backgrounds, in particular lower neutrophil counts are associated with mutations in the ACKR1 gene that results in the Duffy negative phenotype prevalent in African populations (Reich et al., 2009). However, after adjustment for age (see Materials and methods), the marginal distributions of total white counts were comparable between Asian adults and children with severe malaria and African children with high plasma PfHRP2 (Appendix 1). Platelet counts are not age-dependent and do not vary substantially across genetic backgrounds. The marginal distributions of platelet counts were comparable between Asian adults and children with severe malaria and African children with high plasma PfHRP2 (Appendix 2). A low platelet count (thrombocytopenia) is a universal feature of severe malaria (see evidence collated in Materials and methods). To illustrate this important point, in a cohort of 566 severely ill Ugandan children enrolled in the Fluid Expansion as Supportive Therapy (FEAST) trial (Maitland et al., 2011), a trial including all severe illness not restricted to severe malaria, low platelet counts were highly predictive of blood stage parasitaemia and elevated PfHRP2 (p=10-16 for a spline term on the log10 platelet count in a generalised additive logistic regression model predicting PfHRP2 >1000 ng/mL, Appendix 2). Children enrolled in the FEAST trial who had significant thrombocytopenia (<100,000 platelets per μL) had comparable PfHRP2 concentrations to Asian adults diagnosed with severe falciparum malaria (Figure 1B). Figure 1 Download asset Open asset Platelet counts and white blood cell counts as diagnostic predictors of severe falciparum malaria. Panel (A) shows the bivariate marginal distribution for the reference data (thought to be highly specific to severe malaria, green triangles, n = 1704, summarised in Table 1) and for the Kenyan case data (pink squares, n = 2220; black diamonds: HbAS). The dashed ellipses show the 50% and 95% bivariate normal probability contours approximating each dataset (dark green: reference data; purple: Kenyan data). Panel (B) shows the relationship between platelet counts and plasma PfHRP2 in adults with severe malaria from Bangladesh (green circles, n = 172, the dashed green line shows a linear fit) and in children enrolled in the FEAST trial (n = 567, not specific to severe malaria, Maitland et al., 2011). Undetectable plasma PfHRP2 concentrations were set to 1 ng/mL ± random jitter. Orange squares: malaria-positive blood slide; black triangles: malaria-negative blood slide. The brown line shows a spline fit to the FEAST data (smooth.spline function in R with default parameters) including the data points where PfHRP2 was below the lower limit of detection. Table 1 Summary of severe disease datasets used in our analyses. For age and parasite density, we show the median values as the distributions are highly skewed. *For the FEAST trial, the severe malaria reference dataset only included platelet and white count data from the 121 patients who had PfHRP2 >1000 ng/mL and >1000 parasites per μL. IQR: interquartile range. Bangladesh-ThailandVietnamFEAST (Uganda)KenyaDescriptionObservational studies of severe malariaRandomised controlled trials in severe malariaRandomised controlled trial in severe febrile illnessObservational severe malaria cohortPurposeReference dataReference dataReference data* and Figure 1BTesting dataPublished referencesLeopold et al., 2019Hien et al., 1996; Phu et al., 2010Maitland et al., 2011MalariaGEN Consortium et al., 2018n6539305672220Age (years, range)28 (2–80)30 (15–79)2.1 (0–12)2.3 (0–13)Parasite density (per μL, IQR)48,984 (8289–187,395)83,084 (13,047–316,512)400 (0–53,200)72,000 (6208–315,250)Mortality (%)18.212.911.311.6 Estimating the proportion of children mis-diagnosed with severe malaria We can consider the hospitalised Kenyan children in this series as a mixture of two latent sub-populations, ‘severe malaria’ and ‘not severe malaria’ (i.e an alternative aetiology for severe illness). To estimate the proportion of each, we use the distribution of HbAS, the human polymorphism most protective against all forms of clinical falciparum malaria. HbAS provides at least 90% protection against severe malaria (Taylor et al., 2012; Malaria Genomic Epidemiology Network, 2014). The causal SNP rs334 was genotyped in 2213 of the Kenyan children, of whom 57 were HbAS. The causal pathways (a) or (b) in Figure 2 (note all children have been selected into the study on the basis of clinical symptoms consistent with severe malaria) show how the distribution of HbAS can be used to infer the marginal probability P(Severe malaria) in the Kenyan cohort as the prevalence of HbAS is expected to differ in the two latent sub-populations. Figure 2 Download asset Open asset Theoretical causal pathways that lead to the clinical diagnosis of severe malaria under the current WHO definition (World Health Organisation, 2014). Pathways (a) and (b) represent the two ways patients can be mis-classified as severe malaria. For both pathways (a) and (b), we expect a higher prevalence of HbAS relative to the population with true severe malaria as a consequence of the protective bottlenecks. In this causal model, we assume that HbAS does not protect against asymptomatic parasitaemia, although this assumption is not strictly necessary. Adapted with permission from Small et al., 2017. We assumed that cases with the highest likelihood values P(Data | Severe malaria) under the reference model (a bivariate t-distribution fit to the severe malaria reference data) had a diagnosis of severe malaria that was 100% specific (top 40% of cases, a sensitivity analysis varied this threshold). The cases with lower likelihood values were assumed to be drawn from a mixture of the two latent populations with an unknown mixing proportion; the prevalence of HbAS in the ‘not severe malaria’ subgroup was estimated from a cohort of hospitalised children enrolled in the same hospital and who were malaria blood slide positive but were clinically diagnosed as not having severe malaria (n = 6748 of whom 364 were HbAS; Uyoga et al., 2019). We assumed that this diagnosis of ‘not severe malaria’ was 100% specific. Under these assumptions, we estimated that P(Severe malaria) = 0.64 (95% credible interval [C.I.] 0.46–0.8), implying that approximately one-third of the 2200 cases are from the ‘not severe malaria’ sub-population (they have malaria parasitaemia in addition to another severe illness – likely to be bacterial sepsis – Figure 2). Estimating individual probabilities of severe malaria We then estimated P(Severe malaria | Data) for each Kenyan case by fitting a mixture model to the reference data and to the Kenyan data jointly. The model assumed that the platelet and white count data for the Kenyan children were drawn from a mixture of P(Data | Severe malaria) and P(Data | Not severe malaria). The reference data (Asian adults and children with severe malaria and African children with PfHRP2 >1000 ng/mL) were assumed to be drawn only from P(Data | Severe malaria). P(Data | Not severe malaria) was modelled itself as a mixture of bivariate t-distributions. We used an informative prior on the mixture proportion (‘severe malaria’ versus ‘not severe malaria’) in the Kenyan cases, a beta distribution approximating the posterior estimate from the analysis of HbAS prevalence. Figure 3A shows the bimodal distribution of the posterior individual estimates of P(Severe malaria | Data). As expected, the individual posterior probabilities of severe malaria were highly predictive of HbAS (p=10-6 from a generalised additive logistic regression model fit, Figure 3C). The individual probabilities were also predictive of in-hospital mortality (p=10-9 from a generalised additive model fit; Figure 3D) and admission peripheral blood parasite density (p=10-25 from a generalised additive model fit; Figure 3E). In the top quintile of patients with the highest estimated P(Severe malaria | Data), the prevalence of HbAS was 0.7% (3 out of 446). In contrast, for patients in the lowest quintile of estimated P(Severe malaria | Data), the prevalence of HbAS was 4.8% (21 out of 444). The patients with a low probability of severe malaria had a substantially higher case fatality ratio (18.8% mortality for patients in the bottom quintile of P[Severe malaria | Data] versus 6.1% mortality for the top quintile of P[Severe malaria | Data]). This may be explained by the higher case-specific mortality of severe bacterial sepsis (the most likely alternative cause of severe illness). The admission parasite densities in patients with a probability of severe malaria close to 1 were approximately fivefold higher than in patients with a probability of severe malaria close to 0. The blood culture positive rate was 2.1% in the top quintile of P(Severe malaria | Data) and 4.4% in the lowest quintile of P(Severe malaria | Data), and the individual probabilities were predictive of blood culture results (p=0.004 under a generalised additive logistic regression model fit). Figure 3 Download asset Open asset Model estimates of P(Severe malaria | Data) in 2220 Kenyan children clinically diagnosed with severe malaria. Panel (A) shows the distribution of posterior probabilities of severe malaria being the correct diagnosis. Panel (B) shows these same probabilities plotted as a function of the platelet and white counts on which they are based (dark red: probability close to 0; dark blue: probability close to 1). The black diamonds show the HbAS individuals. Panels (C–E) show the relationship between the estimated probabilities of severe malaria and HbAS, in-hospital mortality and admission parasite density, respectively. The black lines (shaded areas) show the mean estimated values (95% confidence intervals) from a generalised additive logistic regression model with a smooth spline term for the likelihood (R package mgcv). The horizontal lines in panels (C–E) show the mean values in the data. Accounting for case imprecision in case-control studies ‘False-positive’ cases reduce statistical power and dilute effect size estimates in case-control studies. We propose a novel approach for case-control studies with phenotypic imprecision based on data-tilting (Nie et al., 2013). The idea is to ‘tilt’ the cases towards a pseudo-population with higher specificity for severe malaria. We can do this by re-weighting the data by the probabilities P(Severe malaria | Data), that is, re-weighting the contribution to the log-likelihood in an association model. We applied this approach as proof of concept to a genome-wide association study using the subset of Kenyan children who had clinical and genome-wide data available (after quality control checks n = 1297 cases) and a set of matched population controls (n = 1614), across 9.6 million biallelic variants on the autosomal chromosomes (Band et al., 2019). We compared the data-tilting method to the standard non-weighted approach by estimating local FDRs (Storey, 2002). Compared to the standard non-weighted GWAS, data-tilting substantially increased the number of significant associations for local FDRs in the range of 1–5% (Figure 4). For example, at an FDR of 2%, the number of significant hits is more than doubled with the additional hits all around known loci associated with protection from severe malaria. We note that if the data weights were not predictive of the true latent phenotype, we would expect fewer significant hits for a given FDR because of the reduction in effective sample size. This is demonstrated by permuting the data weights (for the cases only), which results in 50–75% reduction in the number of significant hits at FDRs < 5% (Appendix 3). Figure 4 Download asset Open asset The number of significant hits as a function of the FDR for the genome-wide association study across 9.6 million biallelic variants. This analysis is based on a subset of the Kenyan children with whole-genome data available and passing quality checks n = 1297 and n = 1614 controls. Dashed line: weighted model; thick line: non-weighted model. Examining three major genetic regions strongly associated with protection from severe malaria in East Africa (HBB: HbAS; ABO: O blood group; FREM3: in close linkage with the GYPA/B/E structural variants that encode the Dantu blood group; Band et al., 2019), the data-tilting approach estimated larger effect sizes compared to the non-weighted model in all three regions (effect size increases: 30% around HBB, 9% around ABO and 5% around FREM3). This resulted in larger –log10 p-values for HBB and ABO, but slightly smaller for FREM3 (Figure 5). We note that there was no signal of association at ATP2B4 in this subset, most likely due to limited power (ATP2B4 had the third largest Bayes factor for association in the largest multicentre GWAS to date, Band et al., 2019). Figure 5 Download asset Open asset The three regions in the human genome with the greatest evidence for protection against severe malaria in East Africa (HBB, ABO and FREM3; Band et al., 2019). The Manhattan plots (left panels) compare p-values from the weighted model (blue) and the non-weighted model (orange). Each Manhattan plot is centred around the known causal position shown by the vertical dashed line (0.5 Mb region). The horizontal dashed line shows p=10-7 (threshold often used for defining genome-wide significance). The 10 positions with the greatest –log10 p-values under the non-weighted model are shown as large diamonds. The scatter plots on the right compare absolute effect size estimates under both models with the same top 10 hits shown by the larger purple diamonds. Increases of 30, 9 and 5% are seen for the 10 top hits for HBB, ABO and FREM3, respectively. Reappraisal of directly typed polymorphisms We re-analysed case-control associations for 120 polymorphisms on 70 candidate malaria-protective genes which were typed directly in the 2220 Kenyan children along with 3940 population controls. In this case-control cohort, 14 polymorphisms had previously been identified as associated with protection or increased risk in severe malaria (MalariaGEN Consortium et al., 2018). A re-analysis of these 14 variants using the same models of association as previously published and down-weighting the likely mis-classified cases replicated the majority of associations, with increased effect sizes and increased –log10 p-values (Appendix 4). For the three major genes (HBB, ABO, FREM3), effect sizes were increased by 10–30% and associations all had higher significance levels on the –log10 scale (0.25–1.7). The allele frequencies of all three polymorphisms were directly associated with the probability weights, showing increased protection in individuals more likely to have severe malaria (Appendix 5). Two polymorphisms on the genes ARL14 and LOC727982, reported previously as associated with protection in severe malaria (neither of which are related to red cells), showed decreased effect sizes and –log10 p-values and are thus potentially spurious hits. We explored whether there was evidence of differential effects in the Kenyan cases using P[Severe malaria | Data] to assign probabilistically each case to the ‘severe malaria’ versus ‘not severe malaria’ sub-populations. We fitted a categorical logistic regression model predicting the latent sub-population label versus control, where the latent case label was estimated from the weights shown in Figure 3A. This resulted in approximately 1279 cases in the ‘severe malaria’ sub-population and 941 cases in the ‘not severe malaria’ sub-population. Differential effects were tested by comparing the estimated log-odds for the two sub-populations. After accounting for multiple testing, two polymorphisms showed significant differential effects: rs334 (derived allele encodes haemoglobin S, p=10-6) and rs1050828 (derived allele encodes G6PD + 202T, p=10-3 in the model fit to females only), see Figure 6. As expected, rs334 was associated with protection in both sub-populations (Scott et al., 2011; Uyoga et al., 2019) but the effect was almost eight times larger on the log-odds scale in the ‘severe malaria’ sub-population relative to the ‘not severe malaria’ sub-population (odds ratio of 0.029 [95% C.I. 0.0088–0.094] in the ‘severe malaria’ population versus 0.63 [95% C.I. 0.48–0.83] in the ‘not severe malaria’ population). For rs1050828 (G6PD + 202T allele), approximately the same absolute log-odds were estimated for both sub-populations but they had opposite signs. Under an additive model in females, the rs1050828 T allele was associated with protection in the ‘severe malaria’ sub-population (odds ratio of 0.71 [95% C.I. 0.57–0.88]) but with increased risk in the ‘not severe malaria’ sub-population (odds ratio of 1.30 [95% C.I. 1.00–1.70]). The additive model including both males and females was consistent with these opposing effects but significant only at a nominal threshold (p=0.02). Opposing effects across the two sub-populations are consistent with the hypothesis that G6PD deficiency leads to a greater risk of being erroneously classified as severe malaria as under the severe anaemia criterion (Watson et al., 2019), shown in more detail in Appendix 5. Investigation of haemoglobin concentrations as a function of P(Severe malaria | Data)