Addressing censoring issues in estimating the serial interval for tuberculosis
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The serial interval (SI), defined as the symptom time between an infector and an infectee, is widely used to better understand transmission patterns of an infectious disease. Estimating the SI for tuberculosis (TB) is complicated by the slow progression from asymptomatic infection to active, symptomatic disease, and the fact that there is only a 5-10% lifetime risk of developing active TB disease. Furthermore, the time of symptom onset for infectors and infectees is rarely observed accurately. In this dissertation, we first conduct a systematic literature review to demonstrate the limited methods currently available to estimate the serial interval for TB as well as the few estimates that have been published. Secondly, under the assumption of an ideal scenario where all SIs are observed with precision, we evaluate the effect of prior information on estimating the SI in a Bayesian framework. Thirdly, we apply cure models, proposed by Boag in 1949, to estimate the SI for TB in a Bayesian framework. We show that the cure models perform better in the presence of credible prior information on the proportion of the study population that develop active TB disease, and should be chosen over traditional survival models which assume that all of the study population will eventually have the event of interest—active TB disease. Next, we modify the method by Reich et al. in 2009 by using a Riemann sum to approximate the likelihood function that involves a double integral. In doing so, we are able to reduce the computing time of the approximation method by around 50%. We are also able to relax the assumption of uniformity on the censoring intervals. We show that when using weights that are consistent with the underlying skewness of the intervals, the proposed approaches consistently produce more accurate estimates than the existing approaches. We provide SI estimates for TB using empirical datasets from Brazil and USA/Canada.