Joint model for recurrent event data with a cured fraction and a terminal event

In a longitudinal study where the recurrence of an event and a terminal event such as death are observed, a certain portion of the subjects may experience no event during a long follow-up period; this often denoted as the cure group which is assumed to be the risk-free from both recurrent events and death. However, this assumption ignores the possibility of death, which subjects in the cure group may experience. In the present study, such misspecification is investigated with the addition of a death hazard model to the cure group. We propose a joint model using a frailty effect, which reflects the association between a recurrent event and death. For the estimation, an expectation-maximization (EM) algorithm was developed and PROC NLMIXED in SAS was incorporated under a piecewise constant baseline. Simulation studies were performed to check the performance of the suggested method. The proposed method was applied to leukemia patients experiencing both infection and death after bone marrow transplant.     

Association of Metformin Use with Outcomes in Advanced Endometrial Cancer Treated with Chemotherapy

There is increasing evidence that metformin, a commonly used treatment for diabetes, might have the potential to be repurposed as an economical and safe cancer therapeutic. The aim of this study was to determine whether stage III-IV or recurrent endometrial cancer patients who are using metformin during treatment with chemotherapy have improved survival. To test this we analyzed a retrospective cohort of subjects at two independent institutions who received chemotherapy for stage III-IV or recurrent endometrial cancer from 1992 to 2011. Diagnosis of diabetes, metformin use, demographics, endometrial cancer clinico-pathologic parameters, and survival duration were abstracted. The primary outcome was overall survival. The final cohort included 349 patients, 31 (8.9%) had diabetes and used metformin, 28 (8.0%) had diabetes but did not use metformin, and 291 (83.4%) did not have diabetes. The results demonstrate that the median overall survival was 45.6 months for patients with diabetes who used metformin compared to 12.5 months for patients with diabetes who did not use metformin and 28.5 months for patients without diabetes (log-rank test comparing the three groups P = 0.006). In a model adjusted for confounders, the difference in survival between the three groups remained statistically significant (P = 0.023). The improvement in survival among metformin users was not explained by better baseline health status or more aggressive use of chemotherapy. Overall, the findings in this retrospective cohort of endometrial cancer patients with stage III-IV or recurrent disease treated with chemotherapy indicate that patients with diabetes who were concurrently treated with metformin survived longer than patients with diabetes who did not use metformin.     

The Design of Intervention Trials Involving Recurrent and Terminal Events

Clinical trials are often designed to assess the effect of therapeutic interventions on the incidence of recurrent events in the presence of a dependent terminal event such as death. Statistical methods based on multistate analysis have considerable appeal in this setting since they can incorporate changes in risk with each event occurrence, a dependence between the recurrent event and the terminal event, and event-dependent censoring. To date, however, there has been limited development of statistical methods for the design of trials involving recurrent and terminal events. Based on the asymptotic distribution of regression coefficients from a multiplicative intensity Markov regression model, we derive sample size formulas to address power requirements for both the recurrent and terminal event processes. We consider the design of trials for which separate marginal hypothesis tests are of interest for the recurrent and terminal event processes and deal with both superiority and non-inferiority tests. Simulation studies confirm that the designs satisfy the nominal power requirements in both settings, and an application to a trial evaluating the effect of a bisphosphonate on skeletal complications is given for illustration.     

Are short (blue) wavelengths necessary for light treatment of seasonal affective disorder?

Despite widely published speculation regarding a potential potency advantage of short-wavelength (blue-appearing) light for Seasonal Affective Disorder (SAD) treatment, there have been few systematic studies. Those comparing short-wavelength to broad-wavelength (white) light under actual clinical conditions suggest equivalent effectiveness. This multicenter, parallel-group design trial was undertaken to compare the effects of light therapy on SAD using blue (~465 nm) versus blue-free (595–612 nm) LED lights. Fifty-six medication-free subjects aged 21–64 years who met DSM-IV-TR criteria for recurrent major depression with winter-type seasonal pattern were enrolled in this blinded study at five participating centers between January and March 2012. Thirty-five subjects met the criteria for randomization to 30 min of either blue (~465 nm) or blue-free (595–612 nm) daily morning light therapy. Twenty-nine subjects completed the study; three subjects withdrew due to treatment-related adverse events, including migraines, and three withdrew for non-study-related reasons. The primary effectiveness variable was depression score (SIGH-ADS) after six weeks of daily light treatment. Secondary effectiveness variables included quality-of-life (QoL) and suicidality ratings. Using an intent-to-treat analysis, mean depression scores were different at baseline for the blue group (29 ± 5 versus 26 ± 5, p = 0.05 blue versus blue-free, respectively), and the initial score was used as a covariate. Baseline scores were not significantly different between treatment groups among those who completed the study, and no significant differences in depression scores were observed after 6 weeks (mean ± SD scores at 6 weeks: 5.6 ± 6.1 versus 4.5 ± 5.3, p = 0.74, blue versus blue-free, respectively). In addition, the proportion of subjects who met remission criteria, defined as a depression score ≤8, was not significantly different between the two groups (p = 0.41); among the 29 subjects who completed the study, 76% of subjects experienced remission by the end of the trial, which coincided with the beginning of spring. The QoL and suicidality ratings were also significantly improved from pre- to post-treatment, with no significant difference between treatments. No subject experienced worsening or non-improved symptoms over the 6-week trial. The main finding of this study is that subjects treated with blue light did not improve more than subjects treated with blue-free light; both showed substantial improvement on multiple measures. Failure to find differences may have resulted from methodological constraints, including a small sample size. Recruitment began mid-winter during an unusually mild season, and the trial was terminated earlier than planned by the study sponsor due to a failure to detect a difference. However, if confirmed in a larger randomized sample, these results suggest that blue wavelengths are not necessary for successful SAD treatment.     

Marginal hazard ratio estimates in joint frailty models for heart failure trials

This work is motivated by clinical trials in chronic heart failure disease, where treatment has effects both on morbidity (assessed as recurrent non‐fatal hospitalisations) and on mortality (assessed as cardiovascular death, CV death). Recently, a joint frailty proportional hazards model has been proposed for these kind of efficacy outcomes to account for a potential association between the risk rates for hospital admissions and CV death. However, more often clinical trial results are presented by treatment effect estimates that have been derived from marginal proportional hazards models, that is, a Cox model for mortality and an Andersen–Gill model for recurrent hospitalisations. We show how these marginal hazard ratios and their estimates depend on the association between the risk processes, when these are actually linked by shared or dependent frailty terms. First we derive the marginal hazard ratios as a function of time. Then, applying least false parameter theory, we show that the marginal hazard ratio estimate for the hospitalisation rate depends on study duration and on parameters of the underlying joint frailty model. In particular, we identify parameters, for example the treatment effect on mortality, that determine if the marginal hazard ratio estimate for hospitalisations is smaller, equal or larger than the conditional one. How this affects rejection probabilities is further investigated in simulation studies. Our findings can be used to interpret marginal hazard ratio estimates in heart failure trials and are illustrated by the results of the CHARM‐Preserved trial (where CHARM is the ‘Candesartan in Heart failure Assessment of Reduction in Mortality and morbidity’ programme).     

Joint frailty models for recurring events and death using maximum penalized likelihood estimation: application on cancer events

The observation of repeated events for subjects in cohort studies could be terminated by loss to follow-up, end of study, or a major failure event such as death. In this context, the major failure event could be correlated with recurrent events, and the usual assumption of noninformative censoring of the recurrent event process by death, required by most statistical analyses, can be violated. Recently, joint modeling for 2 survival processes has received considerable attention because it makes it possible to study the joint evolution over time of 2 processes and gives unbiased and efficient parameters. The most commonly used estimation procedure in the joint models for survival events is the expectation maximization algorithm. We show how maximum penalized likelihood estimation can be applied to nonparametric estimation of the continuous hazard functions in a general joint frailty model with right censoring and delayed entry. The simulation study demonstrates that this semiparametric approach yields satisfactory results in this complex setting. As an illustration, such an approach is applied to a prospective cohort with recurrent events of follicular lymphomas, jointly modeled with death.     

Clinical Trials Testing Cardiovascular Benefits of Antioxidant Supplementation

Self-selected supplementation of vitamin E has been associated with reduced coronary events and atherosclerotic progression, but the evidence from clinical trials is controversial. ASAP was a 6-year randomized trial to study the effect of supplementation with vitamin E plus slow-release vitamin C on carotid atherosclerotic progression in 520 hypercholesterolemic men and women aged 45-69 years. The supplementation reduced the progression of carotid atherosclerosis by 26% ( P =0.014), by 33% ( P =0.024) in men and 14% (not significant) in women. The effect was larger in subjects with low baseline vitamin C or atherosclerotic plaques. In the Harvard IVUS trial, the combined supplementation with vitamins E and C significantly inhibited the progression of coronary atherosclerosis in one year. These data confirm that the supplementation with a combination of vitamins E and C can retard atherosclerotic progression. The findings of completed trials testing the effect on cardiovascular events are less consistent. The major on-going clinical trials include the SU.VI.MAX, WHS, WACS and WAVE studies. These involve in total over 80,000 subjects, who are treated with antioxidative supplements for years. The results of these studies will become available during 2003-2006. They may provide the necessary additional information concerning the effect of antioxidants on cardiovascular events.     

Clinical trials testing cardiovascular benefits of antioxidant supplementation

Self-selected supplementation of vitamin E has been associated with reduced coronary events and atherosclerotic progression, but the evidence from clinical trials is controversial. ASAP was a 6-year randomized trial to study the effect of supplementation with vitamin E plus slow-release vitamin C on carotid atherosclerotic progression in 520 hypercholesterolemic men and women aged 45-69 years. The supplementation reduced the progression of carotid atherosclerosis by 26% ( P =0.014), by 33% ( P =0.024) in men and 14% (not significant) in women. The effect was larger in subjects with low baseline vitamin C or atherosclerotic plaques. In the Harvard IVUS trial, the combined supplementation with vitamins E and C significantly inhibited the progression of coronary atherosclerosis in one year. These data confirm that the supplementation with a combination of vitamins E and C can retard atherosclerotic progression. The findings of completed trials testing the effect on cardiovascular events are less consistent. The major on-going clinical trials include the SU.VI.MAX, WHS, WACS and WAVE studies. These involve in total over 80,000 subjects, who are treated with antioxidative supplements for years. The results of these studies will become available during 2003-2006. They may provide the necessary additional information concerning the effect of antioxidants on cardiovascular events.     

Penalized survival models for the analysis of alternating recurrent event data

Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length-of-stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance-covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end-stage renal disease patients.     

Sequential Testing with Recurrent Events over Multiple Treatment Periods

Recurrent event outcomes are adopted increasingly often as a basis for evaluating experimental interventions. In clinical trials involving recurrent events, patients are frequently observed for a baseline period while under standard care, and then randomised to receive either an experimental treatment or continue on standard care. When events are generated according to a mixed Poisson model, having baseline data permits a conditional analysis which can eliminate the subject-specific random effect and yield a more efficient analysis regarding treatment effect. When studies are expected to recruit a large number of patients over an extended period of accrual, or if the period of follow-up is long, sequential testing is desirable to ensure the study is stopped as soon as sufficient data have been collected to establish treatment benefits. We describe methods which facilitate sequential analysis of data arising from trials with recurrent event responses observed over two treatment periods where one is a baseline period of observation. Formulae to help schedule analyses at approximately equal increments of information are given. Simulation studies show that the sequential testing procedures have rejection rates compatible with the nominal error rates under the null and alternative hypotheses. Data from a trial of patients with herpes simplex virus infection are analysed to illustrate the utility of these methods.     

A Bayesian approach for the analysis of panel-count data with dependent termination

We consider modeling and Bayesian analysis for panel-count data when the termination time for each subject may depend on its history of the recurrent events. We propose a fully specified semiparametric model for the joint distribution of the recurrent events and the termination time. For this model, we provide a natural motivation, derive several novel properties, and develop a Bayesian analysis based on a Markov chain Monte Carlo algorithm. Comparisons are made to other existing models and methods for panel-count data. We demonstrate the usefulness of our new models and methodologies through the reanalysis of a data set from a clinical trial.     

Estimation and interpretation of incidence rate difference for recurrent events when the estimation model is misspecified

Recurrent events data are common in experimental and observational studies. It is often of interest to estimate the effect of an intervention on the incidence rate of the recurrent events. The incidence rate difference is a useful measure of intervention effect. A weighted least squares estimator of the incidence rate difference for recurrent events was recently proposed for an additive rate model in which both the baseline incidence rate and the covariate effects were constant over time. In this article, we relax this model assumption and examine the properties of the estimator under the additive and multiplicative rate models assumption in which the baseline incidence rate and covariate effects may vary over time. We show analytically and numerically that the estimator gives an appropriate summary measure of the time‐varying covariate effects. In particular, when the underlying covariate effects are additive and time‐varying, the estimator consistently estimates the weighted average of the covariate effects over time. When the underlying covariate effects are multiplicative and time‐varying, and if there is only one binary covariate indicating the intervention status, the estimator consistently estimates the weighted average of the underlying incidence rate difference between the intervention and control groups over time. We illustrate the method with data from a randomized vaccine trial.     

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.     

A randomized, placebo-controlled, double-blind clinical trial of curcuminoids in oral lichen planus.

We studied the efficacy of curcuminoids in the treatment of oral lichen planus (OLP), a chronic, mucocutaneous, immunological disease. Curcuminoids are components of turmeric (Curcuma longa) that have anti-inflammatory activity. Turmeric has been used in Ayurveda (Indian traditional medicine) for centuries. A randomized, double-blind, placebo-controlled trial was conducted. In all, 100 consecutive, eligible patients with OLP presenting to the oral medicine clinic at the University of California, San Francisco, were to be selected. Two interim analyses were to be conducted during the trial. The trial was conducted between February 2003 and September 2004. The first interim analysis was conducted in October 2004 using data from the first 33 subjects. Study subjects were randomized to receive either placebo or curcuminoids at 2000 mg/day for 7 weeks. In addition, all subjects received prednisone at 60 mg/day for the first 1 week. The primary outcome was a change in symptoms from baseline. Secondary outcomes were changes in clinical signs and occurrence of side effects. The first interim analysis did not show a significant difference between the placebo and curcuminoids groups. Conditional power calculations suggested a less than 2% chance that the curcuminoids group would have a significantly better outcome as compared with the placebo group if the trial were continued to completion. Therefore, the study was ended early for futility. Reaching a conclusion regarding the efficacy of curcuminoids based on the results of this study is not possible as it was ended early for futility. Curcuminoids at this dose were well tolerated and the results suggest that for future studies a larger sample size, a higher dose and/or longer duration of curcuminoids administration should be considered; however, for the next step, an RCT of a shorter duration, using a higher dose of curcuminoids, and without an initial course of prednisone, should be considered.     

No Additional Prognostic Value of Genetic Information in the Prediction of Vascular Events after Cerebral Ischemia of Arterial Origin: The PROMISe Study

Background

Patients who have suffered from cerebral ischemia have a high risk of recurrent vascular events. Predictive models based on classical risk factors typically have limited prognostic value. Given that cerebral ischemia has a heritable component, genetic information might improve performance of these risk models. Our aim was to develop and compare two models: one containing traditional vascular risk factors, the other also including genetic information.

Methods and Results

We studied 1020 patients with cerebral ischemia and genotyped them with the Illumina Immunochip. Median follow-up time was 6.5 years; the annual incidence of new ischemic events (primary outcome, n=198) was 3.0%. The prognostic model based on classical vascular risk factors had an area under the receiver operating characteristics curve (AUC-ROC) of 0.65 (95% confidence interval 0.61-0.69). When we added a genetic risk score based on prioritized SNPs from a genome-wide association study of ischemic stroke (using summary statistics from the METASTROKE study which included 12389 cases and 62004 controls), the AUC-ROC remained the same. Similar results were found for the secondary outcome ischemic stroke.

Conclusions

We found no additional value of genetic information in a prognostic model for the risk of ischemic events in patients with cerebral ischemia of arterial origin. This is consistent with a complex, polygenic architecture, where many genes of weak effect likely act in concert to influence the heritable risk of an individual to develop (recurrent) vascular events. At present, genetic information cannot help clinicians to distinguish patients at high risk for recurrent vascular events.     

Joint monitoring and prediction of accrual and event times in clinical trials

In many clinical trials, the primary endpoint is time to an event of interest, for example, time to cardiac attack or tumor progression, and the statistical power of these trials is primarily driven by the number of events observed during the trials. In such trials, the number of events observed is impacted not only by the number of subjects enrolled but also by other factors including the event rate and the follow‐up duration. Consequently, it is important for investigators to be able to monitor and predict accurately patient accrual and event times so as to predict the times of interim and final analyses and enable efficient allocation of research resources, which have long been recognized as important aspects of trial design and conduct. The existing methods for prediction of event times all assume that patient accrual follows a Poisson process with a constant Poisson rate over time; however, it is fairly common in real‐life clinical trials that the Poisson rate changes over time. In this paper, we propose a Bayesian joint modeling approach for monitoring and prediction of accrual and event times in clinical trials. We employ a nonhomogeneous Poisson process to model patient accrual and a parametric or nonparametric model for the event and loss to follow‐up processes. Compared to existing methods, our proposed methods are more flexible and robust in that we model accrual and event/loss‐to‐follow‐up times jointly and allow the underlying accrual rates to change over time. We evaluate the performance of the proposed methods through simulation studies and illustrate the methods using data from a real oncology trial.     

Month 2 Culture Status and Treatment Duration as Predictors of Tuberculosis Relapse Risk in a Meta-Regression Model

Background

New drugs and regimens with the potential to transform tuberculosis treatment are presently in early stage clinical trials.

Objective

The goal of the present study was to infer the required duration of these treatments.

Method

A meta-regression model was developed to predict relapse risk using treatment duration and month 2 sputum culture positive rate as predictors, based on published historical data from 24 studies describing 58 regimens in 7793 patients. Regimens in which rifampin was administered for the first 2 months but not subsequently were excluded. The model treated study as a random effect.

Results

The model predicted that new regimens of 4 or 5 months duration with rates of culture positivity after 2 months of 1% or 3%, would yield relapse rates of 4.0% or 4.1%, respectively. In both cases, the upper limit of the 2-sided 80% prediction interval for relapse for a hypothetical trial with 680 subjects per arm was <10%. Analysis using this model of published month 2 data for moxifloxacin-containing regimens indicated they would result in relapse rates similar to standard therapy only if administered for ≥5 months.

Conclusions

This model is proposed to inform the required duration of treatment of new TB regimens, potentially hastening their accelerated approval by several years.     

Early and long-term outcome of elective stenting of the infarct-related artery in patients with viability in the infarct-area: Rationale and design of the Viability-guided Angioplasty after acute Myocardial Infarction-trial (The VIAMI-trial)

BACKGROUND: Although percutaneous coronary intervention (PCI) is becoming the standard therapy in ST-segment elevation myocardial infarction (STEMI), to date most patients, even in developed countries, are reperfused with intravenous thrombolysis or do not receive a reperfusion therapy at all. In the post-lysis period these patients are at high risk for recurrent ischemic events. Early identification of these patients is mandatory as this subgroup could possibly benefit from an angioplasty of the infarct-related artery.Since viability seems to be related to ischemic adverse events, we initiated a clinical trial to investigate the benefits of PCI with stenting of the infarct-related artery in patients with viability detected early after acute myocardial infarction. METHODS: The VIAMI-study is designed as a prospective, multicenter, randomized, controlled clinical trial. Patients who are hospitalized with an acute myocardial infarction and who did not have primary or rescue PCI, undergo viability testing by low-dose dobutamine echocardiography (LDDE) within 3 days of admission. Consequently, patients with demonstrated viability are randomized to an invasive or conservative strategy. In the invasive strategy patients undergo coronary angiography with the intention to perform PCI with stenting of the infarct-related coronary artery and concomitant use of abciximab. In the conservative group an ischemia-guided approach is adopted (standard optimal care).The primary end point is the composite of death from any cause, reinfarction and unstable angina during a follow-up period of three years. CONCLUSION: The primary objective of the VIAMI-trial is to demonstrate that angioplasty of the infarct-related coronary artery with stenting and concomitant use of abciximab results in a clinically important risk reduction of future cardiac events in patients with viability in the infarct-area, detected early after myocardial infarction.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.