Abstract

In large clinical studies, data may be collected from multiple sources (for example, locations). In such analyses, it is desirable to obtain a single, interpretable estimate of the treatment effect to facilitate downstream actions, such as regulatory approval. For other variables that may be of lesser interest, it is important to flexibly model their effects while allowing for source- (location-) specific heterogeneity. In this study, for survival data, we assume a semiparametric accelerated failure time model for each source. These models share a common treatment effect, which is modeled parametrically. The effects of the other variables are modeled nonparametrically and estimated using deep neural networks. To regularize estimation and obtain more interpretable models, penalization is imposed on the neural networks for variable selection. Estimation and selection properties are rigorously established, and extensive simulations are conducted. We further analyze SEER–Medicare breast cancer data to examine the treatment effects of mastectomy and lumpectomy.