Flexible time-to-event models for double-interval-censored infectious disease data with clearance of the infection as a competing risk

Abstract

The observed induction time from an infection to an event of interest is often double-interval-censored and moreover, often prevented from being observed by the clearance of the infection (a competing risk). Double-interval-censoring and the presence of competing risks complicate the statistical analysis extremely and are therefore usually ignored in infectious disease studies. Often, the times at which events are detected are used as a proxy for the exact times and interpretation has to be made on the detected induction time and not on the actual latent induction time. In this paper, we first explain the concepts of double interval censoring and competing risks, propose multiple (semi-) parametric models for this kind of data and derive a formula for the corresponding likelihood function. We describe algorithms for the maximization of the likelihood and provide code. The proposed models vary in complexity. Therefore, results of simulation studies are presented to illustrate the advantages and disadvantages of each model. The methodology is illustrated by applying them to malaria data where the interest lies in the time from incident malaria infection to gametocyte initiation.