Estimating the Malaria Attributable Fever Fraction Accounting for Parasites Being Killed by Fever and Measurement Error

Abstract

Malaria is a parasitic disease that is a major health problem in many tropical regions. The most characteristic symptom of malaria is fever. The fraction of fevers that are attributable to malaria, the malaria attributable fever fraction (MAFF), is an important public health measure for assessing the effect of malaria control programs and other purposes. Estimating the MAFF is not straightforward because there is no gold standard diagnosis of a malaria attributable fever; an individual can have malaria parasites in her blood and a fever, but the individual may have developed partial immunity that allows her to tolerate the parasites and the fever is being caused by another infection. We define the MAFF using the potential outcome framework for causal inference and show what assumptions underlie current estimation methods. Current estimation methods rely on an assumption that the parasite density is correctly measured. However, this assumption does not generally hold because (i) fever kills some parasites and (ii) the measurement of parasite density has measurement error. In the presence of these problems, we show current estimation methods do not perform well. We propose a novel maximum likelihood estimation method based on exponential family g-modeling. Under the assumption that the measurement error mechanism and the magnitude of the fever killing effect are known, we show that our proposed method provides approximately unbiased estimates of the MAFF in simulation studies. A sensitivity analysis can be used to assess the impact of different magnitudes of fever killing and different measurement error mechanisms. We apply our proposed method to estimate the MAFF in Kilombero, Tanzania. ). The Authors thank Thomas Smith for insightful suggestions and providing the data.

Estimating Malaria Vaccine Efficacy in the Absence of a Gold Standard Case Definition: Mendelian Factorial Design

“…However, computing sensitivity and specificity of a case definition requires an estimate of the malaria attributable fraction of fevers (MAFF). Lee and Small (2018) show that obtaining unbiased estimates of MAFF in the presence of measurement error of D and fever killing effects on parasite density is a difficult task, especially when malaria and non-malaria infections can work in conjunction to trigger a fever. Still, when unbiased estimates of MAFF can be obtained, this case definition will, by design, result in false positive and false negative cases, which may bias corresponding estimates of vaccine efficacy.…”

“…Potential outcomes are a useful framework to precisely define causal effects of interest (Rubin, 2005). The potential outcomes that we define now are closely related to those defined in Lee and Small (2018). In what follows, we consider Y to indicate the presence of fever but note that the framework we describe is also suitable when Y indicates death.…”

“…If we assume that there is no combined effect of malaria and non-malaria infections on fevers (Assumption 2(iii) of Lee and Small (2018)), then we can provide an alternative decomposition of Y to the decomposition presented in (1):…”

A fiducial approach to nonparametric deconvolution problem: discrete case

“…, n}, where the only requirement is a known specification of the distribution for X i given Θ i . The empirical Bayes deconvolution since developed has seen tremendous success in many scientific applications including causal inference (Lee and Small, 2019), single-cell analysis (Wang et al, 2018), cancer study (Gholami et al, 2015;Shen and Xu, 2019), clinical trials Li, 2018, 2019) and many other fields (Dulek, 2018). Moreover, for a classic Bayesian data analysis, as noted in (Ross and Markwick, 2018, p19) and Gelman et al (2013), a single distribution prior may sometimes be unsuitable and hence the prior choice is dubious.…”