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

ABSTRACT

Malaria is a major health problem in many tropical regions. Fever is a characteristic symptom of malaria. The fraction of fevers that are attributable to malaria, the malaria attributable fever fraction (MAFF), is an important public health measure in that the MAFF can be used to calculate the number of fevers that would be avoided if malaria was eliminated. Despite such causal interpretation, the MAFF has not been considered in the framework of causal inference. We define the MAFF using the potential outcome framework, and define causal assumptions that current estimation methods rely on. Furthermore, we demonstrate that one of the assumptions—that the parasite density is correctly measured—generally does not hold because (i) fever kills some parasites and (ii) parasite density is measured with error. In the presence of these problems, we reveal that current MAFF estimators can be significantly biased. To develop a consistent estimator, 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 is developed to assess the impact of different magnitudes of fever killing and different measurement error mechanisms. Finally, we apply our proposed method to estimate the MAFF in Kilombero, Tanzania. Supplementary materials for this article are available online.

KEYWORDS:

• Bayes deconvolution problem
• Causal inference
• Exponential family g-modeling
• Sufficient cause model
• Two-component mixture model

Acknowledgments

The authors are grateful to Tom Smith for valuable discussion, encouragement and sharing the data from the Kilombero Malaria Project.