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.

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.

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.

Nonparametric analysis of doubly truncated and interval-censored data.

In epidemiological studies, it is easier to collect data only from individuals whose failure events are within a calendar time interval, the so-called interval sampling, which leads to doubly truncated data. In many situations, the calendar time of the failure event can only be recorded within time intervals, leading to doubly truncated and interval censored (DTIC) data. Firstly, we point out that although the existing methods for DTIC data work adequately under the sampling scheme (Scheme 1) for doubly truncated data, Scheme 1 is not realistic for DTIC data. Secondly, we consider a commonly used sampling scheme (Scheme 2) , under which the individuals are included in the sample based on diagnosis date. We point out that under Scheme 2, due to violation of assumptions for Scheme 1, the NPMLE of the cumulative distribution function is severely biased if the likelihood function for Scheme 1 is used. To overcome this difficulty, we define a target population, under which a sampling scheme (Scheme 3) can be implemented such that appropriate truncation variables can be defined and the NPMLE of the cumulative distribution function can be obtained using the expectation-maximization algorithm. We also consider estimation of the joint distribution function for successive duration times. Using the imputed first failure times based on the NPMLE from Scheme 3, we then obtain the imputed right censored data of the second failure event. Based on the imputed data, we propose a nonparametric estimator of the joint distribution function using the inverse-probability-weighted approach. Simulation studies demonstrate that the proposed method performs well with moderate sample sizes.

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.

Cost-effectiveness of freeze-all policy - A retrospective study based upon the outcome of cumulative live births.

OBJECT: We have previously reported that cumulative live birth rates (CLBRs) are higher in the freeze-all group compared with controls (64.3% vs. 45.8%, p = 0.001). Here, we aim to determine if the freeze-all policy is more cost-effective than fresh embryo transfer followed by frozen-thawed embryo transfer (FET). MATERIALS AND METHODS: The analysis consisted of 704 ART (Assisted reproductive technology) cycles, which included in IVF (In vitro fertilisation) and ICSI (Intra Cytoplasmic Sperm Injection) cycles performed in Taichung Veterans General Hospital, Taiwan between January 2012 and June 2014. The freeze-all group involved 84 patients and the fresh Group 625 patients. Patients were followed up until all embryos obtained from a single controlled ovarian hyper-stimulation cycle were used up, or a live birth had been achieved. The total cost related to treatment of each patient was recorded. The incremental cost-effectiveness ratio (ICER) was based on the incremental cost per couple and the incremental live birth rate of the freeze-all strategy compared with the fresh ET strategy. Probabilistic sensitivity analysis (PSA) and a cost-effectiveness acceptability curve (CEAC) were performed. RESULTS: The total treatment cost per patient was significantly higher for the freeze-all group than in the fresh group (USD 3419.93 ± 638.13 vs. $2920.59 ± 711.08 p < 0.001). However, the total treatment cost per live birth in the freeze-all group was US $5319.89, vs. US $6382.42 in the fresh group. CEAC show that the freeze-all policy was a cost-effective treatment at a threshold of US $2703.57 for one additional live birth. Considering the Willingness-to-pay threshold per live birth, the probability was 60.1% at the threshold of US $2896.5, with the freeze-all group being more cost-effective than the fresh-ET group; or 90.1% at the threshold of $4183.8. CONCLUSION: The freeze-all policy is a cost-effective treatment, as long as the additional cost of US $2703.57 per additional live birth is financially acceptable for the subjects.

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.

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.

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.

One-year outcomes of a suture-less laparoscopic sacral hysteropexy using polypropylene Y-mesh grafts and fibrin sealant spray: A prospective comparative study.

BACKGROUND: Laparoscopic sacral hysteropexy (SH) is a minimally invasive and effective treatment for uterovaginal prolapse in women who wish to retain the uterus. However, this procedure is limited by a steep learning curve and a long operating time. In this study, we aim to evaluate the surgical outcomes of a modified laparoscopic SH procedure using innovative methods of vaginal mesh attachment, which we hypothesized to be equally effective and time-saving. METHODS: This was a prospective, parallel, comparative study conducted at a tertiary referral hospital. A total of 34 women with advanced (POPQ [Pelvic Organ Prolapse Quantification] stages ≧ 2) uterine prolapse, who underwent a laparoscopic SH procedure using lightweight polypropylene Y-mesh grafts (ALYTE), were studied. In half (n = 17) of the cases, fibrin sealant spray (TISSEEL) was applied to the meshes fixed at the anterior and posterior vaginal wall with fewer (six vs at least ten) sutures. A detailed comparison of one-year outcomes between groups was performed. RESULTS: Patient characteristics and perioperative results were comparable between groups with the exception of a significantly shorter total operating time (247.0 vs 292.9 minutes, p = 0.04) noted in the fibrin group. At 1 year, anatomic success (POPQ stage ≦1) rates (76.5% vs 76.5%) were not different between groups. There were eight patients, with four in each group, who had surgical failure. Notably, most (7/8; 87.5%) surgical failures were at the anterior compartment (i.e, recurrent cystocele). No vaginal mesh extrusions were noted. After statistical analysis, we found "cystocele as the dominant prolapse before operation" was a significant predisposing factor for prolapse recurrence (p = 0.019; odds ratio = 8.04). CONCLUSION: The modified laparoscopic SH procedure using Y-mesh grafts and fibrin sealant spray with fewer vaginal sutures was equally effective as conventional methods but saved time. Laparoscopic SH using Y-mesh grafts might not be as effective in repairing a concomitant dominant cystocele.

Hyaluronic acid improves pain symptoms more than bladder storage symptoms in women with interstitial cystitis.

OBJECTIVE: Intravesical hyaluronic acid (HA) therapy is one of acceptable methods to treat bladder pain and storage symptoms (i.e., urgency, frequency and nocturia) of interstitial cystitis/bladder pain syndrome (IC/BPS). We aim to assess the impacts of intravesical HA on bladder pain and storage symptoms, respectively, and to investigate their associated factors in patients with IC/BPS. MATERIALS AND METHODS: In this prospective, multicenter study, 103 women with refractory IC/BPS undergoing a standard protocol of intravesical HA therapy were enrolled. A pain Visual Analog Scale (VAS) and the Interstitial Cystitis Symptom and Problem Index (ICSI & ICPI) were used to assess symptoms and bother associated with IC/BPS. The Scaled Global Response Assessment (GRA) was used to evaluate patients' perception of overall changes in bladder pain and storage symptoms, respectively, after treatment. RESULTS: Mean age of participants was 43.6 ± 11.8 years. The average duration of symptoms was 5.1 ± 5.0 years. Significant improvements in pain VAS, ICSI and ICPI scores were observed after treatment. However, patients reported significantly different rates of moderate/marked improvement in bladder pain and storage symptoms (73.8% vs. 47.6%; P < 0.001) on the GRA, respectively. "Lower pain VAS score" and "reduced functional bladder capacity" were found to be the factors that adversely affected the treatment responses of bladder pain and storage symptoms, respectively, after repeated statistical analyses. CONCLUSION: Bladder instillation of HA seemed more efficient in improving bladder pain than storage symptoms associated with IC/BPS. The persistence of bladder storage symptoms after treatment might result from a reduced functional bladder capacity.

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.