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Identifying exceptional responders or nonresponders is an area of increased research interest in precision medicine as these patients may have different biological or molecular features and therefore may respond differently to therapies. Our motivation stems from a real example from a clinical trial where we are interested in characterizing exceptional prostate cancer responders. We investigate the outlier detection and robust regression problem in the sparse proportional hazards model for censored survival outcomes. The main idea is to model the irregularity of each observation by assigning an individual weight to the hazard function. By applying a LASSO‐type penalty on both the model parameters and the log transformation of the weight vector, our proposed method is able to perform variable selection and outlier detection simultaneously. The optimization problem can be transformed to a typical penalized maximum partial likelihood problem and thus it is easy to implement. We further extend the proposed method to deal with the potential outlier masking problem caused by censored outcomes. The performance of the proposed estimator is demonstrated with extensive simulation studies and real data analyses in low‐dimensional and high‐dimensional settings. [ABSTRACT FROM AUTHOR]

A major emphasis in precision medicine is to optimally treat subgroups of patients who may benefit from certain therapeutic agents. And as such, enormous resources and innovative clinical trials designs in oncology are devoted to identifying predictive biomarkers. Predictive biomarkers are ones that will identify patients that are more likely to respond to specific therapies and they are usually discovered through retrospective analysis from large randomized phase II or phase III trials. One important design to consider is the stratified biomarker design, where patients will have their specimens obtained at baseline and the biomarker status will be assessed prior to random assignment. Regardless of their biomarker status, patients will be randomized to either an experimental arm or the standard of care arm. The stratified biomarker design can be used to test for a treatment-biomarker interaction in predicting a time-to event outcome. Many biomarkers, however, are derived from tissues from patients, and their levels may be heterogeneous. As a result, biomarker levels may be measured with error and this would have an adverse impact on the power of a stratified biomarker clinical trial. We present a trial design and an analysis framework for the stratified biomarker design. We show that the naïve test is biased and provide bias-corrected estimators for computing the sample size and the 95% confidence interval when testing for a treatment-biomarker interaction in predicting a time to event outcome. We propose a sample size formula that adjusts for misclassification and apply it in the design of a phase III clinical trial in renal cancer. [ABSTRACT FROM AUTHOR]

Clinical trials utilizing predictive biomarkers have become a research focus in personalized medicine. We investigate the effects of biomarker misclassification on the design and analysis of stratified biomarker clinical trials. For a variety of inference problems including marker-treatment interaction in particular, we show that marker misclassification may have profound adverse effects on the coverage of confidence intervals, power of the tests, and required sample sizes. For each inferential problem, we propose methods to adjust for the classification errors. [ABSTRACT FROM AUTHOR]

Prognosis plays a pivotal role in patient management and trial design. A useful prognostic model should correctly identify important risk factors and estimate their effects. In this article, we discuss several challenges in selecting prognostic factors and estimating their effects using the Cox proportional hazards model. Although a flexible semiparametric form, the Cox's model is not entirely exempt from model misspecification. To minimize possible misspecification, instead of imposing traditional linear assumption, flexible modeling techniques have been proposed to accommodate the nonlinear effect. We first review several existing nonparametric estimation and selection procedures and then present a numerical study to compare the performance between parametric and nonparametric procedures. We demonstrate the impact of model misspecification on variable selection and model prediction using a simulation study and an example from a phase III trial in prostate cancer. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The analysis of case-control studies with matched controls per case is well documented in the medical literature. Of primary interest is the estimation of the relative risk of disease. Matched case-control studies fall into two scenarios: the probability of exposure is constant within each of the case and control groups, or the probability of exposure varies within each group. Numerous estimation procedures have been developed for both scenarios. Often these procedures are developed under the rare disease assumption, where the relative risk of disease is approximated by the odds ratio. In this paper, without making the rare disease assumption, we develop consistent estimators of the relative risk of disease for both scenarios. Exact derivations of the relative risk of disease are provided. Estimators, confidence intervals, and test statistics for the relative risk of disease are developed. We then make the following observations based on extensive simulations. First, our estimators are as close or closer to the relative risk of disease than other estimators. Second, our estimators produce mean square errors for the relative risk of disease that are as good as or better than these other estimators. Third, our confidence intervals provide accurate coverage probabilities. Therefore, these new estimators, confidence intervals, and test statistics can be used to either estimate or test the relative risk of disease in matched case-control studies. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Diagnostic accuracy can be improved considerably by combining multiple biomarkers. Although the likelihood ratio provides optimal solution to combination of biomarkers, the method is sensitive to distributional assumptions which are often difficult to justify. Alternatively simple linear combinations can be considered whose empirical solution may encounter intensive computation when the number of biomarkers is relatively large. Moreover, the optimal linear combinations derived under multivariate normality may suffer substantial loss of efficiency if the distributions are apart from normality. In this paper, we propose a new approach that linearly combines the minimum and maximum values of the biomarkers. Such combination only involves searching for a single combination coefficient that maximizes the area under the receiver operating characteristic (ROC) curves and is thus computation-effective. Simulation results show that the min-max combination may yield larger partial or full area under the ROC curves and is more robust against distributional assumptions. The methods are illustrated using the growth-related hormones data from the Growth and Maturation in Children with Autism or Autistic Spectrum Disorder Study (Autism/ASD Study). Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Ahnn and Anderson derived sample size formulae for unstratified and stratified designs assuming equal allocation of subjects to three or more treatment groups. We generalize the sample size formulae to allow for unequal allocation. In addition, we define the overall probability of death to be equal to one minus the censored proportion for the stratified design. This definition also leads to a slightly different definition of the non-centrality parameter than that of Ahnn and Anderson for the stratified case. Assuming proportional hazards, sample sizes are determined for a prespecified power, significance level, hazard ratios, allocation of subjects to several treatment groups, and known censored proportion. In the proportional hazards setting, three cases are considered: (1) exponential failures-exponential censoring, (2) exponential failures-uniform censoring, and (3) Weibull failures (assuming same shape parameter for all groups)-uniform censoring. In all three cases of the unstratified case, it is assumed that the censoring distribution is the same for all of the treatment groups. For the stratified log-rank test, it is assumed the same censoring distribution across the treatment groups and the strata. Further, formulae have been developed to provide approximate powers for the test, based upon the first two or first four-moments of the asymptotic distribution. We observe the following two major findings based on the simulations. First, the simulated power of the log-rank test does not depend on the censoring mechanism. Second, for a significance level of 0.05 and power of 0.80, the required sample size n is independent of the censoring pattern. Moreover, there is very close agreement between the exact (asymptotic) and simulated powers when a sequence of alternatives is close to the null hypothesis. Two-moment and four-moment power series approximations also yield powers in close agreement with the exact (asymptotic) power. With unequal allocations, our simulations show that the empirical powers are consistently above the target value of prespecified power of 0.80 when 50 per cent of the patients are allocated to the treatment group with the smallest hazard. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]