Nonparametric analysis of recurrent events and death

Multivariate recurrent events in the presence of multivariate informative censoring with applications to bleeding and transfusion events in myelodysplastic syndrome

We propose a general novel class of joint models to analyze recurrent events that has a wide variety of applications. The focus in this article is to model the bleeding and transfusion events in myelodysplastic syndrome (MDS) studies, where patients may die or withdraw from the study early due to adverse events or other reasons, such as consent withdrawal or required alternative therapy during the study. The proposed model accommodates multiple recurrent events and multivariate informative censoring through a shared random-effects model. The random-effects model captures both within-subject and within-event dependence simultaneously. We construct the likelihood function for the semiparametric joint model and develop an expectation-maximization (EM) algorithm for inference. The computational burden does not increase with the number of types of recurrent events. We utilize the MDS clinical trial data to illustrate our proposed methodology. We also conduct a number of simulations to examine the performance of the proposed model.

Nonparametric estimation with recurrent competing risks data

Nonparametric estimators of component and system life distributions are developed and presented for situations where recurrent competing risks data from series systems are available. The use of recurrences of components' failures leads to improved efficiencies in statistical inference, thereby leading to resource-efficient experimental or study designs or improved inferences about the distributions governing the event times. Finite and asymptotic properties of the estimators are obtained through simulation studies and analytically. The detrimental impact of parametric model misspecification is also vividly demonstrated, lending credence to the virtue of adopting nonparametric or semiparametric models, especially in biomedical settings. The estimators are illustrated by applying them to a data set pertaining to car repairs for vehicles that were under warranty.

Bayesian Semi-parametric Analysis of Semi-competing Risks Data: Investigating Hospital Readmission after a Pancreatic Cancer Diagnosis

In the U.S., the Centers for Medicare and Medicaid Services uses 30-day readmission, following hospitalization, as a proxy outcome to monitor quality of care. These efforts generally focus on treatable health conditions, such as pneumonia and heart failure. Expanding quality of care systems to monitor conditions for which treatment options are limited or non-existent, such as pancreatic cancer, is challenging because of the non-trivial force of mortality; 30-day mortality for pancreatic cancer is approximately 30%. In the statistical literature, data that arise when the observation of the time to some non-terminal event is subject to some terminal event are referred to as 'semi-competing risks data'. Given such data, scientific interest may lie in at least one of three areas: (i) estimation/inference for regression parameters, (ii) characterization of dependence between the two events, and (iii) prediction given a covariate profile. Existing statistical methods focus almost exclusively on the first of these; methods are sparse or non-existent, however, when interest lies with understanding dependence and performing prediction. In this paper we propose a Bayesian semi-parametric regression framework for analyzing semi-competing risks data that permits the simultaneous investigation of all three of the aforementioned scientific goals. Characterization of the induced posterior and posterior predictive distributions is achieved via an efficient Metropolis-Hastings-Green algorithm, which has been implemented in an R package. The proposed framework is applied to data on 16,051 individuals diagnosed with pancreatic cancer between 2005-2008, obtained from Medicare Part A. We found that increased risk for readmission is associated with a high comorbidity index, a long hospital stay at initial hospitalization, non-white race, male, and discharge to home care.

A dynamic Mover-Stayer model for recurrent event processes subject to resolution

In studies of affective disorder, individuals are often observed to experience recurrent symptomatic exacerbations warranting hospitalization. Interest may lie in modeling the occurrence of such exacerbations over time and identifying associated risk factors. In some patients, recurrent exacerbations are temporally clustered following disease onset, but cease to occur after a period of time. We develop a dynamic Mover-Stayer model in which a canonical binary variable associated with each event indicates whether the underlying disease has resolved. An individual whose disease process has not resolved will experience events following a standard point process model governed by a latent intensity. When the disease process resolves, the complete data intensity becomes zero and no further event will occur. An expectation-maximization algorithm is described for parametric and semiparametric model fitting based on a discrete time dynamic Mover-Stayer model and a latent intensity-based model of the underlying point process.

Optimization of individualized dynamic treatment regimes for recurrent diseases

Patients with cancer or other recurrent diseases may undergo a long process of initial treatment, disease recurrences, and salvage treatments. It is important to optimize the multi-stage treatment sequence in this process to maximally prolong patients' survival. Comparing disease-free survival for each treatment stage over penalizes disease recurrences but under penalizes treatment-related mortalities. Moreover, treatment regimes used in practice are dynamic; that is, the choice of next treatment depends on a patient's responses to previous therapies. In this article, using accelerated failure time models, we develop a method to optimize such dynamic treatment regimes. This method utilizes all the longitudinal data collected during the multi-stage process of disease recurrences and treatments, and identifies the optimal dynamic treatment regime for each individual patient by maximizing his or her expected overall survival. We illustrate the application of this method using data from a study of acute myeloid leukemia, for which the optimal treatment strategies for different patient subgroups are identified.

Effect of rosuvastatin on repeat heart failure hospitalizations: the CORONA Trial (Controlled Rosuvastatin Multinational Trial in Heart Failure)

OBJECTIVES

This study sought to examine the effect of statin therapy hospitalizations for heart failure (HFH) in patients in the CORONA (Controlled Rosuvastatin Multinational Trial in Heart Failure) trial.

BACKGROUND

HFH is an important, frequently recurrent event. Conventional time-to-first event analyses do not take account repeat events. We used a number of statistical approaches to examine the effect of treatment on first and repeat HFH in the CORONA trial.

METHODS

In the CORONA trial, 5,011 patients ≥60 years of age with chronic New York Heart Association functional classes II to IV systolic heart failure resulting from ischemia were randomized to receive rosuvastatin or placebo. Poisson, Andersen-Gill, and negative binomial methods (NB) were used to analyze the effect of rosuvastatin on HFH, and the NB and a parametric joint frailty model (JF) were used to examine this effect while accounting for the competing risk of cardiovascular (CV) death. Rosuvastatin/placebo rate ratios were calculated, both unadjusted and adjusted.

RESULTS

A total of 1,291 patients had 1 or more HFH (750 of these had a single HFH only), and there were a total of 2,408 HFHs. The hazard ratio for the conventional time-to-first event analysis for HFH was 0.91 (95% confidence interval [CI]: 0.82 to 1.02, p = 0.105). In contrast, the NB on repeat hospitalizations gave an unadjusted RR (RR) for HFH of 0.86 (95% CI: 0.75 to 0.99, p = 0.030), adjusted 0.82 (95% CI: 0.72 to 0.92, p = 0.001), and after including CV death as the last event, adjusted RR of 0.85 (95% CI: 0.77 to 0.94, p = 0.001). The JF gave an adjusted RR of 0.82 (95% CI: 0.73 to 0.92, p = 0.001). Similar results were found in analyses of all CV hospitalizations and all-cause hospitalizations.

CONCLUSIONS

When repeat events were included, rosuvastatin was shown to reduce the risk of HFH by approximately 15% to 20%, equating to approximately 76 fewer admissions per 1,000 patients treated over a median 33 months of follow-up. Including repeat events could increase the ability to detect treatment effects in heart failure trials.

Nonparametric tests of treatment effect based on combined endpoints for mortality and recurrent events

Terminal events are commonly combined with other outcomes to improve the power for detecting treatment effects in clinical studies. This manuscript explores novel ways to combine information on terminal and recurrent events in constructing two-sample tests. Existing approaches follow either a time-to-first event analysis approach or a recurrent event modeling approach. Nonparametric recurrent event analyses are often restricted by independence assumptions on gap times between events. Although time-to-first event analyses are not subject to this restriction, they discard information that occurs beyond the initial event and are much less powerful for detecting treatment differences. We develop two new approaches for determining treatment effects, motivated by less restrictive assumptions of time-to-first event analyses that combine information from multiple follow-up intervals. The first testing procedure pools (correlated) short-term τ -restricted outcomes from prespecified intervals starting at times t(k), k = 1, . . . , b, and compares estimated τ -restricted mean survival across treatment groups from this combined dataset. The second procedure calculates conditional τ-restricted means from those at risk at times t(k), k = 1, . . . , b, and compares the area under a function of these by treatment. Variances calculations, taking into account correlation of short-term outcomes within individuals, linearize random components of the test statistics following Woodruff (1971. A simple method for approximating the variance of a complicated estimate. Journal of the American Statistical Association 66, 411-414) and more recently Williams (1995. Product-limit survival functions with correlated survival times. Lifetime Data Analysis 1, 171-186). Simulations compare the finite sample performance of our tests to the robust proportional rates model proposed by Lin and others (2000. Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62(4), 711-730) and the Ghosh and Lin (2000. Non-parametric analysis of recurrent events and death. Biometrics 56(2), 554-562) combined test for recurrent events and death. For different treatment effect patterns the proposed methods perform favorably when compared with existing methods. These new analysis approaches also produce correct type I error rates with correlated gap times between events. New methods are applied to data from a trial of azithromycin in patients with chronic obstructive pulmonary disease.

Analysing recurrent hospitalizations in heart failure: a review of statistical methodology, with application to CHARM-Preserved

AIMS

Heart failure is characterized by recurrent hospitalizations, but often only the first event is considered in clinical trial reports. In chronic diseases, such as heart failure, analysing all events gives a more complete picture of treatment benefit. We describe methods of analysing repeat hospitalizations, and illustrate their value in one major trial.

METHODS AND RESULTS

The Candesartan in Heart failure Assessment of Reduction in Mortality and morbidity (CHARM)-Preserved study compared candesartan with placebo in 3023 patients with heart failure and preserved systolic function. The heart failure hospitalization rates were 12.5 and 8.9 per 100 patient-years in the placebo and candesartan groups, respectively. The repeat hospitalizations were analysed using the Andersen-Gill, Poisson, and negative binomial methods. Death was incorporated into analyses by treating it as an additional event. The win ratio method and a method that jointly models hospitalizations and mortality were also considered. Using repeat events gave larger treatment benefits than time to first event analysis. The negative binomial method for the composite of recurrent heart failure hospitalizations and cardiovascular death gave a rate ratio of 0.75 [95% confidence interval (CI) 0.62-0.91, P = 0.003], whereas the hazard ratio for time to first heart failure hospitalization or cardiovascular death was 0.86 (95% CI 0.74-1.00, P = 0.050).

CONCLUSIONS

In patients with preserved EF, candesartan reduces the rate of admissions for worsening heart failure, to a greater extent than apparent from analysing only first hospitalizations. Recurrent events should be routinely incorporated into the analysis of future clinical trials in heart failure.

Forbidden fruit: on the analysis of recurrent events in randomized clinical trials

The conventional analysis of a typical clinical trial focuses on the time to occurrence of the first among a composite set of alternative events such as death or nonfatal myocardial infarction. Subsequent recurrent events are thereby excluded from consideration to ensure that all the observations were mutually exclusive of each other. Thus, not all events occurring during follow-up will be analyzed. Consequently, some investigators are now reporting additional analyses of previously published trials based on a naive comparison of the total number of events-first events plus recurrent events-and are recommending that these additional analyses be routinely conducted in future trials. We have summarized the potential limitations of this proposal and suggest other methods to analyze recurrent events, with a particular focus on kinetic modeling. The application of this approach to several previously published trials illustrates its facility to help elucidate the causal mechanisms underlying empirical demonstrations of safety and efficacy.

An additive-multiplicative rates model for recurrent event data with informative terminal event

In this article, we propose an additive-multiplicative rates model for recurrent event data in the presence of a terminal event such as death. The association between recurrent and terminal events is nonparametric. For inference on the model parameters, estimating equation approaches are developed, and the asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.

Statistical analysis of mixed recurrent event data with application to cancer survivor study

Event history studies occur in many fields including economics, medical studies, and social science. In such studies concerning some recurrent events, two types of data have been extensively discussed in the literature. One is recurrent event data that arise if study subjects are monitored or observed continuously. In this case, the observed information provides the times of all occurrences of the recurrent events of interest. The other is panel count data, which occur if the subjects are monitored or observed only periodically. This can happen if the continuous observation is too expensive or not practical, and in this case, only the numbers of occurrences of the events between subsequent observation times are available. In this paper, we discuss a third type of data, which is a mixture of recurrent event and panel count data and for which there exists little literature. For regression analysis of such data, we present a marginal mean model and propose an estimating equation-based approach for estimation of regression parameters. We conduct a simulation study to assess the finite sample performance of the proposed methodology, and the results indicate that it works well for practical situations. Finally, we apply it to a motivating study on childhood cancer survivors.

Semiparametric additive marginal regression models for multiple type recurrent events

Recurrent event data are often encountered in biomedical research, for example, recurrent infections or recurrent hospitalizations for patients after renal transplant. In many studies, there are more than one type of events of interest. Cai and Schaube (Lifetime Data Anal 10:121-138, 2004) advocated a proportional marginal rate model for multiple type recurrent event data. In this paper, we propose a general additive marginal rate regression model. Estimating equations approach is used to obtain the estimators of regression coefficients and baseline rate function. We prove the consistency and asymptotic normality of the proposed estimators. The finite sample properties of our estimators are demonstrated by simulations. The proposed methods are applied to the India renal transplant study to examine risk factors for bacterial, fungal and viral infections.

Analysis of multi-stage treatments for recurrent diseases

Patients with a non-curable disease such as many types of cancer usually go through the process of initial treatment, a various number of disease recurrences and salvage treatments, and eventually death. The analysis of the effects of initial and salvage treatments on overall survival is not trivial. One may try to use disease recurrences and salvage treatments as time-dependent covariates in a Cox proportional hazards model. However, because disease recurrence is an intermediate outcome between initial treatment and final survival, the interpretation of such an estimation result is awkward. It does not estimate the causal effects of treatments on overall survival. Nevertheless, such causal effect estimates are critical for treatment decision making. Our approach to address this issue is that, at any treatment stage, for each patient, we compute a potential survival time if he or she would receive the optimal subsequent treatments, and use this potential survival time to do comparison between current-stage treatment groups. This potential survival time is assumed to follow an accelerated failure time model at each treatment stage and calculated by backward induction, starting from the last stage of treatment. By doing that, the effects on survival of different treatments at each stage can be consistently estimated and fairly compared. Under suitable conditions, these estimated effects have a causal interpretation. We evaluated the proposed model and estimation method by simulation studies and illustrated using the motivating, real data set that describes initial and salvage treatments for patients with soft tissue sarcoma.

Treatment patterns for neovascular age-related macular degeneration: analysis of 284 380 medicare beneficiaries

PURPOSE

To examine trends in the treatment of newly diagnosed neovascular age-related macular degeneration (AMD).

DESIGN

Retrospective cohort study.

METHODS

Among 284 380 Medicare beneficiaries with a new diagnosis between 2006 and 2008, we used the cumulative incidence function to estimate procedure rates and the mean frequency function to estimate the cumulative mean number of intravitreous injections. We used Cox log-binomial regression to estimate predictors of the use of vascular endothelial growth factor (VEGF) antagonists within 1 year after diagnosis. Discontinuation of anti-VEGF therapy was defined by absence of treatment for 12 months. Discontinuation rates were calculated using the Kaplan-Meier method.

RESULTS

The proportion of patients receiving anti-VEGF therapy increased from 60.3% to 72.7%, photodynamic therapy decreased from 12.8% to 5.3%, and thermal laser treatment decreased from 5.5% to 3.2%. Black patients (hazard ratio, 0.77; 95% confidence interval, 0.75-0.79) and patients of other/unknown race (0.83; 0.81-0.84) were less likely than white patients to receive anti-VEGF therapy. Patients with dementia were less likely to receive anti-VEGF therapy (0.88; 0.88-0.89). Among patients who received anti-VEGF therapy, the mean number of injections within 1 year of the first injection was 4.3 per treated eye. Anti-VEGF therapy was discontinued in 53.6% of eyes within 1 year, and in 61.7% of eyes within 18 months.

CONCLUSIONS

Treatment of new neovascular AMD changed significantly between 2006 and 2008, most notably in the increasing use of anti-VEGF therapies. However, few patients treated with anti-VEGF medications received monthly injections, and discontinuation rates were high.

Estimation of the mean frequency function for recurrent events when ascertainment of events is delayed

In many large clinical trials there are delays between the time at which events occur and the time at which they are reported. Estimators of the mean frequency function for recurrent events that are currently used are inconsistent in these circumstances. We propose two new estimators to be used when events are reported with delay. One method is a basic inverse probability of censoring weighting approach, while the other explicitly estimates the distribution of the reporting delays. The asymptotic properties of these estimators are discussed and variance estimators are given. We examine the results of simulations comparing the new estimators to each other and to existing estimators that do not properly account for the delays. We also calculate some of these quantities using data from TNT, a clinical trial in which there were delays and events of interest were recurrent.

Semiparametric Transformation Rate Model for Recurrent Event Data

In this article, we propose a class of semiparametric transformation rate models for recurrent event data subject to right-censoring and potentially stopped by a terminating event (e.g., death). These transformation models include both additive rates model and proportional rates model as special cases. Respecting the property that no recurrent events can occur after the terminating event, we model the conditional recurrent event rate given survival. Weighted estimating equations are constructed to estimate the regression coefficients and baseline rate function. In particular, the baseline rate function is approximated by wavelet function. Asymptotic properties of the proposed estimators are derived and a data-dependent criterion is proposed for selecting the most suitable transformation. Simulation studies show that the proposed estimators perform well for practical sample sizes. The proposed methods are used in two real-data examples: a randomized trial of rhDNase and a community trial of Vitamin A.

Characteristics and treatment strategy of hepatic angiomyolipoma: a series of 94 patients collected from four institutions

AIM

To report on a Chinese multicenter series of hepatic angiomyolipoma (HAML) patients and to study the characteristics and the treatment strategy of the disease.

METHOD

Data of 94 patients diagnosed with HAML from four institutions of China between December 1997 and January 2008 were reviewed retrospectively. Immunohistochemical assays were performed on the surgical specimens and follow up studies were done in all the patients.

RESULTS

52 of 94 patients (55.3%) showed no significant clinical symptoms. There were no specific findings on laboratory examinations. The correct preoperative diagnostic rate of ultrasound (US), computed tomography (CT), and magnetic resonance imaging (MRI) was 0% (0/94), 15.7% (11/70) and 22.7% (10/44), respectively. Regarding the treatment, 93 patients had a hepatectomy and 1 patient was treated by radiofrequency ablation. The postoperative pathology showed HAML in all the patients: 69 patients were studied with HMB-45 staining by immunohistochemistry and the positive rate was 100% . The postoperative follow-up rate was 91.5% (86/94), no sign of recurrence or metastasis was observed during the follow-up period.

CONCLUSION

This is the largest HAML series reported in the literature. There are no specific signs and symptoms in HAML patients; the preoperative imaging diagnosis (including CT, MRI) is insensitive. The common pathological features include the basic histological components and expression of HMB-45. Conservative treatment is not suggested; surgical resection should be considered as a treatment choice for HAML.

Calcium Upregulation by Percutaneous Administration of Gene Therapy in Cardiac Disease (CUPID): a phase 2 trial of intracoronary gene therapy of sarcoplasmic reticulum Ca2+-ATPase in patients with advanced heart failure

BACKGROUND

Adeno-associated virus type 1/sarcoplasmic reticulum Ca(2+)-ATPase was assessed in a randomized, double-blind, placebo-controlled, phase 2 study in patients with advanced heart failure.

METHODS AND RESULTS

Thirty-nine patients received intracoronary adeno-associated virus type 1/sarcoplasmic reticulum Ca(2+)-ATPase or placebo. Seven efficacy parameters were assessed in 4 domains: symptoms (New York Heart Association class, Minnesota Living With Heart Failure Questionnaire), functional status (6-minute walk test, peak maximum oxygen consumption), biomarker (N-terminal prohormone brain natriuretic peptide), and left ventricular function/remodeling (left ventricular ejection fraction, left ventricular end-systolic volume), plus clinical outcomes. The primary end point success criteria were prospectively defined as achieving efficacy at 6 months in the group-level (concordant improvement in 7 efficacy parameters and no clinically significant worsening in any parameter), individual-level (total score for predefined clinically meaningful changes in 7 efficacy parameters), or outcome end points (cardiovascular hospitalizations and time to terminal events). Efficacy in 1 analysis had to be associated with at least a positive trend in the other 2 analyses. This combination of requirements resulted in a probability of success by chance alone of 2.7%. The high-dose group versus placebo met the prespecified criteria for success at the group-level, individual-level, and outcome analyses (cardiovascular hospitalizations) at 6 months (confirmed at 12 months) and demonstrated improvement or stabilization in New York Heart Association class, Minnesota Living With Heart Failure Questionnaire, 6-minute walk test, peak maximum oxygen consumption, N-terminal prohormone brain natriuretic peptide levels, and left ventricular end-systolic volume. Significant increases in time to clinical events and decreased frequency of cardiovascular events were observed at 12 months (hazard ratio=0.12; P=0.003), and mean duration of cardiovascular hospitalizations over 12 months was substantially decreased (0.4 versus 4.5 days; P=0.05) on high-dose treatment versus placebo. There were no untoward safety findings.

CONCLUSIONS

The Calcium Upregulation by Percutaneous Administration of Gene Therapy in Cardiac Disease (CUPID) study demonstrated safety and suggested benefit of adeno-associated virus type 1/sarcoplasmic reticulum Ca(2+)-ATPase in advanced heart failure, supporting larger confirmatory trials.

CLINICAL TRIAL REGISTRATION

http://www.clinicaltrials.gov. Unique identifier: NCT00454818.

Inference on the rate ratio of recurrent events for the matched pairs design

As statistical methods for testing the null hypothesis of no difference between two groups for the matched pairs design, the paired-t test, Wilcoxon signed rank sum test and McNemar test are well known. However, there is no simple test for the comparison of incidence rate of recurrent events. This paper proposes a simple statistical method and a sample size formula for the comparison of counts of recurrent events over a specified period of observation under the matched pairs design, where the subject-specific incidence of recurrent events is assumed to follow a time-homogeneous Poisson process. As a special case, the proposed method is found to be virtually equivalent in form to Mantel-Haenszel method for a common rate ratio among the set of stratified tables based on person-time data. The proposed methods are illustrated with the within-arm comparison of data from a clinical trial of 59 epileptics with baseline count data.

Regression analysis of multivariate recurrent event data with a dependent terminal event

Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data, 2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest (Ghosh and Lin, Biometrics 56:554-562, 2000; Wang et al., J Am Stat Assoc 96:1057-1065, 2001; Huang and Wang, J Am Stat Assoc 99:1153-1165, 2004; Ye et al., Biometrics 63:78-87, 2007). In addition, sometimes there may exist more than one type of recurrent events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics 5:129-143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of leukemia patients.

Estimating treatment effects on the marginal recurrent event mean in the presence of a terminating event

In biomedical studies where the event of interest is recurrent (e.g., hospitalization), it is often the case that the recurrent event sequence is subject to being stopped by a terminating event (e.g., death). In comparing treatment options, the marginal recurrent event mean is frequently of interest. One major complication in the recurrent/terminal event setting is that censoring times are not known for subjects observed to die, which renders standard risk set based methods of estimation inapplicable. We propose two semiparametric methods for estimating the difference or ratio of treatment-specific marginal mean numbers of events. The first method involves imputing unobserved censoring times, while the second methods uses inverse probability of censoring weighting. In each case, imbalances in the treatment-specific covariate distributions are adjusted out through inverse probability of treatment weighting. After the imputation and/or weighting, the treatment-specific means (then their difference or ratio) are estimated nonparametrically. Large-sample properties are derived for each of the proposed estimators, with finite sample properties assessed through simulation. The proposed methods are applied to kidney transplant data.

Joint covariate-adjusted score test statistics for recurrent events and a terminal event

Recurrent events data are frequently encountered and could be stopped by a terminal event in clinical trials. It is of interest to assess the treatment efficacy simultaneously with respect to both the recurrent events and the terminal event in many applications. In this paper we propose joint covariate-adjusted score test statistics based on joint models of recurrent events and a terminal event. No assumptions on the functional form of the covariates are needed. Simulation results show that the proposed tests can improve the efficiency over tests based on covariate unadjusted model. The proposed tests are applied to the SOLVD data for illustration.

BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS

Stochastic processes often exhibit sudden systematic changes in pattern a short time before certain failure events. Examples include increase in medical costs before death and decrease in CD4 counts before AIDS diagnosis. To study such terminal behavior of stochastic processes, a natural and direct way is to align the processes using failure events as time origins. This paper studies backward stochastic processes counting time backward from failure events, and proposes one-sample nonparametric estimation of the mean of backward processes when follow-up is subject to left truncation and right censoring. We will discuss benefits of including prevalent cohort data to enlarge the identifiable region and large sample properties of the proposed estimator with related extensions. A SEER-Medicare linked data set is used to illustrate the proposed methodologies.

A semiparametric additive rate model for recurrent events with an informative terminal event

We propose a semiparametric additive rate model for modelling recurrent events in the presence of a terminal event. The dependence between recurrent events and terminal event is nonparametric. A general transformation model is used to model the terminal event. We construct an estimating equation for parameter estimation and derive the asymptotic distributions of the proposed estimators. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings. Application to a medical study is presented.

Semi-parametric risk prediction models for recurrent cardiovascular events in the LIPID study

Background

Traditional methods for analyzing clinical and epidemiological cohort study data have been focused on the first occurrence of a health outcome. However, in many situations, recurrent event data are frequently observed. It is inefficient to use methods for the analysis of first events to analyse recurrent event data.

Methods

We applied several semi-parametric proportional hazards models to analyze the risk of recurrent myocardial infarction (MI) events based on data from a very large randomized placebo-controlled trial of cholesterol-lowering drug. The backward selection procedure was used to select the significant risk factors in a model. The best fitting model was selected using the log-likelihood ratio test, Akaike Information and Bayesian Information Criteria.

Results

A total of 8557 persons were included in the LIPID study. Risk factors such as age, smoking status, total cholesterol and high density lipoprotein cholesterol levels, qualifying event for the acute coronary syndrome, revascularization, history of stroke or diabetes, angina grade and treatment with pravastatin were significant for development of both first and subsequent MI events. No significant difference was found for the effects of these risk factors between the first and subsequent MI events. The significant risk factors selected in this study were the same as those selected by the parametric conditional frailty model. Estimates of the relative risks and 95% confidence intervals were also similar between these two methods.

Conclusions

Our study shows the usefulness and convenience of the semi-parametric proportional hazards models for the analysis of recurrent event data, especially in estimation of regression coefficients and cumulative risks.

Uncovering symptom progression history from disease registry data with application to young cystic fibrosis patients

The growing availability of various disease registry data has brought precious opportunities to epidemiologists to understand the natural history of the registered diseases. It also presents challenges to the traditional data analysis techniques because of complicated censoring/truncation schemes and temporal dynamics of covariate influences. In a case study of the Cystic Fibrosis Foundation Patient Registry data, we propose analyses of progressive symptoms using temporal process regressions, as an alternative to the commonly employed proportional hazards models. Two endpoints are considered, the prevalence of ever positive and currently positive for Pseudomonas aeruginosa (PA) infection in the lungs, which capture different aspect of the disease process. The analysis of ever PA positive via a time-varying coefficient model demonstrates the lack of fit, as well as the potential loss of information, in the standard proportional hazards analysis. The analysis of currently PA positive yields results that are clinically meaningful and have not previously been reported in the cystic fibrosis literature. Our analyses demonstrate that prenatal/neonatal screening results in lower prevalence of PA infection compared to traditional diagnosis via signs and symptoms, but this benefit attenuates with age. Calendar years of diagnosis also affect the risk of PA infection; patients diagnosed in more recent cohort show higher prevalence of ever PA positive but lower prevalence of currently PA positive.

Parametric conditional frailty models for recurrent cardiovascular events in the lipid study

BACKGROUND

Analysis of recurrent event data is frequently needed in clinical and epidemiological studies. An important issue in such analysis is how to account for the dependence of the events in an individual and any unobserved heterogeneity of the event propensity across individuals.

METHODS

We applied a number of conditional frailty and nonfrailty models in an analysis involving recurrent myocardial infarction events in the Long-Term Intervention with Pravastatin in Ischaemic Disease study. A multiple variable risk prediction model was developed for both males and females.

RESULTS

A Weibull model with a gamma frailty term fitted the data better than other frailty models for each gender. Among nonfrailty models the stratified survival model fitted the data best for each gender. The relative risk estimated by the elapsed time model was close to that estimated by the gap time model. We found that a cholesterol-lowering drug, pravastatin (the intervention being tested in the trial) had significant protective effect against the occurrence of myocardial infarction in men (HR = 0.71, 95% CI 0.60-0.83). However, the treatment effect was not significant in women due to smaller sample size (HR = 0.75, 95% CI 0.51-1.10). There were no significant interactions between the treatment effect and each recurrent MI event (p = 0.24 for men and p = 0.55 for women). The risk of developing an MI event for a male who had an MI event during follow-up was about 3.4 (95% CI 2.6-4.4) times the risk compared with those who did not have an MI event. The corresponding relative risk for a female was about 7.8 (95% CI 4.4-13.6).

LIMITATIONS

The number of female patients was relatively small compared with their male counterparts, which may result in low statistical power to find real differences in the effect of treatment and other potential risk factors.

CONCLUSIONS

The conditional frailty model suggested that after accounting for all the risk factors in the model, there was still unmeasured heterogeneity of the risk for myocardial infarction, indicating the effect of subject-specific risk factors. These risk prediction models can be used to classify cardiovascular disease patients into different risk categories and may be useful for the most effective targeting of preventive therapies for cardiovascular disease.