  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.
