Bayesian phase II adaptive randomization by jointly modeling efficacy and toxicity as time-to-event outcomes.

The main goals of Phase II trials are to identify the therapeutic efficacy of new treatments and continue monitoring all the possible adverse effects. In Phase II trials, it is important to develop an adaptive randomization (AR) procedure that takes into account both the efficacy and toxicity. In most existing articles, toxicity is modeled as a binary endpoint through an unobservable random effect (frailty) to link the efficacy and toxicity. However, this approach does not capture toxicity profiles that evolve over time. In this article, we propose a new Bayesian adaptive randomization (BAR) procedure using the covariate-adjusted efficacy-toxicity ratio (ETR) index, where efficacy and toxicity are jointly modelled as time-to-event (TTE) outcomes. Furthermore, we also propose early stopping rules for toxicity and futility such that inferior treatments can be dropped at earlier time of trial. Simulation results show that compared to the BAR procedures based solely on the efficacy and that based on TTE efficacy and binary toxicity outcomes, the proposed BAR procedure can better identify the difference in treatment toxicity such that it can assign more patients to the superior treatment arm under some scenarios.

The mean residual life model for the right-censored data in the presence of covariate measurement errors.

In this article, we consider the mean residual life regression model in the presence of covariate measurement errors. In the whole cohort, the surrogate variable of the error-prone covariate is available for each subject, while the instrumental variable (IV), which is related to the underlying true covariates, is measured only for some subjects, the calibration sample. Without specifying distributions of measurement errors but assuming that the IV is missing at random, we develop two estimation methods, the IV calibration and cohort estimators, for the regression parameters by solving estimation equations (EEs) based on the calibration sample and cohort sample, respectively. To improve estimation efficiency, a synthetic estimator is derived by applying the generalized method of moment for all EEs. The large sample properties of the proposed estimators are established and their finite sample performance are evaluated via simulation studies. Simulation results show that the cohort and synthetic estimators outperform the IV calibration estimator and the relative efficiency of the cohort and synthetic estimators mainly depends on the missing rate of IV. In the case of low missing rate, the synthetic estimator is more efficient than the cohort estimator, while the result can be reversed when the missing rate is high. We illustrate the proposed method by application to data from the patients with stage 5 chronic kidney disease in Taiwan.

A robust association test with multiple genetic variants and covariates.

Due to the advancement of genome sequencing techniques, a great stride has been made in exome sequencing such that the association study between disease and genetic variants has become feasible. Some powerful and well-known association tests have been proposed to test the association between a group of genes and the disease of interest. However, some challenges still remain, in particular, many factors can affect the performance of testing power, e.g., the sample size, the number of causal and non-causal variants, and direction of the effect of causal variants. Recently, a powerful test, called TREM , is derived based on a random effects model. TREM has the advantages of being less sensitive to the inclusion of non-causal rare variants or low effect common variants or the presence of missing genotypes. However, the testing power of TREM can be low when a portion of causal variants has effects in opposite directions. To improve the drawback of TREM , we propose a novel test, called TROB , which keeps the advantages of TREM and is more robust than TREM in terms of having adequate power in the case of variants with opposite directions of effect. Simulation results show that TROB has a stable type I error rate and outperforms TREM when the proportion of risk variants decreases to a certain level and its advantage over TREM increases as the proportion decreases. Furthermore, TROB outperforms several other competing tests in most scenarios. The proposed methodology is illustrated using the Shanghai Breast Cancer Study.

Equivalence tests before end of follow-up under the class of log transformation model.

One important topic in clinical trials is to show that the effects of new and standard treatments are equivalent in terms of clinical relevance. In literature, many equivalence tests based on the maximal difference between two survival functions for the two treatments over the whole time axis have been proposed. However, since survival times can only be observed until the end of follow-up, an equivalence test should be based on a comparison only in the observed time-window dictated by the end of follow-up. In this article, under the class of log transformation model, we propose an asymptotical α-level equivalence test for the difference between two survival functions that only addresses equivalence until the end of follow-up. We demonstrate that the hypothesis of equivalence of two survival functions before the end of follow-up can be formulated as interval-based hypothesis testing which involves the treatment effect parameter. Simulation results indicate that when sample size is sufficiently large the proposed test controls the type I error effectively and performs well at detecting the equivalence. The proposed test is applied to a dataset from veteran's administration lung cancer trial.

Equivalence tests under the Cox-Aalen model and the partly Aalen model.

For the equivalence trial with survivor outcomes from two treatment groups, the most popular testing procedure is the test proposed by under the proportional hazards (PH) model. In this article, when the treatment effect is time invariant, we demonstrate that the result under the PH model can be extended to the Cox-Aalen model. When the treatment effect is time-variant, we propose an equivalent test for the differences of two cumulative hazard functions under the partly Aalen model. Simulation studies show that the proposed tests perform well in finite samples. We illustrate the proposed tests using bladder cancer data and the primary biliary cirrhosis (PBC) data.

Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction.

Left-truncated data are often encountered in epidemiological cohort studies, where individuals are recruited according to a certain cross-sectional sampling criterion. Length-biased data, a special case of left-truncated data, assume that the incidence of the initial event follows a homogeneous Poisson process. In this article, we consider an analysis of length-biased and interval-censored data with a nonsusceptible fraction. We first point out the importance of a well-defined target population, which depends on the prior knowledge for the support of the failure times of susceptible individuals. Given the target population, we proceed with a length-biased sampling and draw valid inferences from a length-biased sample. When there is no covariate, we show that it suffices to consider a discrete version of the survival function for the susceptible individuals with jump points at the left endpoints of the censoring intervals when maximizing the full likelihood function, and propose an EM algorithm to obtain the nonparametric maximum likelihood estimates of nonsusceptible rate and the survival function of the susceptible individuals. We also develop a novel graphical method for assessing the stationarity assumption. When covariates are present, we consider the Cox proportional hazards model for the survival time of the susceptible individuals and the logistic regression model for the probability of being susceptible. We construct the full likelihood function and obtain the nonparametric maximum likelihood estimates of the regression parameters by employing the EM algorithm. The large sample properties of the estimates are established. The performance of the method is assessed by simulations. The proposed model and method are applied to data from an early-onset diabetes mellitus study.

Tests for equivalence of two survival functions: alternatives to the PH and PO models.

For the equivalence trial with survivor outcomes from two treatment groups, the most popular testing procedure is the extension of log-rank test under proportional hazards (PH) model. In literature, an alternative test has been proposed under the  proportional odds (PO) survival model. In practice, both PH and PO hazards assumptions can be violated. One alternative is the log transformation model other than the PH or PO models. Another alternative model is the partly Aalen's additive risk model which allows the influence of some covariates to vary over time. In this article, we propose equivalence tests for the difference of two survival functions under the class of log transformation model and that of two cumulative hazard functions under the partly Aalen's model. Simulation studies demonstrate that the proposed tests perform well in finite samples.

Semiparametric mixture cure model analysis with competing risks data: Application to vascular access thrombosis data.

The article is motivated by a nephrology study in Taiwan, which enrolled hemodialysis patients who suffered from vascular access thrombosis. After treatment, some patients were cured of thrombosis, while some may experience recurrence of either type (acute or nonacute) of vascular access thrombosis. Our major interest is to estimate the cumulative incidence probability of time to the first recurrence of acute thrombosis after therapy. Since the occurrence of one type of vascular access thrombosis precludes occurrence of the other type, patients are subject to competing risks. To account for the presence of competing risks and cured patients, we develop a mixture model approach to the regression analysis of competing-risks data with a cure fraction. We make inference about the effects of factors on both the cure rate and cumulative incidence function (CIF) for a failure of interest, which are separately specified in the logistic regression model and semiparametric regression model with time-varying and time-invariant effects. Based on two-stage method, we develop novel estimation equations using the inverse probability censoring weight techniques. The asymptotic properties of the estimators are rigorously studied and the plug-in variance estimators can be obtained for constructing interval estimators. We also propose a lack-of-fit test for assessing the adequacy of the proposed model and several tests for time-varying effects. The simulation studies and vascular access thrombosis data analysis are conducted to illustrate the proposed method.

Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation.

It is well known that the nonparametric maximum likelihood estimator (NPMLE) can severely underestimate the survival probabilities at early times for left-truncated and interval-censored (LT-IC) data. For arbitrarily truncated and censored data, Pan and Chappel (JAMA Stat Probab Lett 38:49-57, 1998a, Biometrics 54:1053-1060, 1998b) proposed a nonparametric estimator of the survival function, called the iterative Nelson estimator (INE). Their simulation study showed that the INE performed well in overcoming the under-estimation of the survival function from the NPMLE for LT-IC data. In this article, we revisit the problem of inconsistency of the NPMLE. We point out that the inconsistency is caused by the likelihood function of the left-censored observations, where the left-truncated variables are used as the left endpoints of censoring intervals. This can lead to severe underestimation of the survival function if the NPMLE is obtained using Turnbull's (JAMA 38:290-295, 1976) EM algorithm. To overcome this problem, we propose a modified maximum likelihood estimator (MMLE) based on a modified likelihood function, where the left endpoints of censoring intervals for left-censored observations are the maximum of left-truncated variables and the estimated left endpoint of the support of the left-censored times. Simulation studies show that the MMLE performs well for finite sample and outperforms both the INE and NPMLE.

Correction to: Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation.

The original version of this article unfortunately contains mistakes. It has been corrected with this Correction.

Semiparametric transformation models for interval-censored data in the presence of a cure fraction.

Mixed case interval-censored data arise when the event of interest is known only to occur within an interval induced by a sequence of random examination times. Such data are commonly encountered in disease research with longitudinal follow-up. Furthermore, the medical treatment has progressed over the last decade with an increasing proportion of patients being cured for many types of diseases. Thus, interest has grown in cure models for survival data which hypothesize a certain proportion of subjects in the population are not expected to experience the events of interest. In this article, we consider a two-component mixture cure model for regression analysis of mixed case interval-censored data. The first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric transformation model that describes the distribution of event time for the uncured subjects. We propose semiparametric maximum likelihood estimation for the considered model. We develop an EM type algorithm for obtaining the semiparametric maximum likelihood estimators (SPMLE) of regression parameters and establish their consistency, efficiency, and asymptotic normality. Extensive simulation studies indicate that the SPMLE performs satisfactorily in a wide variety of settings. The proposed method is illustrated by the analysis of the hypobaric decompression sickness data from National Aeronautics and Space Administration.

Factors that affect outcomes of prolapse repair using single-incision vaginal mesh procedures.

AIMS: Single-incision vaginal mesh (SIVM) procedures for pelvic organ prolapse (POP) differed in mesh fabrication and implantation that may affect treatment outcomes. We aim to evaluate and compare the safety and effectiveness of two SIVM procedures, and explore factors that may have associations with surgical effectiveness. METHODS: Our data of using two SIVM procedures for a total (anterior and posterior) vaginal mesh repair were studied. Patients who had ≧stage 2 POP and underwent either Elevate (n = 85) using anchored, lightweight meshes or Prosima procedures (n = 95) using non-anchored, original meshes were assessed. A detailed comparison of 1 year outcomes was made. RESULTS: Of the 180 patients, 172 (95.6%) attended the 1-year follow-up. Demographic data were similar between groups except a higher average age (64.5 vs 60.4, P = 0.001) was noted in the Elevate (n = 84) group compared to the Prosima (n = 88) group. Surgical results were also similar except a significantly higher objective cure (POP stage ≦1) rate (89.3% vs 78.4%, P = 0.042) was noted in the Elevate group. The safety profile favored Elevate with a lower, but not statistically significant, rate (4.7% vs 12.5%, P = 0.106) of vaginal mesh exposure. After a statistical analysis, we found anatomic recurrence (POP stage ≧2) after the SIVM procedures had strong (P < 0.05) associations with "early surgical cases," "Prosima procedure," "advanced cystocele (Ba > +3 cm)," and "prior prolapse repair," respectively. CONCLUSIONS: Beyond a learning curve, Elevate performed better than Prosima in POP repair regarding surgical effectiveness. Meanwhile, several predisposing factors that may affect recurrence after SIVM procedures were found.

Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data.

Left-truncated data often arise in epidemiology and individual follow-up studies due to a biased sampling plan since subjects with shorter survival times tend to be excluded from the sample. Moreover, the survival time of recruited subjects are often subject to right censoring. In this article, a general class of semiparametric transformation models that include proportional hazards model and proportional odds model as special cases is studied for the analysis of left-truncated and right-censored data. We propose a conditional likelihood approach and develop the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of these models. The derived score equations for regression parameter and infinite-dimensional function suggest an iterative algorithm for cMLE. The cMLE is shown to be consistent and asymptotically normal. The limiting variances for the estimators can be consistently estimated using the inverse of negative Hessian matrix. Intensive simulation studies are conducted to investigate the performance of the cMLE. An application to the Channing House data is given to illustrate the methodology.

Semiparametric regression analysis of failure time data with dependent interval censoring.

Interval-censored failure-time data arise when subjects are examined or observed periodically such that the failure time of interest is not examined exactly but only known to be bracketed between two adjacent observation times. The commonly used approaches assume that the examination times and the failure time are independent or conditionally independent given covariates. In many practical applications, patients who are already in poor health or have a weak immune system before treatment usually tend to visit physicians more often after treatment than those with better health or immune system. In this situation, the visiting rate is positively correlated with the risk of failure due to the health status, which results in dependent interval-censored data. While some measurable factors affecting health status such as age, gender, and physical symptom can be included in the covariates, some health-related latent variables cannot be observed or measured. To deal with dependent interval censoring involving unobserved latent variable, we characterize the visiting/examination process as recurrent event process and propose a joint frailty model to account for the association of the failure time and visiting process. A shared gamma frailty is incorporated into the Cox model and proportional intensity model for the failure time and visiting process, respectively, in a multiplicative way. We propose a semiparametric maximum likelihood approach for estimating model parameters and show the asymptotic properties, including consistency and weak convergence. Extensive simulation studies are conducted and a data set of bladder cancer is analyzed for illustrative purposes. Copyright © 2017 John Wiley & Sons, Ltd.

A semiparametric mixture cure survival model for left-truncated and right-censored data.

In follow-up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left-truncated and right-censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum-likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput-wall distance event for patients with ankylosing spondylitis.

The partly Aalen's model for recurrent event data with a dependent terminal event.

Recurrent event data are commonly observed in biomedical longitudinal studies. In many instances, there exists a terminal event, which precludes the occurrence of additional repeated events, and usually there is also a nonignorable correlation between the terminal event and recurrent events. In this article, we propose a partly Aalen's additive model with a multiplicative frailty for the rate function of recurrent event process and assume a Cox frailty model for terminal event time. A shared gamma frailty is used to describe the correlation between the two types of events. Consequently, this joint model can provide the information of temporal influence of absolute covariate effects on the rate of recurrent event process, which is usually helpful in the decision-making process for physicians. An estimating equation approach is developed to estimate marginal and association parameters in the joint model. The consistency of the proposed estimator is established. Simulation studies demonstrate that the proposed approach is appropriate for practical use. We apply the proposed method to a peritonitis cohort data set for illustration.

Nonparametric association analysis of bivariate left-truncated competing risks data.

We develop time-varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left-truncated by ages of entry and competing-risk censored by deaths. Two types of association estimators are proposed based on conditional cause-specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections.

Two-stage estimation for multivariate recurrent event data with a dependent terminal event.

Recurrent event data arise in longitudinal follow-up studies, where each subject may experience the same type of events repeatedly. The work in this article is motivated by the data from a study of repeated peritonitis for patients on peritoneal dialysis. Due to the aspects of medicine and cost, the peritonitis cases were classified into two types: Gram-positive and non-Gram-positive peritonitis. Further, since the death and hemodialysis therapy preclude the occurrence of recurrent events, we face multivariate recurrent event data with a dependent terminal event. We propose a flexible marginal model, which has three characteristics: first, we assume marginal proportional hazard and proportional rates models for terminal event time and recurrent event processes, respectively; second, the inter-recurrences dependence and the correlation between the multivariate recurrent event processes and terminal event time are modeled through three multiplicative frailties corresponding to the specified marginal models; third, the rate model with frailties for recurrent events is specified only on the time before the terminal event. We propose a two-stage estimation procedure for estimating unknown parameters. We also establish the consistency of the two-stage estimator. Simulation studies show that the proposed approach is appropriate for practical use. The methodology is applied to the peritonitis cohort data that motivated this study.

Changes in sexual function of women with refractory interstitial cystitis/bladder pain syndrome after intravesical therapy with a hyaluronic acid solution.

INTRODUCTION: Intravesical instillation with a hyaluronic acid (HA) solution is an effective treatment for interstitial cystitis/bladder pain syndrome (IC/BPS), but its impact on sexual functioning of patients is not known. AIM: The aim of this study was to evaluate the changes in sexual function of women with refractory IC/BPS who underwent a second-line intravesical HA therapy. METHODS: A total of 103 women diagnosed with refractory IC/BPS were enrolled in this prospective, multicenter study. Sexual function was evaluated using the short form of the Pelvic Organ Prolapse/Urinary Incontinence Sexual Function Questionnaire (PISQ-9). Bladder-related symptoms and bother were assessed by the Interstitial Cystitis Symptom Index (ICSI) and Interstitial Cystitis Problem Index (ICPI), and a pain visual analog scale (VAS), respectively. Data were analyzed with univariate methods or multivariate logistic regression analysis accordingly. MAIN OUTCOMES MEASURES: Changes in PISQ-9, ICSI, ICPI, and pain VAS scores after treatment were assessed. RESULTS: Mean age and duration of symptoms was 43.6 ± 11.8 and 5.1 ± 5.0 years, respectively. ICSI, ICPI, and pain VAS scores were significantly (P < 0.001) improved after 1 month and 6 months of treatment. Of the 87 (84.5%) sexually active women evaluated, PISQ-9 total scores improved significantly (P < 0.001) from the baseline (mean 18.9 ± 6.4), after 1 month (20.4 ± 5.8), and 6-months (21.5 ± 5.6) of treatment. Significantly improved PISQ-9 items included "dyspareunia" (P < 0.001) and "negative reactions" (P = 0.015) during sexual intercourse, and "intensity" (P < 0.001) of sexual orgasms. After a logistic regression analysis, we found that a baseline PISQ-9 score was negatively correlated with the duration of IC/BPS symptoms (P = 0.022). Meanwhile, the changes in PISQ-9 scores were positively correlated with the reduction in ICSI scores after treatment (P = 0.045). CONCLUSIONS: Intravesical HA is an effective treatment for refractory IC/BPS. A longer duration of IC/BPS symptoms may be a predictor of poor sexual function. However, intravesical HA may improve sexual function along with the reduction of IC/BPS symptoms.