Malaria Incidence Rates from Time Series of 2-Wave Panel Surveys

Methodology to estimate malaria incidence rates from a commonly occurring form of interval-censored longitudinal parasitological data—specifically, 2-wave panel data—was first proposed 40 years ago based on the theory of continuous-time homogeneous Markov Chains. Assumptions of the methodology were suitable for settings with high malaria transmission in the absence of control measures, but are violated in areas experiencing fast decline or that have achieved very low transmission. No further developments that can accommodate such violations have been put forth since then. We extend previous work and propose a new methodology to estimate malaria incidence rates from 2-wave panel data, utilizing the class of 2-component mixtures of continuous-time Markov chains, representing two sub-populations with distinct behavior/attitude towards malaria prevention and treatment. Model identification, or even partial identification, requires context-specific a priori constraints on parameters. The method can be applied to scenarios of any transmission intensity. We provide an application utilizing data from Dar es Salaam, an area that experienced steady decline in malaria over almost five years after a larviciding intervention. We conducted sensitivity analysis to account for possible sampling variation in input data and model assumptions/parameters, and we considered differences in estimates due to submicroscopic infections. Results showed that, assuming defensible a priori constraints on model parameters, most of the uncertainty in the estimated incidence rates was due to sampling variation, not to partial identifiability of the mixture model for the case at hand. Differences between microscopy- and PCR-based rates depend on the transmission intensity. Leveraging on a method to estimate incidence rates from 2-wave panel data under any transmission intensity, and from the increasing availability of such data, there is an opportunity to foster further methodological developments, particularly focused on partial identifiability and the diversity of a priori parameter constraints associated with different human-ecosystem interfaces. As a consequence there can be more nuanced planning and evaluation of malaria control programs than heretofore.Author Summary: Incidence rates measure the transitions between the states of noninfected to infected per unit of time and per person at risk. Usually calculated from longitudinal observations, they provide an indication of how rapidly a disease develops in a population over time. In the context of malaria, longitudinal data on infection status are obtained through consecutive survey rounds, separated by a certain time interval. Depending on the length of the interval, some changes of infection status may be missed, and thus only uncensored information would be available. Methodology to calculate incidence rates from this type of data was first proposed in 1976, but its assumptions were not applicable to low transmission settings, particularly in the presence of control measures. No alternative methodology has been proposed in the past 40 years, limiting attempts to obtain estimates of incidence rates in the current scenario of declining malaria transmission worldwide. In this paper we address this gap and introduce new methodology to estimate malaria incidence rates from longitudinal data that can be applied to settings with any transmission level. We provide a complete example of the method, including sensitivity analysis, and an assessment of possible differences between data based on microscopy vs. PCR diagnostics. To facilitate replication and wide use of the method, we make available a programming code in R language and the example dataset.