Bayesian semiparametric joint model of multivariate longitudinal and survival data with dependent censoring.

We consider a novel class of semiparametric joint models for multivariate longitudinal and survival data with dependent censoring. In these models, unknown-fashion cumulative baseline hazard functions are fitted by a novel class of penalized-splines (P-splines) with linear constraints. The dependence between the failure time of interest and censoring time is accommodated by a normal transformation model, where both nonparametric marginal survival function and censoring function are transformed to standard normal random variables with bivariate normal joint distribution. Based on a hybrid algorithm together with the Metropolis-Hastings algorithm within the Gibbs sampler, we propose a feasible Bayesian method to simultaneously estimate unknown parameters of interest, and to fit baseline survival and censoring functions. Intensive simulation studies are conducted to assess the performance of the proposed method. The use of the proposed method is also illustrated in the analysis of a data set from the International Breast Cancer Study Group.

Multivariate piecewise joint models with random change-points for skewed-longitudinal and survival data.

Methodological development and application of joint models for longitudinal and time-to-event data have mostly coupled a single longitudinal outcome-based linear mixed-effects model with normal distribution and Cox proportional hazards model. In practice, however, (i) profile of subject's longitudinal response may follow a `broken-stick nonlinear' (piecewise) trajectory. Such multiple phases are an important indicator to help quantify treatment effect, disease diagnosis and clinical decision-making. (ii) Normality in longitudinal models is a routine assumption, but it may be unrealistically obscuring important features of subject variations. (iii) Data collected are often featured by multivariate longitudinal outcomes which are significantly correlated, ignoring their correlation may lead to biased estimation. (iv) It is of importance to investigate how multivariate longitudinal outcomes are associated with event time of interest. In the article, driven by a motivating example, we propose Bayesian multivariate piecewise joint models with a skewed distribution and random change-points for longitudinal measures with an attempt to cope with correlated multivariate longitudinal data, adjust departures from normality, mediate accuracy from longitudinal trajectories with random change-point and tailor linkage in specifying a time-to-event process. A real example is analyzed to demonstrate methodology and simulation studies are conducted to evaluate performance of the proposed models and method.

Bayesian Joint Modeling of Multivariate Longitudinal and Survival Data With an Application to Diabetes Study.

Joint models of longitudinal and time-to-event data have received a lot of attention in epidemiological and clinical research under a linear mixed-effects model with the normal assumption for a single longitudinal outcome and Cox proportional hazards model. However, those model-based analyses may not provide robust inference when longitudinal measurements exhibit skewness and/or heavy tails. In addition, the data collected are often featured by multivariate longitudinal outcomes which are significantly correlated, and ignoring their correlation may lead to biased estimation. Under the umbrella of Bayesian inference, this article introduces multivariate joint (MVJ) models with a skewed distribution for multiple longitudinal exposures in an attempt to cope with correlated multiple longitudinal outcomes, adjust departures from normality, and tailor linkage in specifying a time-to-event process. We develop a Bayesian joint modeling approach to MVJ models that couples a multivariate linear mixed-effects (MLME) model with the skew-normal (SN) distribution and a Cox proportional hazards model. Our proposed models and method are evaluated by simulation studies and are applied to a real example from a diabetes study.

Influence analysis for skew-normal semiparametric joint models of multivariate longitudinal and multivariate survival data.

The normality assumption of measurement error is a widely used distribution in joint models of longitudinal and survival data, but it may lead to unreasonable or even misleading results when longitudinal data reveal skewness feature. This paper proposes a new joint model for multivariate longitudinal and multivariate survival data by incorporating a nonparametric function into the trajectory function and hazard function and assuming that measurement errors in longitudinal measurement models follow a skew-normal distribution. A Monte Carlo Expectation-Maximization (EM) algorithm together with the penalized-splines technique and the Metropolis-Hastings algorithm within the Gibbs sampler is developed to estimate parameters and nonparametric functions in the considered joint models. Case deletion diagnostic measures are proposed to identify the potential influential observations, and an extended local influence method is presented to assess local influence of minor perturbations. Simulation studies and a real example from a clinical trial are presented to illustrate the proposed methodologies. Copyright © 2017 John Wiley & Sons, Ltd.

Bayesian variable selection and estimation in semiparametric joint models of multivariate longitudinal and survival data.

This paper presents a novel semiparametric joint model for multivariate longitudinal and survival data (SJMLS) by relaxing the normality assumption of the longitudinal outcomes, leaving the baseline hazard functions unspecified and allowing the history of the longitudinal response having an effect on the risk of dropout. Using Bayesian penalized splines to approximate the unspecified baseline hazard function and combining the Gibbs sampler and the Metropolis-Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates in SJMLS. Simulation studies are conducted to investigate the finite sample performance of the proposed techniques. An example from the International Breast Cancer Study Group (IBCSG) is used to illustrate the proposed methodologies.

Confidence intervals construction for difference of two means with incomplete correlated data.

BACKGROUND: Incomplete data often arise in various clinical trials such as crossover trials, equivalence trials, and pre and post-test comparative studies. Various methods have been developed to construct confidence interval (CI) of risk difference or risk ratio for incomplete paired binary data. But, there is little works done on incomplete continuous correlated data. To this end, this manuscript aims to develop several approaches to construct CI of the difference of two means for incomplete continuous correlated data. METHODS: Large sample method, hybrid method, simple Bootstrap-resampling method based on the maximum likelihood estimates (B 1) and Ekbohm's unbiased estimator (B 2), and percentile Bootstrap-resampling method based on the maximum likelihood estimates (B 3) and Ekbohm's unbiased estimator (B 4) are presented to construct CI of the difference of two means for incomplete continuous correlated data. Simulation studies are conducted to evaluate the performance of the proposed CIs in terms of empirical coverage probability, expected interval width, and mesial and distal non-coverage probabilities. RESULTS: Empirical results show that the Bootstrap-resampling-based CIs B 1, B 2, B 4 behave satisfactorily for small to moderate sample sizes in the sense that their coverage probabilities could be well controlled around the pre-specified nominal confidence level and the ratio of their mesial non-coverage probabilities to the non-coverage probabilities could be well controlled in the interval [0.4, 0.6]. CONCLUSIONS: If one would like a CI with the shortest interval width, the Bootstrap-resampling-based CIs B 1 is the optimal choice.

Confidence interval construction for the difference between two correlated proportions with missing observations.

Under the assumption of missing at random, eight confidence intervals (CIs) for the difference between two correlated proportions in the presence of incomplete paired binary data are constructed on the basis of the likelihood ratio statistic, the score statistic, the Wald-type statistic, the hybrid method incorporated with the Wilson score and Agresti-Coull (AC) intervals, and the Bootstrap-resampling method. Extensive simulation studies are conducted to evaluate the performance of the presented CIs in terms of coverage probability and expected interval width. Our empirical results evidence that the Wilson-score-based hybrid CI and the Wald-type CI together with the constrained maximum likelihood estimates perform well for small-to-moderate sample sizes in the sense that (i) their empirical coverage probabilities are quite close to the prespecified confidence level, (ii) their expected interval widths are shorter, and (iii) their ratios of the mesial non-coverage to non-coverage probabilities lie in interval [0.4, 0.6]. An example from a neurological study is used to illustrate the proposed methodologies.

Semiparametric Bayesian inference on skew-normal joint modeling of multivariate longitudinal and survival data.

We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies.

Testing non-inferiority of a new treatment in three-arm clinical trials with binary endpoints.

BACKGROUND: A two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns. Selection of the non-inferiority margin and establishment of assay sensitivity are two major issues in the design, analysis and interpretation for two-arm non-inferiority trials. Alternatively, a three-arm non-inferiority clinical trial including a placebo is usually conducted to assess the assay sensitivity and internal validity of a trial. Recently, some large-sample approaches have been developed to assess the non-inferiority of a new treatment based on the three-arm trial design. However, these methods behave badly with small sample sizes in the three arms. This manuscript aims to develop some reliable small-sample methods to test three-arm non-inferiority. METHODS: Saddlepoint approximation, exact and approximate unconditional, and bootstrap-resampling methods are developed to calculate p-values of the Wald-type, score and likelihood ratio tests. Simulation studies are conducted to evaluate their performance in terms of type I error rate and power. RESULTS: Our empirical results show that the saddlepoint approximation method generally behaves better than the asymptotic method based on the Wald-type test statistic. For small sample sizes, approximate unconditional and bootstrap-resampling methods based on the score test statistic perform better in the sense that their corresponding type I error rates are generally closer to the prespecified nominal level than those of other test procedures. CONCLUSIONS: Both approximate unconditional and bootstrap-resampling test procedures based on the score test statistic are generally recommended for three-arm non-inferiority trials with binary outcomes.

Confidence-interval construction for rate ratio in matched-pair studies with incomplete data.

Matched-pair design is often used in clinical trials to increase the efficiency of establishing equivalence between two treatments with binary outcomes. In this article, we consider such a design based on rate ratio in the presence of incomplete data. The rate ratio is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials. In this article, we propose 10 confidence-interval estimators for the rate ratio in incomplete matched-pair designs. A hybrid method that recovers variance estimates required for the rate ratio from the confidence limits for single proportions is proposed. It is noteworthy that confidence intervals based on this hybrid method have closed-form solution. The performance of the proposed confidence intervals is evaluated with respect to their exact coverage probability, expected confidence interval width, and distal and mesial noncoverage probability. The results show that the hybrid Agresti-Coull confidence interval based on Fieller's theorem performs satisfactorily for small to moderate sample sizes. Two real examples from clinical trials are used to illustrate the proposed confidence intervals.

Homogeneity test of difference between two correlated proportions in stratified matched-pair studies.

Stratified matched-pair studies are often designed for adjusting stratification factors in modern medical researches. This article investigates a homogeneity test of differences between two correlated proportions in stratified matched-pair studies. We propose three test procedures, including an asymptotic test, bootstrap test, and multiple comparison procedures, and determine sample size requirements for such tests in a stratified matched-pair study. Simulation studies are conducted to evaluate the performance of the three test procedures and the accuracy of our derived sample size formulas. Empirical results show that (1) the likelihood ratio statistic is robust, while the score statistic and the modified score statistic are conservative in some cases of our considered settings; (2) the likelihood ratio statistic and the score statistic with the bootstrap method and the MaxT procedure behave satisfactorily in the sense that their type I error rates are close to the pre-given significance level; and (3) the derived sample size formulas are rather accurate. A real example from a clinical laboratory study is used to illustrate the proposed methodologies.

Simultaneous confidence intervals of risk differences in stratified paired designs.

In stratified matched-pair studies, risk difference between two proportions is one of the most frequently used indices in comparing efficiency between two treatments or diagnostic tests. This article presents five simultaneous confidence intervals and two bootstrap simultaneous confidence intervals for risk differences in stratified matched-pair designs. The proposed confidence intervals are evaluated with respect to their coverage probabilities, expected widths, and ratios of the mesial noncoverage to noncoverage probability. Empirical results show that (1) hybrid simultaneous confidence intervals outperform nonhybrid simultaneous confidence intervals; (2) hybrid simultaneous confidence intervals based on median estimator outperform those based on maximum likelihood estimator; and (3) hybrid simultaneous confidence intervals incorporated with Wilson score and Agresti coull intervals and the bootstrap t-percentile simultaneous interval based on median unbiased estimators behave satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the prespecified nominal confidence level, and their ratios of the mesial noncoverage to noncoverage probabilities lie in [0.4,0.6] and are hence recommended. Real examples from clinical studies are used to illustrate the proposed methodologies.

Test procedures for disease prevalence with partially validated data.

Investigating the prevalence of a disease is an important topic in medical studies. Such investigations are usually based on the classification results of a group of subjects according to whether they have the disease. To classify subjects, screening tests that are inexpensive and nonintrusive to the test subjects are frequently used to produce results in a timely manner. However, such screening tests may suffer from high levels of misclassification. Although it is often possible to design a gold-standard test or device that is not subject to misclassification, such devices are usually costly and time-consuming, and in some cases intrusive to the test subjects. As a compromise between these two approaches, it is possible to use data that are obtained by the method of double-sampling. In this article, we derive and investigate four test statistics for testing a hypothesis on disease prevalence with double-sampling data. The test statistics are implemented through both the asymptotic method suitable for large samples and approximate unconditional method suitable for small samples. Our simulation results show that the approximate unconditional method usually produces a more satisfactory empirical type I error rate and power than its asymptotic counterpart, especially for small to moderate sample sizes. The results also suggest that the score test and the Wald test based on an estimate of variance with parameters estimated under the null hypothesis outperform the others. An real example is used to illustrate the proposed methods.

Confidence interval construction for proportion ratio in paired studies based on hybrid method.

In this article, we consider confidence interval construction for proportion ratio in paired samples. Previous studies usually reported that score-based confidence intervals consistently outperformed other asymptotic confidence intervals for correlated proportion difference and ratio. However, score-based confidence intervals may not possess closed-form solutions and iterative procedures are therefore required. This article investigates the problem of confidence interval construction for ratio of two correlated proportions based on a hybrid method. Briefly, the hybrid method simply combines two separate confidence intervals for two individual proportions to produce a hybrid confidence interval for the ratio of the two individual proportions in paired studies. Most importantly, confidence intervals based on this hybrid method possess explicit solutions. Our simulation studies indicate that hybrid Wilson score confidence intervals based on Fieller's theorem performs well. The proposed confidence intervals will be illustrated with three real examples.

Homogeneity test of rate ratios in stratified matched-pair studies.

This paper investigates homogeneity test of rate ratios in stratified matched-pair studies on the basis of asymptotic and bootstrap-resampling methods. Based on the efficient score approach, we develop a simple and computationally tractable score test statistic. Several other homogeneity test statistics are also proposed on the basis of the weighted least-squares estimate and logarithmic transformation. Sample size formulae are derived to guarantee a pre-specified power for the proposed tests at the pre-given significance level. Empirical results confirm that (i) the modified score statistic based on the bootstrap-resampling method performs better in the sense that its empirical type I error rate is much closer to the pre-specified nominal level than those of other tests and its power is greater than those of other tests, and is hence recommended, whilst the statistics based on the weighted least-squares estimate and logarithmic transformation are slightly conservative under some of the considered settings; (ii) the derived sample size formulae are rather accurate in the sense that their empirical powers obtained from the estimated sample sizes are very close to the pre-specified nominal powers. A real example is used to illustrate the proposed methodologies.

Testing equality of correlations of two paired binary responses from two treated groups in a randomized trial.

We explore measuring Scleroderma patient disease improvement at the paired body part level and account for their correlation with the long term goal of possibly redefining disease progression using a shorter clinical examination. We propose using a binary outcome to measure disease progression at each paired body part level, construct tests for assessing equality of the correlations between groups for each paired body part and determine sample size requirements for such tests in a two-arm randomized clinical trial. Simulations are performed to evaluate properties of the tests and the accuracy of our sample size formulae. We demonstrate our method with data from a multi-center two-arm randomized clinical trial.

Sample size determination for the non-randomised triangular model for sensitive questions in a survey.

Sample size determination is an essential component in public health survey designs on sensitive topics (e.g. drug abuse, homosexuality, induced abortions and pre or extramarital sex). Recently, non-randomised models have been shown to be an efficient and cost effective design when comparing with randomised response models. However, sample size formulae for such non-randomised designs are not yet available. In this article, we derive sample size formulae for the non-randomised triangular design based on the power analysis approach. We first consider the one-sample problem. Power functions and their corresponding sample size formulae for the one- and two-sided tests based on the large-sample normal approximation are derived. The performance of the sample size formulae is evaluated in terms of (i) the accuracy of the power values based on the estimated sample sizes and (ii) the sample size ratio of the non-randomised triangular design and the design of direct questioning (DDQ). We also numerically compare the sample sizes required for the randomised Warner design with those required for the DDQ and the non-randomised triangular design. Theoretical justification is provided. Furthermore, we extend the one-sample problem to the two-sample problem. An example based on an induced abortion study in Taiwan is presented to illustrate the proposed methods.

Asymptotic confidence interval construction for proportion difference in medical studies with bilateral data.

Bilateral dichotomous data are very common in modern medical comparative studies (e.g. comparison of two treatments in ophthalmologic, orthopaedic and otolaryngologic studies) in which information involving paired organs (e.g. eyes, ears and hips) is available from each subject. In this article, we study various confidence interval estimators for proportion difference based on Wald-type statistics, Fieller theorem, likelihood ratio statistic, score statistics and bootstrap resampling method under the dependence or/and independence models for bilateral binary data. Performance is evaluated with respect to the coverage probability and expected width via simulation studies. Our empirical results show that (1) ignoring the dependence feature of bilateral data could lead to severely incorrect coverage probabilities; and (2) Wald-type, score-type and bootstrap confidence intervals based on the dependence model perform satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the pre-specified nominal confidence level and are hence recommended. A real data from an otolaryngologic study is used to illustrate the proposed methods.

A comparison of methods for the construction of confidence interval for relative risk in stratified matched-pair designs.

A stratified matched-pair study is often designed for adjusting a confounding effect or effect of different trails/centers/ groups in modern medical studies. The relative risk is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials. In this paper, we propose seven confidence interval estimators for the common relative risk and three simultaneous confidence interval estimators for the relative risks in stratified matched-pair designs. The performance of the proposed methods is evaluated with respect to their type I error rates, powers, coverage probabilities, and expected widths. Our empirical results show that the percentile bootstrap confidence interval and bootstrap-resampling-based Bonferroni simultaneous confidence interval behave satisfactorily for small to large sample sizes in the sense that (i) their empirical coverage probabilities can be well controlled around the pre-specified nominal confidence level with reasonably shorter confidence widths; and (ii) the empirical type I error rates of their associated test statistics are generally closer to the pre-specified nominal level with larger powers. They are hence recommended. Two real examples from clinical laboratory studies are used to illustrate the proposed methodologies.

Statistical inference of risk difference in K correlated 2 x 2 tables with structural zero.

K correlated 2 x 2 tables with structural zero are commonly encountered in infectious disease studies. A hypothesis test for risk difference is considered in K independent 2 x 2 tables with structural zero in this paper. Score statistic, likelihood ratio statistic and Wald-type statistic are proposed to test the hypothesis on the basis of stratified data and pooled data. Sample size formulae are derived for controlling a pre-specified power or a pre-determined confidence interval width. Our empirical results show that score statistic and likelihood ratio statistic behave better than Wald-type statistic in terms of type I error rate and coverage probability, sample sizes based on stratified test are smaller than those based on the pooled test in the same design. A real example is used to illustrate the proposed methodologies.