Variable Selection in General Frailty Models Using Penalized H-Likelihood

A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection

We recently developed a new method random-intercept accelerated failure time model with Bayesian additive regression trees (riAFT-BART) to draw causal inferences about population treatment effect on patient survival from clustered and censored survival data while accounting for the multilevel data structure. The practical utility of this method goes beyond the estimation of population average treatment effect. In this work, we exposit how riAFT-BART can be used to solve two important statistical questions with clustered survival data: estimating the treatment effect heterogeneity and variable selection. Leveraging the likelihood-based machine learning, we describe a way in which we can draw posterior samples of the individual survival treatment effect from riAFT-BART model runs, and use the drawn posterior samples to perform an exploratory treatment effect heterogeneity analysis to identify subpopulations who may experience differential treatment effects than population average effects. There is sparse literature on methods for variable selection among clustered and censored survival data, particularly ones using flexible modeling techniques. We propose a permutation-based approach using the predictor's variable inclusion proportion supplied by the riAFT-BART model for variable selection. To address the missing data issue frequently encountered in health databases, we propose a strategy to combine bootstrap imputation and riAFT-BART for variable selection among incomplete clustered survival data. We conduct an expansive simulation study to examine the practical operating characteristics of our proposed methods, and provide empirical evidence that our proposed methods perform better than several existing methods across a wide range of data scenarios. Finally, we demonstrate the methods via a case study of predictors for in-hospital mortality among severe COVID-19 patients and estimating the heterogeneous treatment effects of three COVID-specific medications. The methods developed in this work are readily available in the R ${\textsf {R}}$ package riAFTBART $\textsf {riAFTBART}$ .

Penalized variable selection in multi-parameter regression survival modeling

Standard survival models such as the proportional hazards model contain a single regression component, corresponding to the scale of the hazard. In contrast, we consider the so-called "multi-parameter regression" approach whereby covariates enter the model through multiple distributional parameters simultaneously, for example, scale and shape parameters. This approach has previously been shown to achieve flexibility with relatively low model complexity. However, beyond a stepwise type selection method, variable selection methods are underdeveloped in the multi-parameter regression survival modeling setting. Therefore, we propose penalized multi-parameter regression estimation procedures using the following penalties: least absolute shrinkage and selection operator, smoothly clipped absolute deviation, and adaptive least absolute shrinkage and selection operator. We compare these procedures using extensive simulation studies and an application to data from an observational lung cancer study; the Weibull multi-parameter regression model is used throughout as a running example.

Efficient algorithms for survival data with multiple outcomes using the frailty model

Survival data with multiple outcomes are frequently encountered in biomedical investigations. An illustrative example comes from Alzheimer's Disease Neuroimaging Initiative study where the cognitively normal subjects may clinically progress to mild cognitive impairment and/or Alzheimer's disease dementia. Transition time from normal cognition to mild cognitive impairment and that from mild cognitive impairment to Alzheimer's disease are expected to be correlated within subjects and the dependence is often accommodated by the frailty (random effects). Estimation in the frailty model unavoidably involves multiple integrations which may be intractable and hence leads to severe computational challenges, especially in the presence of high-dimensional covariates. In this paper, we propose efficient minorization-maximization algorithms in the frailty model for survival data with multiple outcomes. The alternating direction method of multipliers is further incorporated for simultaneous variable selection and homogeneity pursuit via regularization and fusion. Extensive simulation studies are conducted to assess the performance of the proposed algorithms. An application to the Alzheimer's Disease Neuroimaging Initiative data is also provided to illustrate their practical utilities.

Penalized variable selection for cause-specific hazard frailty models with clustered competing-risks data

Competing risks data usually arise when an occurrence of an event precludes other types of events from being observed. Such data are often encountered in a clustered clinical study such as a multi-center clinical trial. For the clustered competing-risks data which are correlated within a cluster, competing-risks models allowing for frailty terms have been recently studied. To the best of our knowledge, however, there is no literature on variable selection methods for cause-specific hazard frailty models. In this article, we propose a variable selection procedure for fixed effects in cause-specific competing risks frailty models using a penalized h-likelihood (HL). Here, we study three penalty functions, LASSO, SCAD, and HL. Simulation studies demonstrate that the proposed procedure using the HL penalty works well, providing a higher probability of choosing the true model than LASSO and SCAD methods without losing prediction accuracy. The proposed method is illustrated by using two kinds of clustered competing-risks cancer data sets.

Penalized variable selection for accelerated failure time models with random effects

Accelerated failure time (AFT) models allowing for random effects are linear mixed models under the log-transformation of survival time with censoring and describe dependence in correlated survival data. It is well known that the AFT models are useful alternatives to frailty models. To the best of our knowledge, however, there is no literature on variable selection methods for such AFT models. In this paper, we propose a simple but unified variable-selection procedure of fixed effects in the AFT random-effect models using penalized h-likelihood (HL). We consider four penalty functions (ie, least absolute shrinkage and selection operator (LASSO), adaptive LASSO, smoothly clipped absolute deviation (SCAD), and HL). We show that the proposed method can be easily implemented via a slight modification to existing h-likelihood estimation procedures. We thus demonstrate that the proposed method can also be easily extended to AFT models with multilevel (or nested) structures. Simulation studies also show that the procedure using the adaptive LASSO, SCAD, or HL penalty performs well. In particular, we find via the simulation results that the variable selection method with HL penalty provides a higher probability of choosing the true model than other three methods. The usefulness of the new method is illustrated using two actual datasets from multicenter clinical trials.