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Ma, H., Liu, C., Xu, S. and Yang, J. (2022), Subgroup analysis for functional partial linear regression model. Can J Statistics. https://doi.org/10.1002/cjs.11696
Subgroup analysis has been widely used in many fields, such as finance, business, and healthcare. There is often heterogeneity in the response of a population to a certain promotion strategy or medical treatment. Therefore, correctly identifying the different subgroups plays a crucial role in decision-making. At the same time, measurement errors can occur during data collection due many reasons, such as the accuracy of the device or the collection method. However, most statistical models assume that all the observations are correctly measured. Thus, ignoring measurement error in analysis will cause bias in estimation. Similarly, subgroup analysis mentioned above cannot be applied directly to data when there exist measurement errors in the covariates. With few discussions on subgroup analysis with the existence of measurement error, we propose a novel method of subgroup analysis with measurement error under the linear regression model. The proposed method can identify the subgroups and estimate coefficients simultaneously with the consideration of measurement error and has good large sample properties. We also derive an algorithm for this method and prove its convergence. Finally, we apply this method to the data from the Lifestyle Education for Activity and Nutrition study and identify two subgroup with one group having a significant treatment effect, which was not found in previous studies. Our work is a good attempt to combine the fields of subgroup analysis and measurement error.More Details