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Propensity score methods are commonly used in statistical analyses of observational data to reduce the impact of confounding bias in estimations of average treatment effect. While the propensity score is defined as the conditional probability of a subject being in the treatment group given that subject's covariates, the most precise estimation of average treatment effect results from specifying the propensity score as a function of true confounders and predictors only. This property has been demonstrated via simulation in multiple prior research articles. However, we have seen no theoretical explanation as to why this should be so. This paper provides that theoretical proof. Furthermore, this paper presents a method for performing the necessary variable selection by means of elastic net regression, and then estimating the propensity scores so as to obtain optimal estimates of average treatment effect. The proposed method is compared against two other recently introduced methods, outcome-adaptive lasso and covariate balancing propensity score. Extensive simulation analyses are employed to determine the circumstances under which each method appears most effective. We applied the proposed methods to examine the effect of pre-cardiac surgery coagulation indicator on mortality based on a linked dataset from a retrospective review of 1390 patient medical records at Jewish Hospital (Louisville, KY) with the Society of Thoracic Surgeons database. [ABSTRACT FROM AUTHOR]

There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian additive regression trees in such settings. First, we compare Bayesian additive regression trees to several approaches that have been proposed for continuous outcomes, including inverse probability of treatment weighting, targeted maximum likelihood estimator, vector matching, and regression adjustment. Results suggest that under conditions of non-linearity and non-additivity of both the treatment assignment and outcome generating mechanisms, Bayesian additive regression trees, targeted maximum likelihood estimator, and inverse probability of treatment weighting using generalized boosted models provide better bias reduction and smaller root mean squared error. Bayesian additive regression trees and targeted maximum likelihood estimator provide more consistent 95% confidence interval coverage and better large-sample convergence property. Second, we supply Bayesian additive regression trees with a strategy to identify a common support region for retaining inferential units and for avoiding extrapolating over areas of the covariate space where common support does not exist. Bayesian additive regression trees retain more inferential units than the generalized propensity score-based strategy, and shows lower bias, compared to targeted maximum likelihood estimator or generalized boosted model, in a variety of scenarios differing by the degree of covariate overlap. A case study examining the effects of three surgical approaches for non-small cell lung cancer demonstrates the methods. [ABSTRACT FROM AUTHOR]

Constructing causal inference methods to handle longitudinal data in observational studies is of high interest. In an observational setting, treatment assignment at each clinical visit follows a decision strategy where the treating clinician selects treatment based on current and past clinical measurements as well as treatment histories. These time-dependent structures, coupled with inherent correlations between and within each visit, add on to the data complexity. Despite recent interest in Bayesian causal methods, only a limited literature has explored approaches to handle longitudinal data and no method handles repeatedly measured outcomes. In this paper, we extended two Bayesian approaches: Bayesian estimation of marginal structural models and two-stage Bayesian propensity score analysis to handle a repeatedly measured outcome. Our proposed methods permit causal estimation of treatment effects at each visit. Time-dependent inverse probability of treatment weights are obtained from the Markov chain Monte Carlo samples of the posterior treatment assignment model for each follow-up visit. We use a simulation study to validate and compare the proposed methods and illustrate our approaches through a study of intravenous immunoglobulin therapy in treating newly diagnosed juvenile dermatomyositis. [ABSTRACT FROM AUTHOR]

When establishing an effective treatment with binary data in a two-stage design, one-sided tests for a proportion p are employed. Researchers use the parameter configuration at the boundary of the null hypothesis space to determine a rejection region and an optimal design. However, it is unclear whether the (maximum) Type I error rate is achieved at the boundary especially when the sample size in stage 2 varies. In this paper, we first prove that this is true for a large family of tests in adaptive two-stage designs by showing that any test in the family has a nondecreasing power in p and then derive optimal designs. Second, similar results are established for m-stage designs with m > 2. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure or treatment effects in observational studies. Routine practice is often based on stepwise selection procedures that use hypothesis testing, change-in-estimate assessments or the lasso, which have all been criticised for - amongst other things - not giving sufficient priority to the selection of confounders. This has prompted vigorous recent activity in developing procedures that prioritise the selection of confounders, while preventing the selection of so-called instrumental variables that are associated with exposure, but not outcome (after adjustment for the exposure). A major drawback of all these procedures is that there is no finite sample size at which they are guaranteed to deliver treatment effect estimators and associated confidence intervals with adequate performance. This is the result of the estimator jumping back and forth between different selected models, and standard confidence intervals ignoring the resulting model selection uncertainty. In this paper, we will develop insight into this by evaluating the finite-sample distribution of the exposure effect estimator in linear regression, under a number of the aforementioned confounder selection procedures. We will show that by making clever use of propensity scores, a simple and generic solution is obtained in the context of generalized linear models, which overcomes this concern (under weaker conditions than competing proposals). Specifically, we propose to use separate regularized regressions for the outcome and propensity score models in order to construct a doubly robust 'g-estimator'; when these models are sufficiently sparse and correctly specified, standard confidence intervals for the g-estimator implicitly incorporate the uncertainty induced by the variable selection procedure. [ABSTRACT FROM AUTHOR]

Non-adherence to assigned treatment is a common issue in cluster randomised trials. In these settings, the efficacy estimand may also be of interest. Many methodological contributions in recent years have advocated using instrumental variables to identify and estimate the local average treatment effect. However, the clustered nature of randomisation in cluster randomised trials adds to the complexity of such analyses. In this paper, we show that the local average treatment effect can be estimated via two-stage least squares regression using cluster-level summaries of the outcome and treatment received under certain assumptions. We propose the use of baseline variables to adjust the cluster-level summaries before performing two-stage least squares in order to improve efficiency. Implementation needs to account for the reduced sample size, as well as the possible heteroscedasticity, to obtain valid inferences. Simulations are used to assess the performance of two-stage least squares of cluster-level summaries under cluster-level or individual-level non-adherence, with and without weighting and robust standard errors. The impact of adjusting for baseline covariates and of appropriate degrees of freedom correction for inference is also explored. The methods are then illustrated by re-analysing a cluster randomised trial carried out in a specific UK primary care setting. Two-stage least squares estimation using cluster-level summaries provides estimates with small to negligible bias and coverage close to nominal level, provided the appropriate small sample degrees of freedom correction and robust standard errors are used for inference. [ABSTRACT FROM AUTHOR]

Ordinal responses are common in clinical studies. Although the proportional odds model is a popular option for analyzing ordered-categorical data, it cannot control the type I error rate when the proportional odds assumption fails to hold. The latent Weibull model was recently shown to be a superior candidate for modeling ordinal data, with remarkably better performance than the latent normal model when the data are highly skewed. In clinical trials with ordinal responses, a balanced design is common, with equal sample allocation for each treatment. However, a more ethical approach is to adopt a response-adaptive allocation scheme in which more patients receive the better treatment. In this paper, we propose the use of the doubly adaptive biased coin design to generate treatment allocations that benefit the trial participants. The proposed treatment allocation scheme not only allows more patients to receive the better treatment, it also maintains compatible test power for the comparison of treatment efficiencies. A clinical example is used to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]

Since the early work of RA Fisher, exact methods have been recognized as important tools in data analysis because they provide valid statistical inference even with small sample sizes, or with sparse or skewed data. With the recent advance of computational power and the availability of commercial software packages, exact methods have gained substantial popularity over the past two decades. However, most of these exact methods have been devoted to testing classical null hypotheses of no differences, and until recently little was known about exact methods dealing with non-inferiority or equivalence hypotheses. The presence of nuisance parameters in testing non-inferiority/equivalence hypotheses presents a special challenge for exact methods because of the intense computational requirement. In this paper, we review exact methods available for proving non-inferiority or equivalence of two treatments with a dichotomous endpoint. First, we present the general methodology for conducting exact tests for non-inferiority or equivalence; we then discuss several unconditional and conditional methods available for constructing hypothesis tests and confidence intervals based on three commonly used measures, namely, the difference, relative risk, and odds ratio of two independent proportions or rates. Finally, we illustrate with several examples the application of these exact methods in analysing and planning non-inferiority or equivalence trials. [ABSTRACT FROM AUTHOR]

All models of this paper involve R x C contingency tables in which the total frequency is fixed (full multinomial model), or in which the row totals are fixed (product multinomial model). For the most part, we assume that the column categories are ordered. For the full multinomial model the null hypothesis of interest is independence, i.e., the (ij)th cell probability is the product of the marginal probabilities of the ith row and jth column. In the product multinomial model the null hypothesis is that the R multinomial distributions have the same vector of cell probabilities. Our review includes (1) a careful listing of two-sided and one-sided alternatives, and (2) methodology to reduce the loss of efficiency of tests because of the discreteness of the model (The methodologies discussed are efficient in several senses. Tests are exact. Tests have very favorable and robust power properties. Tests make use of back-up statistics, thereby providing a finer grid of p-values. In some special cases, e.g., a 2 x C table and a one-sided alternative, conditional p-values are found, within seconds, simply by entering row frequencies into a given website. Thus, computational efficiency is exceptional.), and (3) a critique of some exact linear permutation tests (that are conditional on row and column margins) for both two-sided and some one-sided alternatives. Furthermore, recommendations as to which tests to use for specific alternatives are made. [ABSTRACT FROM AUTHOR]

Randomized clinical trials are considered as the gold standard for estimating causal effects. Nevertheless, in studies that are aimed at examining adverse effects of interventions, randomized trials are often impractical because of ethical and financial considerations. In observational studies, matching on the generalized propensity scores was proposed as a possible solution to estimate the treatment effects of multiple interventions. However, the derivation of point and interval estimates for these matching procedures can become complex with non-continuous or censored outcomes. We propose a novel Approximate Bayesian Bootstrap algorithm that results in statistically valid point and interval estimates of the treatment effects with categorical outcomes. The procedure relies on the estimated generalized propensity scores and multiply imputes the unobserved potential outcomes for each unit. In addition, we describe a corresponding interpretable sensitivity analysis to examine the unconfoundedness assumption. We apply this approach to examine the cardiovascular safety of common, real-world anti-diabetic treatment regimens for type 2 diabetes mellitus in a large observational database. [ABSTRACT FROM AUTHOR]

Master protocol designs are often proposed to improve the efficiency of drug development with multiple subgroups. In the basket trial design, different subgroups can have similar biological pathogenesis pathways. Hence, a target therapy can result in similar responses. A good information sharing strategy between different subgroups can potentially improve the efficiency of evaluating treatment efficacy. In traditional hierarchical models, based on the exchangeability assumption, all subgroups are placed into the same sharing pool for cross subgroup information sharing. However, due to the heterogeneity between subgroups, there can be large differences in drug efficacy. Under such cases, strong borrowing across all subgroups is not suitable and no borrowing can be inefficient, because the treatment effect is analyzed in each subgroup separately. We propose a Bayesian cluster hierarchical model (BCHM) to improve the operating characteristics of estimating the treatment effect in multiple subgroups in basket trials. Bayesian nonparametric method is applied to dynamically calculate the number of clusters by conducting a multiple cluster classification based on subgroup outcomes. A hierarchical model is used to compute the posterior probability of the treatment effect, with the borrowing strength determined by the Bayesian nonparametric clustering and the similarities between subgroups. We apply the BCHM to clinical trials with binary endpoints. For treatment effect estimation, the BCHM yields lower mean squared error values, when compared to the independent analyses. In scenarios with a heterogeneous treatment effect, the BCHM provides lower mean squared error values compared to traditional hierarchical models. In addition, we can construct a loss function to optimize the design parameters. BCHM provides a balanced approach and smart borrowing, which yields better results in assessing the treatment effect in different scenarios compared to other conventional methods. [ABSTRACT FROM AUTHOR]

Matching on an estimated propensity score is frequently used to estimate the effects of treatments from observational data. Since the 1970s, different authors have proposed methods to combine matching at the design stage with regression adjustment at the analysis stage when estimating treatment effects for continuous outcomes. Previous work has consistently shown that the combination has generally superior statistical properties than either method by itself. In biomedical and epidemiological research, survival or time-to-event outcomes are common. We propose a method to combine regression adjustment and propensity score matching to estimate survival curves and hazard ratios based on estimating an imputed potential outcome under control for each successfully matched treated subject, which is accomplished using either an accelerated failure time parametric survival model or a Cox proportional hazard model that is fit to the matched control subjects. That is, a fitted model is then applied to the matched treated subjects to allow simulation of the missing potential outcome under control for each treated subject. Conventional survival analyses (e.g., estimation of survival curves and hazard ratios) can then be conducted using the observed outcome under treatment and the imputed outcome under control. We evaluated the repeated-sampling bias of the proposed methods using simulations. When using nearest neighbor matching, the proposed method resulted in decreased bias compared to crude analyses in the matched sample. We illustrate the method in an example prescribing beta-blockers at hospital discharge to patients hospitalized with heart failure. [ABSTRACT FROM AUTHOR]

The use of a quantitative treatment selection marker to choose between two treatment options requires the estimate of an optimal threshold above which one of these two treatments is preferred. Herein, the optimal threshold expression is based on the definition of a utility function which aims to quantify the expected utility of the population (e.g. life expectancy, quality of life) by taking into account both efficacy (success or failure) and toxicity of each treatment option. Therefore, the optimal threshold is the marker value that maximizes the expected utility of the population. A method modelling the marker distribution in patient subgroups defined by the received treatment and the outcome is proposed to calculate the parameters of the utility function so as to estimate the optimal threshold and its 95% credible interval using the Bayesian inference. The simulation study found that the method had low bias and coverage probability close to 95% in multiple settings, but also the need of large sample size to estimate the optimal threshold in some settings. The method is then applied to the PETACC-8 trial that compares the efficacy of chemotherapy with a combined chemotherapy + anti-epidermal growth factor receptor in stage III colorectal cancer. [ABSTRACT FROM AUTHOR]

In multi-arm adaptive trials, several treatments are assessed simultaneously and accumulating data are used to inform decisions about the trial, such as whether treatments are dropped or continued. Different methodological approaches have been developed for such trials and research has compared the performance of different subsets of these. One particular approach, for which we use the acronym MAMS(R), has generally not been included in these comparisons because control of the family-wise error rate (FWER) could not be guaranteed. Recently, the MAMS(R) approach has been extended to facilitate the generation of efficient designs which strongly control the FWER. We consider multi-arm two-stage trials with binary outcomes and propose parameterising treatment effects using the log odds ratio. We conduct a simulation study comparing the extended MAMS(R) framework with the well-established combination method both for trials where a different outcome is used for mid-trial analysis and for trials where the same outcome is used throughout. We show how the MAMS(R) framework compares favourably only in scenarios where the same outcome is used. We propose a hybrid selection rule within MAMS(R) methodology and demonstrate that this makes it possible to use the MAMS(R) framework in trials incorporating comparative treatment selection. [ABSTRACT FROM AUTHOR]

Prediction intervals are commonly used in meta-analysis with random-effects models. One widely used method, the Higgins-Thompson-Spiegelhalter prediction interval, replaces the heterogeneity parameter with its point estimate, but its validity strongly depends on a large sample approximation. This is a weakness in meta-analyses with few studies. We propose an alternative based on bootstrap and show by simulations that its coverage is close to the nominal level, unlike the Higgins-Thompson-Spiegelhalter method and its extensions. The proposed method was applied in three meta-analyses. [ABSTRACT FROM AUTHOR]

Researchers are increasingly using complex population-based sample surveys to estimate the effects of treatments, exposures and interventions. In such analyses, statistical methods are essential to minimize the effect of confounding due to measured covariates, as treated subjects frequently differ from control subjects. Methods based on the propensity score are increasingly popular. Minimal research has been conducted on how to implement propensity score matching when using data from complex sample surveys. We used Monte Carlo simulations to examine two critical issues when implementing propensity score matching with such data. First, we examined how the propensity score model should be formulated. We considered three different formulations depending on whether or not a weighted regression model was used to estimate the propensity score and whether or not the survey weights were included in the propensity score model as an additional covariate. Second, we examined whether matched control subjects should retain their natural survey weight or whether they should inherit the survey weight of the treated subject to which they were matched. Our results were inconclusive with respect to which method of estimating the propensity score model was preferable. In general, greater balance in measured baseline covariates and decreased bias was observed when natural retained weights were used compared to when inherited weights were used. We also demonstrated that bootstrap-based methods performed well for estimating the variance of treatment effects when outcomes are binary. We illustrated the application of our methods by using the Canadian Community Health Survey to estimate the effect of educational attainment on lifetime prevalence of mood or anxiety disorders. [ABSTRACT FROM AUTHOR]

In most medical research, treatment effectiveness is assessed using the average treatment effect or some version of subgroup analysis. The practice of individualized or precision medicine, however, requires new approaches that predict how an individual will respond to treatment, rather than relying on aggregate measures of effect. In this study, we present a conceptual framework for estimating individual treatment effects, referred to as predicted individual treatment effects. We first apply the predicted individual treatment effect approach to a randomized controlled trial designed to improve behavioral and physical symptoms. Despite trivial average effects of the intervention, we show substantial heterogeneity in predicted individual treatment response using the predicted individual treatment effect approach. The predicted individual treatment effects can be used to predict individuals for whom the intervention may be most effective (or harmful). Next, we conduct a Monte Carlo simulation study to evaluate the accuracy of predicted individual treatment effects. We compare the performance of two methods used to obtain predictions: multiple imputation and non-parametric random decision trees. Results showed that, on average, both predictive methods produced accurate estimates at the individual level; however, the random decision trees tended to underestimate the predicted individual treatment effect for people at the extreme and showed more variability in predictions across repetitions compared to the imputation approach. Limitations and future directions are discussed. [ABSTRACT FROM AUTHOR]

Heterogeneity in treatment efficacy is a major concern in clinical trials. Clustering may help to identify the treatment responders and the non-responders. In the context of longitudinal cluster analyses, sample size and variability of the times of measurements are the main issues with the current methods. Here, we propose a new two-step method for the Clustering of Longitudinal data by using an Extended Baseline. The first step relies on a piecewise linear mixed model for repeated measurements with a treatment-time interaction. The second step clusters the random predictions and considers several parametric (model-based) and non-parametric (partitioning, ascendant hierarchical clustering) algorithms. A simulation study compares all options of the clustering of longitudinal data by using an extended baseline method with the latent-class mixed model. The clustering of longitudinal data by using an extended baseline method with the two model-based algorithms was the more robust model. The clustering of longitudinal data by using an extended baseline method with all the non-parametric algorithms failed when there were unequal variances of treatment effect between clusters or when the subgroups had unbalanced sample sizes. The latent-class mixed model failed when the between-patients slope variability is high. Two real data sets on neurodegenerative disease and on obesity illustrate the clustering of longitudinal data by using an extended baseline method and show how clustering may help to identify the marker(s) of the treatment response. The application of the clustering of longitudinal data by using an extended baseline method in exploratory analysis as the first stage before setting up stratified designs can provide a better estimation of treatment effect in future clinical trials. [ABSTRACT FROM AUTHOR]

We introduce an automated method of record linkage that has two key features, automated selection of match field interactions to include in the model for estimation and automated threshold determination for classifying record pairs to matches or non-matches. We applied our method to two real-world examples. The first example demonstrated results consistent with our earlier work: When data quality is adequate and the match field discriminating power is high, matching algorithms exhibit similar performance. The second example demonstrated that our method yields a lower false positive rate and higher positive predictive value than the Fellegi-Sunter model in the face of low data quality. When compared to the Fellegi-Sunter model, simulation studies suggest that our method exhibits better overall performance as indicated by higher area under the curve, and less biased estimates for both the match prevalence rate and the m- and u-probabilities over a range of data scenarios, especially when the match prevalence is extreme. Computationally, our method is as efficient as the Fellegi-Sunter model. We recommend this method in situations that an unsupervised linking algorithm is needed. [ABSTRACT FROM AUTHOR]

Outlier detection covers the wide range of methods aiming at identifying observations that are considered unusual. Novelty detection, on the other hand, seeks observations among newly generated test data that are exceptional compared with previously observed training data. In many applications, the general existence of novelty is of more interest than identifying the individual novel observations. For instance, in high-throughput cancer treatment screening experiments, it is meaningful to test whether any new treatment effects are seen compared with existing compounds. Here, we present hypothesis tests for such global level novelty. The problem is approached through a set of very general assumptions, making it innovative in relation to the current literature. We introduce test statistics capable of detecting novelty. They operate on local neighborhoods and their null distribution is obtained by the permutation principle. We show that they are valid and able to find different types of novelty, e.g. location and scale alternatives. The performance of the methods is assessed with simulations and with applications to real data sets. [ABSTRACT FROM AUTHOR]

Background/aims: Bone mass density values have been related with risk of vertebral fractures in post-menopausal women. However, bone mass density is not perfectly accurate in predicting risk of fracture, which decreases its usefulness as a surrogate in clinical trials. We propose a modeling framework with three interconnected parts to improve the evaluation of bone mass density accuracy in forecasting fractures after treatment.Methods: The modeling framework includes: (1) a piecewise regression to describe non-linear temporal BMD changes more accurately than crude percent changes, (2) a structural equation model to analyze interdependencies among vertebral fractures and their potential risk factors in preference to regression techniques that consider only directional associations, and (3) a counterfactual causal interpretation of the direct and indirect relationships between treatment and occurrence of vertebral fractures. We apply the methods to BMD repeated measurements from a study of the effect of bazedoxifene acetate on incident vertebral fractures in three different geographical regions.Results: We made four observations: (1) bone mass density changes varied largely across participants, (2) baseline age and body mass index influenced baseline bone mass density that, in turn, had an effect on prevalent fractures, (3) direct and/or indirect effects of bazedoxifene acetate on incident fractures were different across regions, and (4) estimates of indirect effects were sensible to the presence of post-treatment unmeasured confounders. In one region, around 40% of the bazedoxifene acetate effect on the occurrence of fracture is explained by its effect on bone mass density. Under the counterfactual approach, these 40% represent the average difference in the occurrence of fracture observed for untreated individuals when their bone mass density values are set at the value under bazedoxifene acetate versus under placebo.Conclusions: Computational methods are available to evaluate and interpret the surrogacytic capability of a biomarker of a primary outcome. [ABSTRACT FROM AUTHOR]

Mendelian randomisation is an epidemiological method for estimating causal associations from observational data by using genetic variants as instrumental variables. Typically the genetic variants explain only a small proportion of the variation in the risk factor of interest, and so large sample sizes are required, necessitating data from multiple sources. Meta-analysis based on individual patient data requires synthesis of studies which differ in many aspects. A proposed Bayesian framework is able to estimate a causal effect from each study, and combine these using a hierarchical model. The method is illustrated for data on C-reactive protein and coronary heart disease (CHD) from the C-reactive protein CHD Genetics Collaboration (CCGC). Studies from the CCGC differ in terms of the genetic variants measured, the study design (prospective or retrospective, population-based or case-control), whether C-reactive protein was measured, the time of C-reactive protein measurement (pre- or post-disease), and whether full or tabular data were shared. We show how these data can be combined in an efficient way to give a single estimate of causal association based on the totality of the data available. Compared to a two-stage analysis, the Bayesian method is able to incorporate data on 23% additional participants and 51% more events, leading to a 23-26% gain in efficiency. [ABSTRACT FROM AUTHOR]

Ordered categorical data are frequently encountered in clinical studies. A popular method for comparing the efficacy of treatments is to use logistic regression with the proportional odds assumption. The test statistic is based on the Wilcoxon-Mann-Whitney test. However, the proportional odds assumption may not be appropriate. In such cases, the probability of rejecting the null hypothesis is much inflated even though the treatments have the same mean efficacy. An alternative approach that does not rely on the proportional odds assumption is to conceptualize the responses as manifestations of some underlying continuous variables. However, statistical procedures were developed only for the comparison of two treatments. In this article, we derive testing procedures that compare several treatments to a control, utilizing a latent normal distribution with the latent variable model. The proposed procedure is useful because multiple comparisons with a control is very frequently an objective of a clinical study. Data from clinical trials are used to illustrate the proposed procedures. [ABSTRACT FROM AUTHOR]

The observation of time to tumour progression (TTP) or progression-free survival (PFS) may be terminated by a terminal event. In this context, deaths may be due to tumour progression, and the time to the major failure event (death) may be correlated with the TTP. The usual assumption of independence between the TTP process and death, required by many commonly used statistical methods, can be violated. Furthermore, although the relationship between TTP and time to death is most relevant to the anti-cancer drug development or to evaluation of TTP as a surrogate endpoint, statistical models that try to describe the dependence structure between these two characteristics are not frequently used. We propose a joint frailty model for the analysis of two survival endpoints, TTP and time to death, or PFS and time to death, in the context of data clustering (e.g. at the centre or trial level). This approach allows us to simultaneously evaluate the prognostic effects of covariates on the two survival endpoints, while accounting both for the relationship between the outcomes and for data clustering. We show how a maximum penalized likelihood estimation can be applied to a nonparametric estimation of the continuous hazard functions in a general joint frailty model with right censoring and delayed entry. The model was motivated by a large meta-analysis of randomized trials for head and neck cancers (Meta-Analysis of Chemotherapy in Head and Neck Cancers), in which the efficacy of chemotherapy on TTP or PFS and overall survival was investigated, as adjunct to surgery or radiotherapy or both. [ABSTRACT FROM AUTHOR]

We propose a fully parametric model for the analysis of competing risks data where the types of failure may not be independent. We show how the dependence between the cause-specific survival times can be modelled with a copula function. Features include: identifiability of the problem; accessible understanding of the dependence structures; and flexibility in choosing marginal survival functions. The model is constructed in such a way that it allows us to adjust for concomitant variables and for a dependence parameter to assess the effects of these on each marginal survival model and on the relationship between the causes of death. The methods are applied to a prostate cancer data set. We find that, with the copula model, more accurate inferences are obtained than with the use of a simpler model such as the independent competing risks approach. [ABSTRACT FROM AUTHOR]