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

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.