Nonparametric Estimation of a Recurrent Survival Function

Benefits of plerixafor for mobilization of peripheral blood stem cells prior to autologous transplantation: a dual-center retrospective cohort study

BACKGROUND AIMS

Before autologous stem cell transplantation (ASCT), hematopoietic stem cells must be stimulated to move from the bone marrow to the peripheral blood for harvesting. Plerixafor, a C-X-C chemokine receptor type 4 antagonist, is used to increase stem cell harvests. However, the effects of plerixafor on post-ASCT outcomes remain unclear.

METHODS

In a dual-center retrospective cohort study of 43 Japanese patients who received ASCT, the authors compared transplantation outcomes in patients who underwent stem cell mobilization with granulocyte colony-stimulating factor with (n = 25) or without (n = 18) plerixafor.

RESULTS

The number of days to neutrophil and platelet engraftment was significantly shorter with plerixafor than without plerixafor, as assessed by univariate (neutrophil, P = 0.004, platelet, P = 0.002), subgroup, propensity score matching and inverse probability weighting analyses. Although the cumulative incidence of fever was comparable with or without plerixafor (P = 0.31), that of sepsis was significantly lower with plerixafor than without (P < 0.01). Thus, the present data indicate that plerixafor leads to earlier neutrophil and platelet engraftment and a reduction of infectious risk.

CONCLUSIONS

The authors conclude that plerixafor may be safe to use and that it reduces the risk of infection in patients with a low CD34+ cell count the day before apheresis.

Significance of Omitting Day 11 Mini-Dose Methotrexate for GVHD Prophylaxis After Unrelated Bone Marrow Transplantation

The combination of calcineurin inhibitors and short-term methotrexate has been used as a standard graft-versus-host-disease (GVHD) prophylaxis in allogeneic hematopoietic stem cell transplantation. Mini-dose methotrexate (mini-MTX), consisting of 5 mg/m²/d on days 1, 3, 6, and 11, is occasionally selected as an alternative considering toxicity. The significance of day 11 administration remains unclear. We performed a retrospective study of 135 cases of unrelated bone marrow transplantation at our institute between 2006 and 2019 and compared the outcomes between day 11 MTX dose omitted (n = 72) and full-doses of mini-MTX (n = 63). In total cohort, the 4-year overall survival (OS) was 58.7 %, and the omitted group showed poor GVHD/relapse-free-survival (P = .01) with comparable OS (P = .11) and relapse-free survival (P = .11). Human leukocyte antigen (HLA) mismatch is a major risk factor for severe GVHD. We analyzed the impact of omitting day 11 MTX in 2 cohorts from HLA matched or mismatched donors. In both cohorts, the omitted group had a higher risk of severe acute and chronic GVHD. In conclusion, the omission of day 11 MTX was associated with a higher risk of severe GVHD. Therefore the omission of the day 11 dose is not recommended.

BivRec: an R package for the nonparametric and semiparametric analysis of bivariate alternating recurrent events

Background

Bivariate alternating recurrent event data can arise in longitudinal studies where patients with chronic diseases go through two states that occur repeatedly, e.g., care periods and break periods. However, there was no statistical software that provided tools for the analysis of such data. To meet this software need, we developed BivRec, a package for R that contains a set of tools for exploratory, nonparametric and semiparametric regression analysis of bivariate alternating recurrent events.

Results

The BivRec package provides functions for nonparametric estimations for the joint distribution of bivariate gap times (bivrecNP) and semiparametric regression methods for evaluating covariate effects on the two types of gap times under the accelerated failure time model framework (bivrecReg). The package also provides exploratory data analysis tools such as a visualization of the gap times by groups. We utilize a subset of the South Verona Psychiatric Case Register (PCR) data to illustrate the use of the BivRec package for the reviewed methods.

Conclusions

We demonstrate BivRec’s capability for data visualization, nonparametric and regression based analysis, as well as data simulation. The package has default methods with satisfactory performance despite the complexity of calculations and fills a gap in software for statistical analysis of bivariate alternating recurrent events. BivRec is accessible under the GPL-3 General Public License through CRAN, facilitating its installation.

A varying-coefficient model for gap times between recurrent events

Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however, gap times between recurrent events are of natural interest and moreover the effects may actually vary over time. In this article, we propose a marginal varying-coefficient model for gap times between recurrent events that allows for the intra-individual correlation between events. Estimation and inference procedures are developed for the varying coefficients. Consistency and weak convergence of the proposed estimator are established. Monte Carlo simulation studies demonstrate that the proposed method works well with practical sample sizes. The proposed method is illustrated with an analysis of bladder tumor clinical data.

The semiparametric accelerated trend-renewal process for recurrent event data

Recurrent event data arise in many biomedical longitudinal studies when health-related events can occur repeatedly for each subject during the follow-up time. In this article, we examine the gap times between recurrent events. We propose a new semiparametric accelerated gap time model based on the trend-renewal process which contains trend and renewal components that allow for the intensity function to vary between successive events. We use the Buckley-James imputation approach to deal with censored transformed gap times. The proposed estimators are shown to be consistent and asymptotically normal. Model diagnostic plots of residuals and a method for predicting number of recurrent events given specified covariates and follow-up time are also presented. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to two real data sets.

Polypill with or without Aspirin in Persons without Cardiovascular Disease

BACKGROUND

A polypill comprising statins, multiple blood-pressure-lowering drugs, and aspirin has been proposed to reduce the risk of cardiovascular disease.

METHODS

Using a 2-by-2-by-2 factorial design, we randomly assigned participants without cardiovascular disease who had an elevated INTERHEART Risk Score to receive a polypill (containing 40 mg of simvastatin, 100 mg of atenolol, 25 mg of hydrochlorothiazide, and 10 mg of ramipril) or placebo daily, aspirin (75 mg) or placebo daily, and vitamin D or placebo monthly. We report here the outcomes for the polypill alone as compared with matching placebo, for aspirin alone as compared with matching placebo, and for the polypill plus aspirin as compared with double placebo. For the polypill-alone and polypill-plus-aspirin comparisons, the primary outcome was death from cardiovascular causes, myocardial infarction, stroke, resuscitated cardiac arrest, heart failure, or revascularization. For the aspirin comparison, the primary outcome was death from cardiovascular causes, myocardial infarction, or stroke. Safety was also assessed.

RESULTS

A total of 5713 participants underwent randomization, and the mean follow-up was 4.6 years. The low-density lipoprotein cholesterol level was lower by approximately 19 mg per deciliter and systolic blood pressure was lower by approximately 5.8 mm Hg with the polypill and with combination therapy than with placebo. The primary outcome for the polypill comparison occurred in 126 participants (4.4%) in the polypill group and in 157 (5.5%) in the placebo group (hazard ratio, 0.79; 95% confidence interval [CI], 0.63 to 1.00). The primary outcome for the aspirin comparison occurred in 116 participants (4.1%) in the aspirin group and in 134 (4.7%) in the placebo group (hazard ratio, 0.86; 95% CI, 0.67 to 1.10). The primary outcome for the polypill-plus-aspirin comparison occurred in 59 participants (4.1%) in the combined-treatment group and in 83 (5.8%) in the double-placebo group (hazard ratio, 0.69; 95% CI, 0.50 to 0.97). The incidence of hypotension or dizziness was higher in groups that received the polypill than in their respective placebo groups.

CONCLUSIONS

Combined treatment with a polypill plus aspirin led to a lower incidence of cardiovascular events than did placebo among participants without cardiovascular disease who were at intermediate cardiovascular risk. (Funded by the Wellcome Trust and others; TIPS-3 ClinicalTrials.gov number, NCT01646437.).

SEMIPARAMETRIC REGRESSION MODEL FOR RECURRENT BACTERIAL INFECTIONS AFTER HEMATOPOIETIC STEM CELL TRANSPLANTATION

Patients who undergo hematopoietic stem cell transplantation (HSCT) often experience multiple bacterial infections during the early post-transplant period. In this article, we consider a semiparametric regression model that correlates patient- and transplant-related risk factors with inter-infection gap times. Existing regression methods for recurrent gap times are not directly applicable to study post-transplant infection because the initiating event (transplant) is different than the recurrent events of interest (post-transplant infections); as a result, the time from transplant to the first infection and the time elapsed between consecutive infections have distinct biological meanings and hence follow different distributions. Moreover, risk factors may have different effects on these two types of gap times. We propose a semiparametric estimation procedure to evaluate the covariate effects on time from transplant to thefirst infection and on gap times between consecutive infections simultaneously. The proposed estimator accounts for dependent censoring induced by within-subject correlation among recurrent gap times and length bias in the last censored gap time due to intercept sampling. We study the finite sample properties through simulations and present an application of the proposed method to the post-HSCT bacterial infection data collected at the University of Minnesota.

A Class of Additive Transformation Models for Recurrent Gap Times

The gap time between recurrent events is often of primary interest in many fields such as medical studies (Cook and Lawless 2007; Kang, Sun, and Zhao 2015; Schaubel and Cai 2004), and in this paper, we discuss regression analysis of the gap times arising from a general class of additive transformation models. For the problem, we propose two estimation procedures, the modified within-cluster resampling (MWCR) method and the weighted risk-set (WRS) method, and the proposed estimators are shown to be consistent and asymptotically follow the normal distribution. In particular, the estimators have closed forms and can be easily determined, and the methods have the advantage of leaving the correlation among gap times arbitrary. A simulation study is conducted for assessing the finite sample performance of the presented methods and suggests that they work well in practical situations. Also the methods are applied to a set of real data from a chronic granulomatous disease (CGD) clinical trial.

Limited value of routine follow-up visits in chronic lymphocytic leukemia managed initially by watch and wait: A North Denmark population-based study

INTRODUCTION

The majority of newly diagnosed chronic lymphocytic leukemia (CLL) patients are followed initially by watch and wait (WAW). Clinical practice varies and the value of frequent follow-up visits remains unclear. Thus, in this study we investigated the clinical value of follow-up visits for patients with CLL.

METHODS

We collected data from diagnosis and follow-up visits for patients diagnosed with CLL and managed by WAW in the North Denmark Region between 2007-2014. High- and low-risk group patients were determined by Binet stage, IgVH status, and cytogenetics at diagnosis. The effect of risk group allocation on the probability of receiving CLL-directed treatment within two years was included in a multivariable logistic regression model adjusted for age and blood test results.

RESULTS

273 patients were included in the study with a median follow-up of 3 years (IQR: 1.6-5.4). Overall, the median interval between follow-up visits was 98 days (95% CI: 96-100) (high-risk patients: 91 days [95% CI: 86-95] vs. low-risk patients: 105 days [95% CI: 100-110]). Among 2,312 follow-up visits, only 387 (17%) were associated with interventions. At the following time points: 6 months, 1 year, and 1.5 years, patients with low-risk CLL had significantly lower odds of initiating treatment compared to patients with high-risk CLL.

CONCLUSION

WAW plays an important role in managing CLL. Interventions at follow-up visits were infrequent and low-risk patients had significantly lower risk of treatment initiation. We question the value of routine follow-up in CLL in the absence of changes in symptoms and/or blood test results.

Induced smoothing for rank-based regression with recurrent gap time data

Various semiparametric regression models have recently been proposed for the analysis of gap times between consecutive recurrent events. Among them, the semiparametric accelerated failure time (AFT) model is especially appealing owing to its direct interpretation of covariate effects on the gap times. In general, estimation of the semiparametric AFT model is challenging because the rank-based estimating function is a nonsmooth step function. As a result, solutions to the estimating equations do not necessarily exist. Moreover, the popular resampling-based variance estimation for the AFT model requires solving rank-based estimating equations repeatedly and hence can be computationally cumbersome and unstable. In this paper, we extend the induced smoothing approach to the AFT model for recurrent gap time data. Our proposed smooth estimating function permits the application of standard numerical methods for both the regression coefficients estimation and the standard error estimation. Large-sample properties and an asymptotic variance estimator are provided for the proposed method. Simulation studies show that the proposed method outperforms the existing nonsmooth rank-based estimating function methods in both point estimation and variance estimation. The proposed method is applied to the data analysis of repeated hospitalizations for patients in the Danish Psychiatric Center Register.

Semiparametric regression analysis for alternating recurrent event data

Alternating recurrent event data arise frequently in clinical and epidemiologic studies, where 2 types of events such as hospital admission and discharge occur alternately over time. The 2 alternating states defined by these recurrent events could each carry important and distinct information about a patient's underlying health condition and/or the quality of care. In this paper, we propose a semiparametric method for evaluating covariate effects on the 2 alternating states jointly. The proposed methodology accounts for the dependence among the alternating states as well as the heterogeneity across patients via a frailty with unspecified distribution. Moreover, the estimation procedure, which is based on smooth estimating equations, not only properly addresses challenges such as induced dependent censoring and intercept sampling bias commonly confronted in serial event gap time data but also is more computationally tractable than the existing rank-based methods. The proposed methods are evaluated by simulation studies and illustrated by analyzing psychiatric contacts from the South Verona Psychiatric Case Register.

Methods for Contrasting Gap Time Hazard Functions: Application to Repeat Liver Transplantation

In studies featuring a sequence of ordered events, gap times between successive events are often of interest. Despite the rich literature in this area, very few methods for comparing gap times have been developed. We propose methods for estimating a hazard ratio connecting the first and second gap times. Specifically, a two-stage procedure is developed based on estimating equations. At the first stage, a proportional hazards model is fitted for the first gap time. Weighted estimating equations are then solved at the second stage to estimate the hazard ratio between the first and second gap times. The proposed estimator has a closed form and, being analogous to a standardized mortality ratio, is easy to interpret. Large sample properties of the proposed estimators are derived, with simulation studies used to evaluate finite sample characteristics. Extension of the approach to accommodate a piecewise constant hazard ratio is considered. The proposed methods are applied to contrast repeat (second) versus primary (first) liver transplants with respect to graft failure, based on national registry data.

Alternating event processes during lifetimes: population dynamics and statistical inference

In the literature studying recurrent event data, a large amount of work has been focused on univariate recurrent event processes where the occurrence of each event is treated as a single point in time. There are many applications, however, in which univariate recurrent events are insufficient to characterize the feature of the process because patients experience nontrivial durations associated with each event. This results in an alternating event process where the disease status of a patient alternates between exacerbations and remissions. In this paper, we consider the dynamics of a chronic disease and its associated exacerbation-remission process over two time scales: calendar time and time-since-onset. In particular, over calendar time, we explore population dynamics and the relationship between incidence, prevalence and duration for such alternating event processes. We provide nonparametric estimation techniques for characteristic quantities of the process. In some settings, exacerbation processes are observed from an onset time until death; to account for the relationship between the survival and alternating event processes, nonparametric approaches are developed for estimating exacerbation process over lifetime. By understanding the population dynamics and within-process structure, the paper provide a new and general way to study alternating event processes.

A gap time model based on a multiplicative marginal rate function that accounts for zero-recurrence units

In this article, we propose an alternative gap time model based on a multiplicative marginal rate function, which is formulated considering each gap time conditional on the previous recurrence times. In this formulation, the gap times are treated equally and the relation between successive events is no longer a problem. Furthermore, this article considers the inclusion of a proportion of zero-recurrence units (for which the event of interest will not occur) into the model to analyze recurrent event data. Inference aspects of the proposed model are discussed through maximum likelihood approach. A simulation study is carried out to examine the performance of the estimation procedure. The model is applied to hospital readmission data among colorectal cancer patients.

Additive mixed effect model for recurrent gap time data

Gap times between recurrent events are often of primary interest in medical and observational studies. The additive hazards model, focusing on risk differences rather than risk ratios, has been widely used in practice. However, the marginal additive hazards model does not take the dependence among gap times into account. In this paper, we propose an additive mixed effect model to analyze gap time data, and the proposed model includes a subject-specific random effect to account for the dependence among the gap times. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The finite sample behavior of the proposed methods is evaluated through simulation studies, and an application to a data set from a clinic study on chronic granulomatous disease is provided.

Nonparametric inference for the joint distribution of recurrent marked variables and recurrent survival time

Time between recurrent medical events may be correlated with the cost incurred at each event. As a result, it may be of interest to describe the relationship between recurrent events and recurrent medical costs by estimating a joint distribution. In this paper, we propose a nonparametric estimator for the joint distribution of recurrent events and recurrent medical costs in right-censored data. We also derive the asymptotic variance of our estimator, a test for equality of recurrent marker distributions, and present simulation studies to demonstrate the performance of our point and variance estimators. Our estimator is shown to perform well for a wide range of levels of correlation, demonstrating that our estimators can be employed in a variety of situations when the correlation structure may be unknown in advance. We apply our methods to hospitalization events and their corresponding costs in the second Multicenter Automatic Defibrillator Implantation Trial (MADIT-II), which was a randomized clinical trial studying the effect of implantable cardioverter-defibrillators in preventing ventricular arrhythmia.

Gender differences in the duration of non-work-related sickness absence episodes due to musculoskeletal disorders

BACKGROUND

There is wide evidence that women present longer duration of sickness absence (SA) than men. Musculoskeletal disorders are influenced by gender due to the sexual division of work.

METHODS

354 432 episodes of non-work-related SA due to musculoskeletal disorders, which were registered in Catalonia between 2005 and 2008, were selected. The outcome variable was the duration of SA. Frailty survival models, stratified by sex and adjusted for explanatory variables (age, employment status, case management, economic activity and repeated episode), were fitted to study the association between each variable and the duration of SA, obtaining HRs.

RESULTS

Women presented longer SA episodes than men in all variable categories. A trend from shorter to longer duration of SA with increasing age was observed in men, whereas in women, it had a fluctuating pattern. Analysing most frequent diagnostic subgroups from the sample, only 'non-specific lumbago' and 'sciatic lumbago' showed these age patterns. Frailty survival models applied to these 2 subgroups confirmed the described age patterns in SA duration.

CONCLUSIONS

Women have longer non-work-related SA due to musculoskeletal disorders than men. However, while men have longer absences as their age increases, in women some older groups have shorter absences than younger ones. These findings could be explained by gender differences in the interaction between paid work and family demands. Our results highlight the need for continued research on SA from a gender perspective, in order to improve management of SA in terms of clinical practice and public policies.

Nonparametric methods for analyzing recurrent gap time data with application to infections after hematopoietic cell transplant

Infection is one of the most common complications after hematopoietic cell transplantation. Many patients experience infectious complications repeatedly after transplant. Existing statistical methods for recurrent gap time data typically assume that patients are enrolled due to the occurrence of an event of interest, and subsequently experience recurrent events of the same type; moreover, for one-sample estimation, the gap times between consecutive events are usually assumed to be identically distributed. Applying these methods to analyze the post-transplant infection data will inevitably lead to incorrect inferential results because the time from transplant to the first infection has a different biological meaning than the gap times between consecutive recurrent infections. Some unbiased yet inefficient methods include univariate survival analysis methods based on data from the first infection or bivariate serial event data methods based on the first and second infections. In this article, we propose a nonparametric estimator of the joint distribution of time from transplant to the first infection and the gap times between consecutive infections. The proposed estimator takes into account the potentially different distributions of the two types of gap times and better uses the recurrent infection data. Asymptotic properties of the proposed estimators are established.

Semiparametric methods to contrast gap time survival functions: Application to repeat kidney transplantation

Times between successive events (i.e., gap times) are of great importance in survival analysis. Although many methods exist for estimating covariate effects on gap times, very few existing methods allow for comparisons between gap times themselves. Motivated by the comparison of primary and repeat transplantation, our interest is specifically in contrasting the gap time survival functions and their integration (restricted mean gap time). Two major challenges in gap time analysis are non-identifiability of the marginal distributions and the existence of dependent censoring (for all but the first gap time). We use Cox regression to estimate the (conditional) survival distributions of each gap time (given the previous gap times). Combining fitted survival functions based on those models, along with multiple imputation applied to censored gap times, we then contrast the first and second gap times with respect to average survival and restricted mean lifetime. Large-sample properties are derived, with simulation studies carried out to evaluate finite-sample performance. We apply the proposed methods to kidney transplant data obtained from a national organ transplant registry. Mean 10-year graft survival of the primary transplant is significantly greater than that of the repeat transplant, by 3.9 months (p=0.023), a result that may lack clinical importance.

Nonparametric estimation of the survival function for ordered multivariate failure time data: A comparative study

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions, and the conditional distribution of gap times. In this work, we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a dataset from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

Identifying Some Risk Factors of Time to Relapses in Schizophrenic Patients using Bayesian Approach with Event-Dependent Frailty Model

OBJECTIVES

Schizophrenia patients often experience relapses once and even more with no limit on number of relapses. The time among relapses are rarely considered in studies. The aim of this study was to identify some risk factors of time to elapses in schizophrenic patients with recurrent events model in survival analysis.

METHODS

In a retrospective longitudinal study, the medical records of 159 schizophrenic patients who referred to Razi hospital in Tehran from 2003 to 2005 were conveniently sampled, investigated and followed until the end of 2009. The time to recurrent relapses were considered in weeks. The patients with at least one relapse in this duration were included in the study. Event-dependent frailty model, using Bayesian approach, was applied to fit the data and identify the risk factors of time to relapses.

RESULTS

In this recurrent failure time model, the effects of age of onset (95% CI = (0.058, 0.086)), gender (95% CI = (0.146, 0.686)), marital status (95% CI = (0.475, 0.965)) and family history (95% CI = (0.115, 0.543)) were significant on the hazard time to relapses. According to the credible interval of frailty variance, elapsed time to relapse is dependent on patients' characteristics (95% CI = (0.084, 0.369)). Subsequent relapses are likely to be influenced by the occurrence of the first relapse, too (95% CI = (2.504, 3.079)), with decreasing hazard of time to relapse.

CONCLUSIONS

Subsequent relapses are likely dependent on the first and previous relapses. Age of onset, gender, marital status and family history are important risk factors influencing hazard of time to relapses. More studies are required to clear out the effect of other covariates with this model.

Marginal semiparametric multivariate accelerated failure time model with generalized estimating equations

The semiparametric accelerated failure time (AFT) model is not as widely used as the Cox relative risk model due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations for censored data provide promising tools to make the AFT models more attractive in practice. For multivariate AFT models, we propose a generalized estimating equations (GEE) approach, extending the GEE to censored data. The consistency of the regression coefficient estimator is robust to misspecification of working covariance, and the efficiency is higher when the working covariance structure is closer to the truth. The marginal error distributions and regression coefficients are allowed to be unique for each margin or partially shared across margins as needed. The initial estimator is a rank-based estimator with Gehan's weight, but obtained from an induced smoothing approach with computational ease. The resulting estimator is consistent and asymptotically normal, with variance estimated through a multiplier resampling method. In a large scale simulation study, our estimator was up to three times as efficient as the estimateor that ignores the within-cluster dependence, especially when the within-cluster dependence was strong. The methods were applied to the bivariate failure times data from a diabetic retinopathy study.

Sojourning with the Homogeneous Poisson Process

In this pedagogical article, distributional properties, some surprising, pertaining to the homogeneous Poisson process (HPP), when observed over a possibly random window, are presented. Properties of the gap-time that covered the termination time and the correlations among gap-times of the observed events are obtained. Inference procedures, such as estimation and model validation, based on event occurrence data over the observation window, are also presented. We envision that through the results in this paper, a better appreciation of the subtleties involved in the modeling and analysis of recurrent events data will ensue, since the HPP is arguably one of the simplest among recurrent event models. In addition, the use of the theorem of total probability, Bayes theorem, the iterated rules of expectation, variance and covariance, and the renewal equation could be illustrative when teaching distribution theory, mathematical statistics, and stochastic processes at both the undergraduate and graduate levels. This article is targeted towards both instructors and students.

Nonparametric Comparison for Multivariate Panel Count Data

Multivariate panel count data often occur when there exist several related recurrent events or response variables defined by occurrences of related events. For univariate panel count data, several nonparametric treatment comparison procedures have been developed. However, it does not seem to exist a nonparametric procedure for multivariate cases. Based on differences between estimated mean functions, this paper proposes a class of nonparametric test procedures for multivariate panel count data. The asymptotic distribution of the new test statistics is established and a simulation study is conducted. Also the new procedures are applied to a skin cancer problem that motivated this study.

Quantile regression for recurrent gap time data

Evaluating covariate effects on gap times between successive recurrent events is of interest in many medical and public health studies. While most existing methods for recurrent gap time analysis focus on modeling the hazard function of gap times, a direct interpretation of the covariate effects on the gap times is not available through these methods. In this article, we consider quantile regression that can provide direct assessment of covariate effects on the quantiles of the gap time distribution. Following the spirit of the weighted risk-set method by Luo and Huang (2011, Statistics in Medicine 30, 301-311), we extend the martingale-based estimating equation method considered by Peng and Huang (2008, Journal of the American Statistical Association 103, 637-649) for univariate survival data to analyze recurrent gap time data. The proposed estimation procedure can be easily implemented in existing software for univariate censored quantile regression. Uniform consistency and weak convergence of the proposed estimators are established. Monte Carlo studies demonstrate the effectiveness of the proposed method. An application to data from the Danish Psychiatric Central Register is presented to illustrate the methods developed in this article.

Semiparametric Estimation with Recurrent Event Data under Informative Monitoring

Consider a study where the times of occurrences of a recurrent event for n units are monitored. For the ith unit, T(i1), T(i2), …, denote the successive event interoccurrence times and this unit is monitored over a random period [0, τ(i)] with τ(i) independent of the T(ij)s. Over this monitoring period, [Formula: see text] is the random number of event occurrences. The T(ij)s are independent and identically distributed (IID) from an unknown continuous distribution function F and the τ(i)s are IID from a distribution function G. A generalized Koziol-Green (GKG) structure wherein 1-G = (1-F)(β) for some β > 0 is assumed. Under this model, Nelson-Aalen and product-limit type estimators of Λ = -log(1-F) and F are obtained, as well as an estimator of β. Asymptotic and small-sample properties of these estimators are obtained and the estimator of F is compared to the fully nonparametric estimator in Peña et al. (2001) in terms of their finite-sample and asymptotic efficiency. The performance of the estimators of F are also examined when the GKG structure does not hold through a simulation study.