Identification of drug‐induced toxicity biomarkers for treatment determination

Drug‐induced organ toxicity (DIOT) that leads to the removal of marketed drugs or termination of candidate drugs has been a leading concern for regulatory agencies and pharmaceutical companies. In safety studies, the genomic assays are conducted after the treatment so that drug‐induced adverse effects can occur. Two types of biomarkers are observed: biomarkers of susceptibility and biomarkers of response. This paper presents a statistical model to distinguish two types of biomarkers and procedures to identify susceptible subpopulations. The biomarkers identified are used to develop classification model to identify susceptible subpopulation. Two methods to identify susceptibility biomarkers were evaluated in terms of predictive performance in subpopulation identification, including sensitivity, specificity, and accuracy. Method 1 considered the traditional linear model with a variable‐by‐treatment interaction term, and Method 2 considered fitting a single predictor variable model using only treatment data. Monte Carlo simulation studies were conducted to evaluate the performance of the two methods and impact of the subpopulation prevalence, probability of DIOT, and sample size on the predictive performance. Method 2 appeared to outperform Method 1, which was due to the lack of power for testing the interaction effect. Important statistical issues and challenges regarding identification of preclinical DIOT biomarkers were discussed. In summary, identification of predictive biomarkers for treatment determination highly depends on the subpopulation prevalence. When the proportion of susceptible subpopulation is 1% or less, a very large sample size is needed to ensure observing sufficient number of DIOT responses for biomarker and/or subpopulation identifications. Copyright © 2015 John Wiley & Sons, Ltd.     

An Adaptive Method of Variable Selection in Regression

An adaptive variable selection procedure is proposed which uses an adaptive test along with a stepwise procedure to select variables for a multiple regression model. We compared this adaptive stepwise procedure to methods that use Akaike's information criterion, Schwartz's information criterion, and Sawa's information criterion. The simulation studies demonstrated that the adaptive stepwise method is more effective than the traditional variable selection methods if the error distribution is not normally distributed. If the error distribution is known to be normally distributed, the variable selection method based on Sawa's information criteria appears to be superior to the other methods. Unless the error distribution is known to be normally distributed, the adaptive stepwise method is recommended.     

Variable screening for ultrahigh dimensional censored quantile regression

Quantile regression is a flexible approach to assessing covariate effects on failure time, which has attracted considerable interest in survival analysis. When the dimension of covariates is much larger than the sample size, feature screening and variable selection become extremely important and indispensable. In this article, we introduce a new feature screening method for ultrahigh dimensional censored quantile regression. The proposed method can work for a general class of survival models, allow for heterogeneity of data and enjoy desirable properties including the sure screening property and the ranking consistency property. Moreover, an iterative version of screening algorithm has also been proposed to accommodate more complex situations. Monte Carlo simulation studies are designed to evaluate the finite sample performance under different model settings. We also illustrate the proposed methods through an empirical analysis.     

Modelling heterogeneity of survival in band-recovery data using mixtures

Finite mixture methods are applied to bird band-recovery studies to allow for heterogeneity of survival. Birds are assumed to belong to one of finitely many groups, each of which has its own survival rate (or set of survival rates varying by time and/or age). The group to which a specific animal belongs is not known, so its survival probability is a random variable from a finite mixture. Heterogeneity is thus modelled as a latent effect. This gives a wide selection of likelihood-based models, which may be compared using likelihood ratio tests. These models are discussed with reference to real and simulated data, and compared with previous models.     

Modelling heterogeneity of survival in band-recovery data using mixtures

Finite mixture methods are applied to bird band-recovery studies to allow for heterogeneity of survival. Birds are assumed to belong to one of finitely many groups, each of which has its own survival rate (or set of survival rates varying by time and/or age). The group to which a specific animal belongs is not known, so its survival probability is a random variable from a finite mixture. Heterogeneity is thus modelled as a latent effect. This gives a wide selection of likelihood-based models, which may be compared using likelihood ratio tests. These models are discussed with reference to real and simulated data, and compared with previous models.     

Reducing sample size needed for cox-proportional hazards model analysis using more efficient sampling method

Abstract

In general, survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Models for survival data have frequently been based on the proportional hazards model, proposed by Cox. The Cox model has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This paper demonstrates that this approach provides a more powerful testing procedure as well as a more efficient estimate of hazard ratio than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural study data are used to illustrate the methods developed in this paper.     

A joint-modeling approach to assess the impact of biomarker variability on the risk of developing clinical outcome

In some clinical trials and epidemiologic studies, investigators are interested in knowing whether the variability of a biomarker is independently predictive of clinical outcomes. This question is often addressed via a naïve approach where a sample-based estimate (e.g., standard deviation) is calculated as a surrogate for the “true” variability and then used in regression models as a covariate assumed to be free of measurement error. However, it is well known that the measurement error in covariates causes underestimation of the true association. The issue of underestimation can be substantial when the precision is low because of limited number of measures per subject. The joint analysis of survival data and longitudinal data enables one to account for the measurement error in longitudinal data and has received substantial attention in recent years. In this paper we propose a joint model to assess the predictive effect of biomarker variability. The joint model consists of two linked sub-models, a linear mixed model with patient-specific variance for longitudinal data and a full parametric Weibull distribution for survival data, and the association between two models is induced by a latent Gaussian process. Parameters in the joint model are estimated under Bayesian framework and implemented using Markov chain Monte Carlo (MCMC) methods with WinBUGS software. The method is illustrated in the Ocular Hypertension Treatment Study to assess whether the variability of intraocular pressure is an independent risk of primary open-angle glaucoma. The performance of the method is also assessed by simulation studies.     

The Method to Identify a Biomarker and to Evaluate Its Efficiency for Survival by Using the Joint Model of the Accelerate Failure Time and Longitudinal Data

In this article, we discuss how to identify longitudinal biomarkers in survival analysis under the accelerated failure time model and also discuss the effectiveness of biomarkers under the accelerated failure time model. Two methods proposed by Shcemper et al. are deployed to measure the efficacy of biomarkers. We use simulations to explore how the factors can influence the power of a score test to detect the association of a longitudinal biomarker and the survival time. These factors include the functional form of the random effects from the longitudinal biomarkers, in the different number of individuals, and time points per individual. The simulations are used to explore how the number of individuals, the number of time points per individual influence the effectiveness of the biomarker to predict survival at the given endpoint under the accelerated failure time model. We illustrate our methods using a prothrombin index as a predictor of survival in liver cirrhosis patients.     

Trace pursuit variable selection for multi-population data

Variable selection is a very important tool when dealing with high dimensional data. However, most popular variable selection methods are model based, which might provide misleading results when the model assumption is not satisfied. Sufficient dimension reduction provides a general framework for model-free variable selection methods. In this paper, we propose a model-free variable selection method via sufficient dimension reduction, which incorporates the grouping information into the selection procedure for multi-population data. Theoretical properties of our selection methods are also discussed. Simulation studies suggest that our method greatly outperforms those ignoring the grouping information.     

Application of trajectories from growth curve in identification of longitudinal biomarker for the multivariate survival data

In clinical studies, the researchers measure the patients' response longitudinally. In recent studies, Mixed models are used to determine effects in the individual level. In the other hand, Henderson et al. [3,4] developed a joint likelihood function which combines likelihood functions of longitudinal biomarkers and survival times. They put random effects in the longitudinal component to determine if a longitudinal biomarker is associated with time to an event. In this paper, we deal with a longitudinal biomarker as a growth curve and extend Henderson's method to determine if a longitudinal biomarker is associated with time to an event for the multivariate survival data.     

Variable selection in discrete survival models including heterogeneity

Several variable selection procedures are available for continuous time-to-event data. However, if time is measured in a discrete way and therefore many ties occur models for continuous time are inadequate. We propose penalized likelihood methods that perform efficient variable selection in discrete survival modeling with explicit modeling of the heterogeneity in the population. The method is based on a combination of ridge and lasso type penalties that are tailored to the case of discrete survival. The performance is studied in simulation studies and an application to the birth of the first child.     

A Bayesian phase I/II design to determine subgroup-specific optimal dose for immunotherapy sequentially combined with radiotherapy

Sequential administration of immunotherapy following radiotherapy (immunoRT) has attracted much attention in cancer research. Due to its unique feature that radiotherapy upregulates the expression of a predictive biomarker for immunotherapy, novel clinical trial designs are needed for immunoRT to identify patient subgroups and the optimal dose for each subgroup. In this article, we propose a Bayesian phase I/II design for immunotherapy administered after standard-dose radiotherapy for this purpose. We construct a latent subgroup membership variable and model it as a function of the baseline and pre-post radiotherapy change in the predictive biomarker measurements. Conditional on the latent subgroup membership of each patient, we jointly model the continuous immune response and the binary efficacy outcome using plateau models, and model toxicity using the equivalent toxicity score approach to account for toxicity grades. During the trial, based on accumulating data, we continuously update model estimates and adaptively randomize patients to admissible doses. Simulation studies and an illustrative trial application show that our design has good operating characteristics in terms of identifying both patient subgroups and the optimal dose for each subgroup.     

Clinical utility estimation for assay cutoffs in early phase oncology enrichment trials

Predictive enrichment strategies use biomarkers to selectively enroll oncology patients into clinical trials to more efficiently demonstrate therapeutic benefit. Because the enriched population differs from the patient population eligible for screening with the biomarker assay, there is potential for bias when estimating clinical utility for the screening eligible population if the selection process is ignored. We write estimators of clinical utility as integrals averaging regression model predictions over the conditional distribution of the biomarker scores defined by the assay cutoff and discuss the conditions under which consistent estimation can be achieved while accounting for some nuances that may arise as the biomarker assay progresses toward a companion diagnostic. We outline and implement a Bayesian approach in estimating these clinical utility measures and use simulations to illustrate performance and the potential biases when estimation naively ignores enrichment. Results suggest that the proposed integral representation of clinical utility in combination with Bayesian methods provide a practical strategy to facilitate cutoff decision‐making in this setting. Copyright © 2015 John Wiley & Sons, Ltd.     

High dimensional variable selection with clustered data: an application of random multivariate survival forests for detection of outlier medical device components

In many medical studies patients are nested or clustered within doctor. With many explanatory variables, variable selection with clustered data can be challenging. We propose a method for variable selection based on random forest that addresses clustered data through stratified binary splits. Our motivating example involves the detection orthopedic device components from a large pool of candidates, where each patient belongs to a surgeon. Simulations compare the performance of survival forests grown using the stratified logrank statistic to conventional and robust logrank statistics, as well as a method to select variables using a threshold value based on a variable's empirical null distribution. The stratified logrank test performs superior to conventional and robust methods when data are generated to have cluster-specific effects, and when cluster sizes are sufficiently large, perform comparably to the splitting alternatives in the absence of cluster-specific effects. Thresholding was effective at distinguishing between important and unimportant variables.     

A visualization method measuring the performance of biomarkers for guiding treatment decisions

Biomarkers that predict efficacy and safety for a given drug therapy become increasingly important for treatment strategy and drug evaluation in personalized medicine. Methodology for appropriately identifying and validating such biomarkers is critically needed, although it is very challenging to develop, especially in trials of terminal diseases with survival endpoints. The marker‐by‐treatment predictiveness curve serves this need by visualizing the treatment effect on survival as a function of biomarker for each treatment. In this article, we propose the weighted predictiveness curve (WPC). Based on the nature of the data, it generates predictiveness curves by utilizing either parametric or nonparametric approaches. Especially for nonparametric predictiveness curves, by incorporating local assessment techniques, it requires minimum model assumptions and provides great flexibility to visualize the marker‐by‐treatment relationship. WPC can be used to compare biomarkers and identify the one with the highest potential impact. Equally important, by simultaneously viewing several treatment‐specific predictiveness curves across the biomarker range, WPC can also guide the biomarker‐based treatment regimens. Simulations representing various scenarios are employed to evaluate the performance of WPC. Application on a well‐known liver cirrhosis trial sheds new light on the data and leads to discovery of novel patterns of treatment biomarker interactions. Copyright © 2015 John Wiley & Sons, Ltd.     

Confidence interval estimation of the difference between paired AUCs based on combined biomarkers

In many diagnostic studies, multiple diagnostic tests are performed on each subject or multiple disease markers are available. Commonly, the information should be combined to improve the diagnostic accuracy. We consider the problem of comparing the discriminatory abilities between two groups of biomarkers. Specifically, this article focuses on confidence interval estimation of the difference between paired AUCs based on optimally combined markers under the assumption of multivariate normality. Simulation studies demonstrate that the proposed generalized variable approach provides confidence intervals with satisfying coverage probabilities at finite sample sizes. The proposed method can also easily provide P-values for hypothesis testing. Application to analysis of a subset of data from a study on coronary heart disease illustrates the utility of the method in practice.     

Empirical likelihood based variable selection

Information criteria form an important class of model/variable selection methods in statistical analysis. Parametric likelihood is a crucial part of these methods. In some applications such as the generalized linear models, the models are only specified by a set of estimating functions. To overcome the non-availability of well defined likelihood function, the information criteria under empirical likelihood are introduced. Under this setup, we successfully solve the existence problem of the profile empirical likelihood due to the over constraint in variable selection problems. The asymptotic properties of the new method are investigated. The new method is shown to be consistent at selecting the variables under mild conditions. Simulation studies find that the proposed method has comparable performance to the parametric information criteria when a suitable parametric model is available, and is superior when the parametric model assumption is violated. A real data set is also used to illustrate the usefulness of the new method.     

Discrete‐time survival trees

Tree‐based methods are frequently used in studies with censored survival time. Their structure and ease of interpretability make them useful to identify prognostic factors and to predict conditional survival probabilities given an individual's covariates. The existing methods are tailor‐made to deal with a survival time variable that is measured continuously. However, survival variables measured on a discrete scale are often encountered in practice. The authors propose a new tree construction method specifically adapted to such discrete‐time survival variables. The splitting procedure can be seen as an extension, to the case of right‐censored data, of the entropy criterion for a categorical outcome. The selection of the final tree is made through a pruning algorithm combined with a bootstrap correction. The authors also present a simple way of potentially improving the predictive performance of a single tree through bagging. A simulation study shows that single trees and bagged‐trees perform well compared to a parametric model. A real data example investigating the usefulness of personality dimensions in predicting early onset of cigarette smoking is presented. The Canadian Journal of Statistics 37: 17‐32; 2009 © 2009 Statistical Society of Canada     

A regularized variable selection procedure in additive hazards model with stratified case-cohort design

Case-cohort designs are commonly used in large epidemiological studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large. An efficient variable selection method is needed for case-cohort studies where the covariates are only observed in a subset of the sample. Current literature on this topic has been focused on the proportional hazards model. However, in many studies the additive hazards model is preferred over the proportional hazards model either because the proportional hazards assumption is violated or the additive hazards model provides more relevent information to the research question. Motivated by one such study, the Atherosclerosis Risk in Communities (ARIC) study, we investigate the properties of a regularized variable selection procedure in stratified case-cohort design under an additive hazards model with a diverging number of parameters. We establish the consistency and asymptotic normality of the penalized estimator and prove its oracle property. Simulation studies are conducted to assess the finite sample performance of the proposed method with a modified cross-validation tuning parameter selection methods. We apply the variable selection procedure to the ARIC study to demonstrate its practical use.     

An iterative approach to distance correlation-based sure independence screening

Feature screening and variable selection are fundamental in analysis of ultrahigh-dimensional data, which are being collected in diverse scientific fields at relatively low cost. Distance correlation-based sure independence screening (DC-SIS) has been proposed to perform feature screening for ultrahigh-dimensional data. The DC-SIS possesses sure screening property and filters out unimportant predictors in a model-free manner. Like all independence screening methods, however, it fails to detect the truly important predictors which are marginally independent of the response variable due to correlations among predictors. When there are many irrelevant predictors which are highly correlated with some strongly active predictors, the independence screening may miss other active predictors with relatively weak marginal signals. To improve the performance of DC-SIS, we introduce an effective iterative procedure based on distance correlation to detect all truly important predictors and potentially interactions in both linear and nonlinear models. Thus, the proposed iterative method possesses the favourable model-free and robust properties. We further illustrate its excellent finite-sample performance through comprehensive simulation studies and an empirical analysis of the rat eye expression data set.