Improved Doubly Robust Inference with Nonprobability Survey Samples Using Finite Mixture Models: Application to Health Monitoring SMS Survey Data

Nonprobability sampling has been increasingly used in epidemiologic research, yet direct inference based on such samples is subject to selection bias. Current adjustment methods commonly rely on a reference probability-based survey sample that shares a set of covariates with the nonprobability sample. However, these common covariates are often limited and may bias estimates in the presence of population heterogeneity. Existing methods generally assume population homogeneity in models and fail to address such heterogeneity adequately. To overcome this limitation, we propose the Nonprobability Heterogeneity-adjusted Doubly Robust (NHDR) method, a novel inference framework that explicitly accounts for population heterogeneity during selection bias adjustment. NHDR proceeds in three stages: (1) identifying latent subpopulations via finite mixture modeling; (2) incorporating the resulting latent-class structure as a grouping variable into mixed-effects models for both the propensity score and outcome projection; and (3) constructing a doubly robust estimator that integrates these adjusted models. The key methodological contribution of NHDR is its formal integration of latent-class-based population structure into a doubly robust estimation framework, which enables more reliable inference under heterogeneous population settings. Simulation studies demonstrate that the proposed method control the coverage probabilities well in most scenarios. Under heterogeneous conditions, NHDR consistently outperforms existing methods achieving an average reduction in relative bias of approximately 1.8–4.5% and a corresponding decrease in mean squared error of about 5.1–15.5 compared to the benchmark method. We illustrate the practical utility of NHDR by applying it to estimate nine health indicators using data from the Health Monitoring SMS Survey in Guangzhou, China, with the seventh Guangdong Health Service Survey serving as the reference sample.