Modelling longitudinal binary outcomes with outcome-dependent observation times: an application to a malaria cohort study

Abstract

Inspite of the global reduction of 21% in malaria incidence between 2010 and 2015, the disease still threatens many lives of children and pregnant mothers in African countries. A correct assessment and evaluation of the impact of malaria control strategies still remains quintessential in order to eliminate the disease and its burden. Malaria follow-up studies typically involve routine visits at pre-scheduled time points and/or clinical visits whenever individuals experience malaria-like symptoms. In the latter case, infection triggers outcome assessment, thereby leading to outcome-dependent sampling (ODS). Ordinary methods used to analyse such longitudinal data ignore ODS and potentially lead to biased estimates of malaria-specific transmission parameters, hence, inducing an incorrect assessment and evaluation of malaria control strategies. In this paper, we propose novel methodology to handle ODS using a joint model for the longitudinal binary outcome measured at routine visits and the clinical event times. The methodology is applied to malaria parasitaemia data from a cohort of n = 988 Ugandan children aged 0.5-10 years from 3 regions (Walukuba - 300 children, Kihihi - 355 children and Nagongera - 333 children) with varying transmission intensities (entomological inoculation rate equal to 2.8, 32 and 310 infectious bites per unit year, respectively) collected between 2011-2014. The results indicate that malaria parasite prevalence and force of infection (FOI) increase with age in the region of high malaria intensities with FOI highest in age group 5-10 years. For the region of medium intensity, the prevalence slightly increases with age and the FOI for the routine process is highest in age group 5-10 years yet for the clinically observed infections, the FOI gradually decreases with increasing age. For the region with low intensity, both the prevalence and FOI peak at the age of one year after which the former remains constant with age yet the latter suddenly decreases with age for the clinically observed infections. In all study sites, both the prevalence and FOI are highest among previously asymptomatic children and lowest among their symptomatic counterparts. Using a simulation study inspired by the malaria data at hand, the proposed methodology shows to have the smallest bias, especially when consecutive positive malaria parasitaemia presence results within a time period of 35 days were considered to be due to the same infection.