Subgroup analysis of linear models with measurement error

Heterogeneity exists in populations, and people may benefit differently from the same treatments or services. Correctly identifying subgroups corresponding to outcomes such as treatment response plays an important role in data-based decision making. As few discussions exist on subgroup analysis with measurement error, we propose a new estimation method to consider these two components simultaneously under the linear regression model. First, we develop an objective function based on unbiased estimating equations with two repeated measurements and a concave penalty on pairwise differences between coefficients. The proposed method can identify subgroups and estimate coefficients simultaneously when considering measurement error. Second, we derive an algorithm based on the alternating direction method of multipliers algorithm and demonstrate its convergence. Third, we prove that the proposed estimators are consistent and asymptotically normal. The performance and asymptotic properties of the proposed method are evaluated through simulation studies. Finally, we apply our method to data from the Lifestyle Education for Activity and Nutrition study and identify two subgroups, of which one has a significant treatment effect.