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Register a new userpcoxtime: Penalized Cox Proportional Hazard Model for Time-dependent Covariates
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Added by
Benjamin Bolker
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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The penalized Cox proportional hazard model is a popular analytical approach for survival data with a large number of covariates. Such problems are especially challenging when covariates vary over follow-up time (i.e., the covariates are time-dependent). The standard R packages for fully penalized Cox models cannot currently incorporate time-dependent covariates. To address this gap, we implement a variant of gradient descent algorithm (proximal gradient descent) for fitting penalized Cox models. We apply our implementation to real and simulated data sets.
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For survival data with high-dimensional covariates, results generated in the analysis of a single dataset are often unsatisfactory because of the small sample size. Integrative analysis pools raw data from multiple independent studies with comparable designs, effectively increases sample size, and has better performance than meta-analysis and single-dataset analysis. In this study, we conduct integrative analysis of survival data under the accelerated failure time (AFT) model. The sparsity structures of multiple datasets are described using the homogeneity and heterogeneity models. For variable selection under the homogeneity model, we adopt group penalization approaches. For variable selection under the heterogeneity model, we use composite penalization and sparse group penalization approaches. As a major advancement from the existing studies, the asymptotic selection and estimation properties are rigorously established. Simulation study is conducted to compare different penalization methods and against alternatives. We also analyze four lung cancer prognosis datasets with gene expression measurements.
Nonlinear Mixed effects models are hidden variables models that are widely used in many field such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters such as covariates or correlations which must be selected. Recent development of pharmacogenomics has brought averaged/high dimensional problems to the field of nonlinear mixed effects modeling for which standard covariates selection techniques like stepwise methods are not well suited. This work proposes to select covariates and correlation parameters using a penalized likelihood approach. The penalized likelihood problem is solved using a stochastic proximal gradient algorithm to avoid inner-outer iterations. Speed of convergence of the proximal gradient algorithm is improved by the use of component-wise adaptive gradient step sizes. The practical implementation and tuning of the proximal gradient algorithm is explored using simulations. Calibration of regularization parameters is performed by minimizing the Bayesian Information Criterion using particle swarm optimization, a zero order optimization procedure. The use of warm restart and parallelization allows to reduce significantly computing time. The performance of the proposed method compared to the traditional grid search strategy is explored using simulated data. Finally, an application to real data from two pharmacokinetics studies is provided, one studying an antifibrinolitic and the other studying an antibiotic.
Model fitting often aims to fit a single model, assuming that the imposed form of the model is correct. However, there may be multiple possible underlying explanatory patterns in a set of predictors that could explain a response. Model selection without regarding model uncertainty can fail to bring these patterns to light. We present multi-model penalized regression (MMPR) to acknowledge model uncertainty in the context of penalized regression. In the penalty form explored here, we examine how different settings can promote either shrinkage or sparsity of coefficients in separate models. The method is tuned to explicitly limit model similarity. A choice of penalty form that enforces variable selection is applied to predict stacking fault energy (SFE) from steel alloy composition. The aim is to identify multiple models with different subsets of covariates that explain a single type of response.
Network meta-analysis (NMA) allows the combination of direct and indirect evidence from a set of randomized clinical trials. Performing NMA using individual patient data (IPD) is considered as a gold standard approach as it provides several advantages over NMA based on aggregate data. For example, it allows to perform advanced modelling of covariates or covariate-treatment interactions. An important issue in IPD NMA is the selection of influential parameters among terms that account for inconsistency, covariates, covariate-by-treatment interactions or non-proportionality of treatments effect for time to event data. This issue has not been deeply studied in the literature yet and in particular not for time-to-event data. A major difficulty is to jointly account for between-trial heterogeneity which could have a major influence on the selection process. The use of penalized generalized mixed effect model is a solution, but existing implementations have several shortcomings and an important computational cost that precludes their use for complex IPD NMA. In this article, we propose a penalized Poisson regression model to perform IPD NMA of time-to-event data. It is based only on fixed effect parameters which improve its computational cost over the use of random effects. It could be easily implemented using existing penalized regression package. Computer code is shared for implementation. The methods were applied on simulated data to illustrate the importance to take into account between trial heterogeneity during the selection procedure. Finally, it was applied to an IPD NMA of overall survival of chemotherapy and radiotherapy in nasopharyngeal carcinoma.
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation of the change-point. A new model-based bootstrap approach is proposed and its consistency established. Simulation studies are carried out to assess the performance of various bootstrap schemes.
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