Abstract: Group testing has been used extensively to reduce screening costs in epidemiological studies involving low-prevalence diseases. This testing strategy involves combining specimens (e.g., blood, urine, or swabs) from several individuals to form a pool and then testing the pooled specimen for infection. When the endpoint of interest is a time-to-event outcome, for example, the time until infection or disease, and pools are measured only once, the resulting data are called group-tested current status data (Petito and Jewell, 2016). In this paper, we propose a new type of regression analysis for these data using a semiparametric probit model, an alternative to the proportional hazards model in survival analysis. A sieve maximum likelihood estimation approach is developed that approximates the model’s nonparametric nuisance function by using logarithmic monotone splines, and an efficient expectation-maximization algorithm is proposed. Asymptotic properties of the resulting estimators are investigated by using empirical process techniques and sieve estimation theory. Numerical results from simulation studies suggest our estimation methods perform nominally, even when pools are possibly misclassified due to assay error, and can outperform individual testing when the number of assays (tests) is fixed. We illustrate our work by estimating a time-to-event regression model for Chlamydial infection using group testing data from a large public health laboratory in Iowa.

Key words and phrases: Current status data, EM algorithm, maximum likelihood estimation, pooled testing, sieve estimation.