A threshold linear mixed model for identification of treatment-sensitive subsets in a clinical trial based on longitudinal outcomes and a continuous covariate

Abstract

Identification of a subset of patients who may be sensitive to a specific treatment is an important problem in clinical trials. In this paper, we consider the case where the treatment effect is measured by longitudinal outcomes, such as quality of life scores assessed over the duration of a clinical trial, and the subset is determined by a continuous baseline covariate, such as age and expression level of a biomarker. A threshold linear mixed model is introduced, and a smoothing maximum likelihood method is proposed to obtain the estimation of the parameters in the model. Broyden-Fletcher-Goldfarb-Shanno algorithm is employed to maximize the proposed smoothing likelihood function. The proposed procedure is evaluated through simulation studies and application to the analysis of data from a randomized clinical trial on patients with advanced colorectal cancer.

Subgroup analysis for longitudinal data based on a partial linear varying coefficient model with a change plane

“…The membership in the subgroup is determined by which side a random vector falls with respect to the hyperplane with unknown coefficients, and the effects of covariates may be different on two sides of the hyperplane. Due to its strong interpretability for sample splitting, change plane model has attracted extensive attention and has been studied in different data types: time series 21 and survival, 22 different regression scenarios: mean 5 and quantile; 23 different subgroup characteristics: single subgroup variable with single threshold 24 and multiple subgroup variables with multiple thresholds; 25 different estimation and inference theories: unsmoothed 26 and smoothed estimator. 27 Motivated by the role of change plane model in sample splitting, we propose a partial linear varying coefficient model with a change plane for subgroup analysis of longitudinal data, taking the randomized trial as an illustration:…”

“…𝜸 is a vector of unknown change plane coefficients, W i is a vector of grouping variables, usually some prognostic factors measured at baseline. 24,28 According to whether the linear combination of grouping variables W T i 𝜸 exceeds 0, two subgroups can be identified. Using a classifier calculated from multiple prognostic factors together to define subgroups is increasingly considered in medical research, for example, the polygenic risk score calculated as a weighted sum of genome-wide genotypes, 29 the Nottingham prognostic index calculated by integrating pathological factors of breast cancer patients.…”

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

“…14,15 Another potential model for subgroup analysis is called threshold model, 16,17 which is related to the change point detection or segmented regression and can be used to defined subgroups by sample splitting when the sample split is based on the grouping variable moves across thresholds. Due to its strong interpretability and mature theoretical properties, threshold model has attracted many attentions and the corresponding literature can be divided into different application scenarios: regression 18 and autoregressive; 19 different subgroup characteristics: single biomarker 20 and multiple biomarkers; 21 different estimation and inference theories: unsmoothed estimator 16 and smoothed estimator. 22 However, most of these methods use biomarkers to identify the group structure and estimate the subgroup-specific parameters based on complete independent or time series data, few studies consider the application scenario of incomplete longitudinal data.…”

Multikink Quantile Regression for Longitudinal Data with Application to Progesterone Data Analysis

“…Ge et al. (2020) proposed a threshold linear mixed model to determine the cutpoint of a continuous regressor and to estimate the interaction effect between the treatment and subgroup indicator on longitudinal responses.…”

“…Li and Zhang (2011) also found that there exists a threshold effect between the blood pressure change and the progression of microalbuminuria among individuals with type-I diabetes using censored longitudinal data. Ge et al (2020) proposed a threshold linear mixed model to determine the cutpoint of a continuous regressor and to estimate the interaction effect between the treatment and subgroup indicator on longitudinal responses.…”