Group testing is an effective way to reduce the time and cost associated with conducting large-scale screening studies for infectious diseases. Benefits are realised through testing pools formed by combining specimens, such as blood or urine, from different individuals. In some studies, individuals are assessed only once and a time-to-event endpoint is recorded, for example, the time until infection. Combining group testing with this type of endpoint results in group-tested current status data Petito and Jewell (2016). To analyse these complex data, we propose new methods which estimate a proportional hazards regression model based on test outcomes from measuring only the pools. A sieve maximum likelihood estimation approach is developed that approximates the cumulative baseline hazard function with a piecewise constant function. To identify the sieve estimator, a computationally efficient expectation-maximisation algorithm is derived by using data augmentation. Asymptotic properties of both the parametric and nonparametric components of the sieve estimator are then established by applying modern empirical process theory. Numerical results from simulation studies show our proposed method performs nominally and has desirable advantages over the corresponding estimation method based on individual testing results. We illustrate our work by analyzing a chlamydia data set collected by the State Hygienic Laboratory at University of Iowa.