Establishing a standard method for analysing case detection delay in leprosy using a Bayesian modelling approach

Leprosy is an infectious disease caused by Mycobacterium leprae and remains a source of preventable disability if left undetected. Case detection delay is an important epidemiological indicator for progress in interrupting transmission and preventing disability in a community. However, no standard method exists to effectively analyse and interpret this type of data. In this study, we aim to evaluate the characteristics of leprosy case detection delay data and select an appropriate model for the variability of detection delays based on the best fitting distribution type.

Two sets of leprosy case detection delay data were evaluated: a cohort of 181 patients from the post exposure prophylaxis for leprosy (PEP4LEP) study in high endemic districts of Ethiopia, Mozambique, and Tanzania; and self-reported delays from 87 individuals in 8 low endemic countries collected as part of a systematic literature review. Bayesian models were fit to each dataset to assess which probability distribution (log-normal, gamma or Weibull) best describes variation in observed case detection delays using leave-one-out cross-validation, and to estimate the effects of individual factors.

For both datasets, detection delays were best described with a log-normal distribution combined with covariates age, sex and leprosy subtype [expected log predictive density (ELPD) for the joint model: -1123.9]. Patients with multibacillary (MB) leprosy experienced longer delays compared to paucibacillary (PB) leprosy, with a relative difference of 1.57 [95% Bayesian credible interval (BCI): 1.14-2.15]. Those in the PEP4LEP cohort had 1.51 (95% BCI: 1.08-2.13) times longer case detection delay compared to the self-reported patient delays in the systematic review.

The log-normal model presented here could be used to compare leprosy case detection delay datasets, including PEP4LEP where the primary outcome measure is reduction in case detection delay. We recommend the application of this modelling approach to test different probability distributions and covariate effects in studies with similar outcomes in the field of leprosy and other skin-NTDs.