Repeated events survival models: the conditional frailty model

The quasi-xgamma frailty model with survival analysis under heterogeneity problem, validation testing, and risk analysis for emergency care data

Frailty models are important for survival data because they allow for the possibility of unobserved heterogeneity problem. The problem of heterogeneity can be existed due to a variety of factors, such as genetic predisposition, environmental factors, or lifestyle choices. Frailty models can help to identify these factors and to better understand their impact on survival. In this study, we suggest a novel quasi xgamma frailty (QXg-F) model for the survival analysis. In this work, the test of Rao-Robson and Nikulin is employed to test the validity and suitability of the probabilistic model, we examine the distribution's properties and evaluate its performance in comparison with many relevant cox-frailty models. To show how well the QXg-F model captures heterogeneity and enhances model fit, we use simulation studies and real data applications, including a fresh dataset gathered from an emergency hospital in Algeria. According to our research, the QXg-F model is a viable replacement for the current frailty modeling distributions and has the potential to improve the precision of survival analyses in a number of different sectors, including emergency care. Moreover, testing the ability and the importance of the new QXg-F model in insurance is investigated using simulations via different methods and application to insurance data.

Examining the role of firearm involvement in repeat intimate partner violence assaults

BACKGROUND

Intimate partner violence (IPV) remains a pervasive and complex issue with significant social and public health implications. The nexus of firearms and intimate partner violence (IPV) is an especially dangerous one. However, little is known about how firearm involvement can influence the risk of repeat IPV assaults.

METHODS

We use data from 346 male perpetrated IPV incidents reported to the Detroit Police Department between December 2016 and April 2017 to examine the role of firearm involvement in IPV recidivism during a 5 and half year follow up period. Employing a conditional gap-time frailty model that accommodates heterogeneity among individuals through a frailty term, we analyze time to multiple IPV assaults that occur over the follow up period. We identify various pathways through which firearms impact the likelihood of subsequent IPV incidents, including intimidation, threats, and use of firearms, while controlling for observable perpetrator characteristics to understand the explicit roles of firearms.

RESULTS

Firearm involvement at the index assault was not associated with IPV recidivism. However, involvement of firearms in past IPV assaults significantly increased the risk of subsequent physical IPV. The discrepancy is likely arising from a high degree of censoring among individuals who were armed with a firearm during the index assault.

CONCLUSION

Our research reveals a nuanced relationship between firearm involvement and IPV recidivism, shedding light on the multifaceted dynamics at play. By elucidating the intricate dynamics at the intersection of firearms and intimate partner violence, our study underscores the need for targeted policy interventions and preventative measures aimed at reducing IPV recidivism.

Influenza vaccination reduced myocardial infarctions in United Kingdom older adults: a prior event rate ratio study

OBJECTIVES

We aimed to estimate the real-world effectiveness of the influenza vaccine against myocardial infarction (MI) and influenza in the decade since adults aged ≥ 65 years were first recommended the vaccine.

STUDY DESIGN AND SETTING

We identified annual cohorts, 1997 to 2011, of adults aged ≥ 65 years, without previous influenza vaccination, from UK general practices, registered with the Clinical Practice Research Datalink. Using a quasi-experimental study design to control for confounding bias, we estimated influenza vaccine effectiveness on hospitalization for MI, influenza, and antibiotic prescriptions for lower respiratory tract infections.

RESULTS

Vaccination was moderately effective against influenza, the prior event rate ratio-adjusted hazard ratios ranging from 0.70 in 1999 to 0.99 in 2001. Prior event rate ratio-adjusted hazard ratios demonstrated a protective effect against MIs, varying between 0.40 in 2010 and 0.89 in 2001. Aggregated across the cohorts, influenza vaccination reduced the risk of MIs by 39% (95% confidence interval: 34%, 44%).

CONCLUSION

Effectiveness of the flu vaccine in preventing MIs in older UK adults is consistent with the limited evidence from clinical trials. Similar trends in effectiveness against influenza and against MIs suggest the risk of influenza mediates the effectiveness against MIs, although divergence in some years implies the mechanism may be complex.

Recurrent events analysis with piece-wise exponential additive mixed models

Recurrent events analysis plays an important role in many applications, including the study of chronic diseases or recurrence of infections. Historically, many models for recurrent events have been variants of the Cox model. In this article we introduce and describe the application of the piece-wise exponential Additive Mixed Model (PAMM) for recurrent events analysis and illustrate how PAMMs can be used to flexibly model the dependencies in recurrent events data. Simulations confirm that PAMMs provide unbiased estimates as well as equivalence to the Cox model when proportional hazards are assumed. Applications to recurrence of staphylococcus aureus and malaria in children illustrate the estimation of seasonality, bivariate non-linear effects, multiple timescales and relaxation of the proportional hazards assumption via time-varying effects. The R package pammtools is extended to facilitate estimation and visualization of PAMMs for recurrent events data.

Comparison of statistical methods for the analysis of recurrent adverse events in the presence of non-proportional hazards and unobserved heterogeneity: a simulation study

Background

In preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. Challenges in modelling the risk of the AEs include accounting for time-to-AE and within-patient-correlation, beyond the conventional methods. The correlation comes from two sources; (a) individual patient unobserved heterogeneity (i.e. frailty) and (b) the dependence between AEs characterised by time-dependent treatment effects. Potential AE-dependence can be modelled via time-dependent treatment effects, event-specific baseline and event-specific random effect, while heterogeneity can be modelled via subject-specific random effect. Methods that can improve the estimation of both the unobserved heterogeneity and treatment effects can be useful in understanding the evolution of risk of AEs, especially in preventive trials where time-dependent treatment effect is expected.

Methods

Using both a simulation study and the Chloroquine for Malaria in Pregnancy (NCT01443130) trial data to demonstrate the application of the models, we investigated whether the lognormal shared frailty models with restricted cubic splines and non-proportional hazards (LSF-NPH) assumption can improve estimates for both frailty variance and treatment effect compared to the conventional inverse Gaussian shared frailty model with proportional hazard (ISF-PH), in the presence of time-dependent treatment effects and unobserved patient heterogeneity. We assessed the bias, precision gain and coverage probability of 95% confidence interval of the frailty variance estimates for the models under varying known unobserved heterogeneity, sample sizes and time-dependent effects.

Results

The ISF-PH model provided a better coverage probability of 95% confidence interval, less bias and less precise frailty variance estimates compared to the LSF-NPH models. The LSF-NPH models yielded unbiased hazard ratio estimates at the expense of imprecision and high mean square error compared to the ISF-PH model.

Conclusion

The choice of the shared frailty model for the recurrent AEs analysis should be driven by the study objective. Using the LSF-NPH models is appropriate if unbiased hazard ratio estimation is of primary interest in the presence of time-dependent treatment effects. However, ISF-PH model is appropriate if unbiased frailty variance estimation is of primary interest.

Trial registration

ClinicalTrials.gov; NCT01443130

Left-censored recurrent event analysis in epidemiological studies: a proposal for when the number of previous episodes is unknown

BACKGROUND

When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up. This phenomenon is known as left censoring, and simply ignoring these prior episodes can lead to biased and inefficient estimates. We aimed to propose a statistical method that performs well in this setting.

METHODS

Our proposal was based on the use of models with specific baseline hazards. In this, the number of prior episodes were imputed when unknown and stratified according to whether the subject had been at risk of presenting the event before t = 0. A frailty term was also used. Two formulations were used for this "Specific Hazard Frailty Model Imputed" based on the "counting process" and "gap time." Performance was then examined in different scenarios through a comprehensive simulation study.

RESULTS

The proposed method performed well even when the percentage of subjects at risk before follow-up was very high. Biases were often below 10% and coverages were around 95%, being somewhat conservative. The gap time approach performed better with constant baseline hazards, whereas the counting process performed better with non-constant baseline hazards.

CONCLUSIONS

The use of common baseline methods is not advised when knowledge of prior episodes experienced by a participant is lacking. The approach in this study performed acceptably in most scenarios in which it was evaluated and should be considered an alternative in this context. It has been made freely available to interested researchers as R package miRecSurv.

Is Police Misconduct Contagious? Non-trivial Null Findings from Dallas, Texas

Objectives

Understanding if police malfeasance might be "contagious" is vital to identifying efficacious paths to police reform. Accordingly, we investigate whether an officer's propensity to engage in misconduct is associated with her direct, routine interaction with colleagues who have themselves engaged in misbehavior in the past.

Methods

Recognizing the importance of analyzing the actual social networks spanning a police force, we use data on collaborative responses to 1,165,136 "911" calls for service by 3475 Dallas Police Department (DPD) officers across 2013 and 2014 to construct daily networks of front-line interaction. And we relate these cooperative networks to reported and formally sanctioned misconduct on the part of the DPD officers during the same time period using repeated-events survival models.

Results

Estimates indicate that the risk of a DPD officer engaging in misconduct is not associated with the disciplined misbehavior of her ad hoc, on-the-scene partners. Rather, a greater risk of misconduct is associated with past misbehavior, officer-specific proneness, the neighborhood context of patrol, and, in some cases, officer race, while departmental tenure is a mitigating factor.

Conclusions

Our observational findings-based on data from one large police department in the United States-ultimately suggest that actor-based and ecological explanations of police deviance should not be summarily dismissed in favor of accounts emphasizing negative socialization, where our study design also raises the possibility that results are partly driven by unobserved trait-based variation in the situations that officers find themselves in. All in all, interventions focused on individual officers, including the termination of deviant police, may be fruitful for curtailing police misconduct-where early interventions focused on new offenders may be key to avoiding the escalation of deviance.

Longitudinal Studies 3: Data Modeling Using Standard Regression Models and Extensions

In longitudinal studies, the relationship between exposure and disease can be measured once or multiple times while participants are monitored over time. Traditional regression techniques are used to model outcome data when each epidemiological unit is observed once. These models include generalized linear models for quantitative continuous, discrete, or qualitative outcome responses, and models for time-to-event data. When data come from the same subjects or group of subjects, observations are not independent and the underlying correlation needs to be addressed in the analysis. In these circumstances, extended models are necessary to handle complexities related to clustered data, and repeated measurements of time-varying predictors and/or outcomes.

Learning to kill: Why a small handful of counties generates the bulk of US death sentences

We demonstrate strong self-referential effects in county-level data concerning use of the death penalty. We first show event-dependency using a repeated-event model. Higher numbers of previous events reduce the expected time delay before the next event. Second, we use a cross-sectional time-series approach to model the number of death sentences imposed in a given county in a given year. This model shows that the cumulative number of death sentences previously imposed in the same county is a strong predictor of the number imposed in a given year. Results raise troubling substantive implications: The number of death sentences in a given county in a given year is better predicted by that county’s previous experience in imposing death than by the number of homicides. This explains the previously observed fact that a large share of death sentences come from a small number of counties and documents the self-referential aspects of use the death penalty. A death sentencing system based on racial dynamics and then amplified by self-referential dynamics is inconsistent with equal protection of the law, but this describes the United States system well.

Effectiveness of bevacizumab in first- and second-line treatment for metastatic colorectal cancer: ITACa randomized trial

Background:

Cancer trials involving multiple treatment lines substantially increase our understanding of therapeutic strategies. However, even when the primary end-point of these studies is progression-free survival (PFS), their statistical analysis usually focuses on each line separately, or does not consider repeated events, thus missing potentially relevant information. Consequently, the evaluation of the effectiveness of treatment strategies is highly impaired.

Methods:

We evaluated the potentially different effect of bevacizumab (B) administered for the first- or second-line treatment of metastatic colorectal cancer (mCRC) in the ITACa (Italian Trial in Advanced Colorectal Cancer) randomized trial. The ITACa trial consisted of two arms: first-line chemotherapy (CT)+B followed by second-line CT alone versus first-line CT alone followed by second-line CT+B or CT+B+cetuximab according to KRAS status. Cox models for repeated disease progression were performed, and potential selection bias was adjusted using the inverse probability of censoring weighting method. Hazard ratios (HR) [95% confidence interval (CI)] for PFS (primary endpoint) were reported.

Results:

The overall effect of B across the two lines resulted in a HR = 0.80 (95% CI 0.68–0.95, p = 0.008). Evaluating the differential effect of B in first- and second-line, the addition of B to first-line chemotherapy (CT) produced a 10% risk reduction (HR = 0.90, 95% CI 0.72–1.12, p = 0.340) versus CT alone; B added to second-line CT produced a 36% risk reduction (HR = 0.64, 95% CI 0.49–0.84, p = 0.0011) versus CT alone.

Conclusion:

Our results seem to suggest that B confers a PFS advantage when administered in combination with second-line chemotherapy, which could help to improve current international guidelines on optimal sequential treatment strategies.

Determinants of Bilateral REDD+ Cooperation Recipients in Kyoto Protocol Regime and Their Implications in Paris Agreement Regime

A cooperative approach for REDD+ between developing and developed countries can be a sound means to achieve national and global mitigation targets. To accomplish the Nationally Determined Contribution (NDC) of countries and the global 2 °C climate target more effectively, it is necessary to explore the coordination options, based on the understanding of bilateral REDD+ cooperation. This study explains the current status of bilateral REDD+ cooperation and investigates determinants affecting REDD+ recipient decisions of donor countries, by analyzing bilateral REDD+ arrangements, which has been promoted for 10 years under the the Kyoto Protocol regime from 2006 until 2015. The results show that Norway and Japan supported more than half of the total financial pledges for bilateral REDD+ projects for 10 years. Out of 87 REDD+ recipients, four countries—Brazil, India, Indonesia, and China—accounted for more than half of the 10-year financial pledges. Approximately 78% of total financing was found to be concentrated in the top 10 recipients. The aid darlings and orphans problem, the concentration of bilateral supports in a few developing countries and the exclusion of several developing countries from the recipient selection process, which has been discussed in ODA researches, was also observed. Applying a shared frailty model, recipient need, recipient merit, and donor interest was found to be the main determinants of donors’ REDD+ recipient decision. Donor interest and recipient merit were found to have more significant effects on the decision than recipient need. A balanced two-track approach is further required, in which, along with the bilateral REDD+ cooperation in the REDD+ darling countries, international organizations and multilateral funds for REDD+ need to increase financial accessibility, including the result-based compensation system for the REDD+ orphan countries.

Estimation of the primary, secondary and composite effects of malaria vaccines using data on multiple clinical malaria episodes

BACKGROUND

An effective malaria vaccine affects the risk of malaria directly, through the vaccine-induced immune response (the primary effect), and indirectly, as a consequence of reduced exposure to malaria infection and disease, leading to slower acquisition of natural immunity (the secondary effect). The beneficial primary effect may be offset by a negative secondary effect, resulting in a smaller or nil composite effect. Reports of malaria vaccine trials usually present only the composite effect. We aimed to demonstrate how the primary and secondary effects can also be estimated from trial data.

METHODS

We propose an enhancement to the conditional frailty model for the estimation of primary effect using data on disease episodes. We use the Andersen-Gill model to estimate the composite effect. We consider taking the ratio of the hazard ratios to estimate the secondary effect. We used directed acyclic graphs and data from a randomized trial of the RTS,S/AS02 malaria vaccine to illustrate the problems and solutions. Time-varying effects were estimated by partitioning the follow-up into four time periods.

RESULTS

The primary effect estimates from our proposed model were consistently stronger than the conditional frailty model in the existing literature. The primary effect of the vaccine was consistently stronger than the composite effect across all time periods. Both the primary and composite effects were stronger in the first three months, with hazard ratios (95% confidence interval) 0.62 (0.49-0.79) and 0.68 (0.54-0.84), respectively; the hazard ratios weakened over time. The secondary effect appeared mild, with hazard ratio 1.09 (1.02-1.16) in the first three months.

CONCLUSIONS

The proposed analytic strategy facilitates a more comprehensive interpretation of trial data on multiple disease episodes. The RTS,S/AS02 vaccine had modest primary and secondary effects that waned over time, but the composite effect in preventing clinical malaria remained positive up to the end of the study.

CLINICAL TRIALS REGISTRATION

ClinicalTrials.gov NCT00197041.

Comparison of statistical methods for recurrent event analysis using pediatrics asthma data

When the same type of event is experienced by a subject more than once it is called recurrent event, which possess two important characteristics, namely "within-subject correlation" and "time-varying covariate." As a result, the traditional statistical methods do not work well on recurrent event data. Over the past few decades, many alternatives methods have been proposed for the analysis of recurrent event data. In this article, the six most prominent methods for recurrent event analysis have been compared on pediatric asthma data. Three variance corrected models (viz "Anderson and Gill [AG] model," "Prentice, William, and Peterson-Counting Process [PWP-CP] model," and "Prentice, William, and Peterson-Gap Time [PWP-GT] model") and three corresponding frailty variants (AG-frailty, PWP-CP-frailty, and PWP-GT-frailty) were compared using three mathematical criterion (AIC, BIC, and log-likelihood) and one graphical criteria (Cox-Snell goodness of fit, visual test). All model comparison indices showed the PWP-GT model as the most appropriate model on asthma data over other models. By using PWP-GT model, seven predictors of asthma exacerbation (viz "abdominal pain at previous visit," "Z5 (%) at previous visit," "diagnosis of asthma at previous visit," "calendar month of exacerbation," "history of maternal asthma," "monthly per capita income," and "emotional stress") were identified. The PWP-GT model was identified as the most appropriate model over other models on pediatrics asthma data.

Mixture cure models with time-varying and multilevel frailties for recurrent event data

Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.

Analysis Of Re-Hospitalizations For Patients With Heart Failure Caused By Coronary Heart Disease: Data Of First Event And Recurrent Event

Background

The re-hospitalization rate of patients with heart failure remains at a high level, and studies of the subject have focused mainly on event-time outcomes. In addition to using re-hospitalization data with the outcomes of the event-time-count, this study introduces the conditional frailty model, which could help obtain more reasonable results.

Materials and methods

This prospective observational cohort study enrolled 1484 patients with heart failure caused by coronary heart disease. The outcomes of heart failure readmissions and the case report form data were collected. Based on the traditional Cox model with event-time outcomes, the mixed effects of a conditional frailty model were added to analyze the event-time-count longitudinal data.

Results

The Cox regression model showed that non-manual work, diastolic dysfunction, and better medical compensation increased the risk of heart failure readmission, whereas treatment with beta-blockers decreased the risk. The conditional frailty model further revealed that age, female sex, non-manual work, better medical compensation, longer QRS duration, and treatment with percutaneous coronary intervention increased the risk of heart failure readmission.

Conclusion

This study obtained more reliable, reasonable results based on longitudinal data and a mixed model. The results could provide more clinical epidemiological evidence for the management of heart failure.

Individualization of Treatment Improves the Survival of Children With High-Risk Solid Tumors: Comparative Patient Series Analysis in a Real-Life Scenario

Introduction: The individualization of treatment is attractive, especially in children with high-risk cancer. In such a rare and very heterogeneous group of diseases, large population-based clinical randomized trials are not feasible without international collaboration. We therefore propose comparative patient series analysis in a real-life scenario.

Methods: Open cohort observational study, comparative analysis. Seventy patients with high-risk solid tumors diagnosed between 2003 and 2015 and in whom the treatment was individualized either empirically or based on biomarkers were analyzed. The heterogeneity of the cohort and repeated measurements were advantageously utilized to increase effective sample size using appropriate statistical tools.

Results: We demonstrated a beneficial effect of empirically given low-dose metronomic chemotherapy (HR 0.46 for relapses, p = 0.017) as well as various repurposed or targeted agents (HR 0.15 for deaths, p = 0.004) in a real-life scenario. However, targeted agents given on the basis of limited biological information were not beneficial.

Conclusions: Comparative patient series analysis provides institutional-level evidence for treatment individualization in high-risk pediatric malignancies. Our findings emphasize the need for a comprehensive, multi omics assessment of the tumor and the host as well whenever molecularly driven targeted therapies are being considered. Low-dose metronomic chemotherapy or local control of the disease may be a more rational option in situations where targeted treatment cannot be justified by robust evidence and comprehensive biological information. “Targeted drugs” may be given empirically with a realistic benefit expectation when based on robust rationale.

Increased hospitalization rates following heart failure diagnosis in rheumatoid arthritis as compared to the general population

OBJECTIVE

To compare the frequency of and trends in hospitalizations after heart failure (HF) diagnosis in patients with and without rheumatoid arthritis (RA) during 1987-2015.

METHODS

The study included a retrospectively identified population-based cohort of patients with incident HF and prior RA (age≥18 years, 1987 ACR criteria) and a cohort of incident HF patients without RA matched 3:1 on age, sex, and year of HF diagnosis. Hospitalizations at the time of HF diagnosis were excluded. All subjects were followed until death, migration, or 12/31/2015.

RESULTS

The study included 212 patients with RA (mean age at HF diagnosis 78.3 years; 68% female) and 636 non-RA patients (mean age at HF diagnosis 78.6 years; 68% female). The hospitalization rate after HF diagnosis was higher in RA vs non-RA (rate ratio [RR] 1.17; 95%CI 1.08-1.26). Hospitalization rates in both groups have been declining since 2005 and the difference between patients with and without RA may be decreasing after 2010. The magnitude of the increase was similar in both sexes and across all ages. Patients with RA were more likely to be hospitalized for non-cardiovascular causes (RR 1.26; 95%CI 1.14-1.39), but not for HF or other cardiovascular causes compared to non-RA patients.

CONCLUSIONS

The hospitalization rate following HF diagnosis was higher in RA versus non-RA patients regardless of sex and age. Increased hospitalization risk in patients with RA was driven by increased rates of non-cardiovascular hospitalization.

Systematic review of analytical methods applied to longitudinal studies of malaria

BACKGROUND

Modelling risk of malaria in longitudinal studies is common, because individuals are at risk for repeated infections over time. Malaria infections result in acquired immunity to clinical malaria disease. Prospective cohorts are an ideal design to relate the historical exposure to infection and development of clinical malaria over time, and analysis methods should consider the longitudinal nature of the data. Models must take into account the acquisition of immunity to disease that increases with each infection and the heterogeneous exposure to bites from infected Anopheles mosquitoes. Methods that fail to capture these important factors in malaria risk will not accurately model risk of malaria infection or disease.

METHODS

Statistical methods applied to prospective cohort studies of clinical malaria or Plasmodium falciparum infection and disease were reviewed to assess trends in usage of the appropriate statistical methods. The study was designed to test the hypothesis that studies often fail to use appropriate statistical methods but that this would improve with the recent increase in accessibility to and expertise in longitudinal data analysis.

RESULTS

Of 197 articles reviewed, the most commonly reported methods included contingency tables which comprised Pearson Chi-square, Fisher exact and McNemar's tests (n = 102, 51.8%), Student's t-tests (n = 82, 41.6%), followed by Cox models (n = 62, 31.5%) and Kaplan-Meier estimators (n = 59, 30.0%). The longitudinal analysis methods generalized estimating equations and mixed-effects models were reported in 41 (20.8%) and 24 (12.2%) articles, respectively, and increased in use over time. A positive trend in choice of more appropriate analytical methods was identified over time.

CONCLUSIONS

Despite similar study designs across the reports, the statistical methods varied substantially and often represented overly simplistic models of risk. The results underscore the need for more effort to be channelled towards adopting standardized longitudinal methods to analyse prospective cohort studies of malaria infection and disease.

Changes in the Presentation of Incident Gout and the Risk of Subsequent Flares: A Population-based Study over 20 Years

OBJECTIVE

To examine whether a change in the presentation of incident gout happened over the last 20 years and to determine the risk of subsequent gout flares after an initial gout attack.

METHODS

All incident cases of gout were identified among residents of Olmsted County, Minnesota, diagnosed in 1989-1992 and 2009-2010 according to the earliest date fulfilling the 1977 American Rheumatism Association preliminary criteria, or the New York or Rome criteria for gout. Patients in both cohorts were then followed for up to 5 years. Cumulative incidence and person-year methods were used to compare flare rates, and conditional frailty models were used to examine predictors.

RESULTS

A total of 429 patients with incident gout (158 patients in 1989-1992 and 271 patients in 2009-2010) were identified and followed for a mean of 4.2 years. The majority of patients were male (73%) and the mean age (SD) at gout onset was 59.7 (17.3) years. Classic podagra decreased significantly from 74% to 59% (p < 0.001). Cumulative incidence of first flare was similar in both cohorts (62% vs 60% by 5 yrs in 1989-1992 and 2009-2010, respectively; p = 0.70), but overall flare rate was marginally higher in 2009-2010 compared to 1989-1992 (rate ratio: 1.24). Hyperuricemia (HR 1.59) and kidney disease (HR 1.34) were significant predictors of future flares.

CONCLUSION

Gout flares were common in both time periods. Hyperuricemia and kidney disease were predictors of future flares in patients with gout. Podagra as a presentation of gout has become relatively less frequent in recent years.

Event dependence in the analysis of cardiovascular readmissions postpercutaneous coronary intervention

Recurrent hospitalizations are common in longitudinal studies; however, many forms of cumulative event analyses assume recurrent events are independent. We explore the presence of event dependence when readmissions are spaced apart by at least 30 and 60 days. We set up a comparative framework with the assumption that patients with emergency percutaneous coronary intervention (PCI) will be at higher risk for recurrent cardiovascular readmissions than those with elective procedures. A retrospective study of patients who underwent PCI (January 2008-December 2012) with their follow-up information obtained from a regional database for hospitalization was conducted. Conditional gap time (CG), frailty gamma (FG) and conditional frailty models (CFM) were constructed to evaluate the dependence of events. Relative bias (%RB) in point estimates using CFM as the reference was calculated for comparison of the models. Among 4380 patients, emergent cases were at higher risk as compared with elective cases for recurrent events in different statistical models and time-spaced data sets, but the magnitude of HRs varied across the models (adjusted HR [95% CI]: all readmissions [unstructured data]-CG 1.16 [1.09 to 1.22], FG 1.45 [1.33 to 1.57], CFM 1.24 [1.16 to 1.32]; 30-day spaced-CG1.14 [1.08 to 1.21], FG 1.28 [1.17 to 1.39], CFM 1.17 [1.10 to 1.26]; and 60-day spaced-CG 1.14 [1.07 to 1.22], FG 1.23 [1.13 to 1.34] CFM 1.18 [1.09 to 1.26]). For all of the time-spaced readmissions, we found that the values of %RB were closer to the conditional models, suggesting that event dependence dominated the data despite attempts to create independence by increasing the space in time between admissions. Our analysis showed that independent of the intercurrent event duration, prior events have an influence on future events. Hence, event dependence should be accounted for when analyzing recurrent events and challenges contemporary methods for such analysis.

Hospital Readmission among New Dialysis Patients Associated with Young Age and Poor Functional Status

BACKGROUND/AIMS

Over one-third of hospital discharges among dialysis patients are followed by 30-day readmission. The first year after dialysis start is a high-risk time frame. We examined the rate, causes, timing, and predictors of 30-day readmissions among adult, incident dialysis patients.

METHODS

Hospital readmissions were assessed from the 91st day to the 15th month after the initiation of dialysis using a Mayo Clinic registry linkage to United States Renal Data System claims during the period January 2001-December 2010.

RESULTS

Among 1,727 patients with ≥1 hospitalization, 532 (31%) had ≥1, and 261 (15%) had ≥2 readmissions. Readmission rate was 1.1% per person-day post-discharge, and the highest rates (2.5% per person-day) occurred ≤5 days after index admission. The overall cumulative readmission rate was 33.8% at day 30. Common readmission diagnoses included cardiac issues (22%), vascular disorders (19%), and infection (13%). Similar-cause readmissions to index hospitalization were more common during days 0-14 post-discharge than days 15-30 (37.5 vs. 22.9%; p = 0.004). Younger age at dialysis initiation, inability to transfer/ambulate, serum creatinine ≤5.3 mg/dL, higher number of previous hospitalizations, and longer duration on dialysis were associated with higher readmission rates in multivariable analyses. Patients aged 18-39 were few (8.3%) but comprised 17.7% of "high-readmission" users such that a 30-year-old patient had an 87% chance of being readmitted within 30 days of any hospital discharge, whereas an 80-year-old patient had a 25% chance.

CONCLUSIONS

Overall, 30-day readmissions are common within the first year of dialysis start. The first 10-day period after discharge, young patients, and those with poor functional status represent key areas for targeted interventions to reduce readmissions.

Event dependence in U.S. executions

Since 1976, the United States has seen over 1,400 judicial executions, and these have been highly concentrated in only a few states and counties. The number of executions across counties appears to fit a stretched distribution. These distributions are typically reflective of self-reinforcing processes where the probability of observing an event increases for each previous event. To examine these processes, we employ two-pronged empirical strategy. First, we utilize bootstrapped Kolmogorov-Smirnov tests to determine whether the pattern of executions reflect a stretched distribution, and confirm that they do. Second, we test for event-dependence using the Conditional Frailty Model. Our tests estimate the monthly hazard of an execution in a given county, accounting for the number of previous executions, homicides, poverty, and population demographics. Controlling for other factors, we find that the number of prior executions in a county increases the probability of the next execution and accelerates its timing. Once a jurisdiction goes down a given path, the path becomes self-reinforcing, causing the counties to separate out into those never executing (the vast majority of counties) and those which use the punishment frequently. This finding is of great legal and normative concern, and ultimately, may not be consistent with the equal protection clause of the U.S. Constitution.

Faster Blood Flow Rate Does Not Improve Circuit Life in Continuous Renal Replacement Therapy: A Randomized Controlled Trial

OBJECTIVES

To determine whether blood flow rate influences circuit life in continuous renal replacement therapy.

DESIGN

Prospective randomized controlled trial.

SETTING

Single center tertiary level ICU.

PATIENTS

Critically ill adults requiring continuous renal replacement therapy.

INTERVENTIONS

Patients were randomized to receive one of two blood flow rates: 150 or 250 mL/min.

MEASUREMENTS AND MAIN RESULTS

The primary outcome was circuit life measured in hours. Circuit and patient data were collected until each circuit clotted or was ceased electively for nonclotting reasons. Data for clotted circuits are presented as median (interquartile range) and compared using the Mann-Whitney U test. Survival probability for clotted circuits was compared using log-rank test. Circuit clotting data were analyzed for repeated events using hazards ratio. One hundred patients were randomized with 96 completing the study (150 mL/min, n = 49; 250 mL/min, n = 47) using 462 circuits (245 run at 150 mL/min and 217 run at 250 mL/min). Median circuit life for first circuit (clotted) was similar for both groups (150 mL/min: 9.1 hr [5.5-26 hr] vs 10 hr [4.2-17 hr]; p = 0.37). Continuous renal replacement therapy using blood flow rate set at 250 mL/min was not more likely to cause clotting compared with 150 mL/min (hazards ratio, 1.00 [0.60-1.69]; p = 0.68). Gender, body mass index, weight, vascular access type, length, site, and mode of continuous renal replacement therapy or international normalized ratio had no effect on clotting risk. Continuous renal replacement therapy without anticoagulation was more likely to cause clotting compared with use of heparin strategies (hazards ratio, 1.62; p = 0.003). Longer activated partial thromboplastin time (hazards ratio, 0.98; p = 0.002) and decreased platelet count (hazards ratio, 1.19; p = 0.03) were associated with a reduced likelihood of circuit clotting.

CONCLUSIONS

There was no difference in circuit life whether using blood flow rates of 250 or 150 mL/min during continuous renal replacement therapy.

Bayesian regression model for recurrent event data with event-varying covariate effects and event effect

In the course of hypertension, cardiovascular disease events (e.g., stroke, heart failure) occur frequently and recurrently. The scientific interest in such study may lie in the estimation of treatment effect while accounting for the correlation among event times. The correlation among recurrent event times come from two sources: subject-specific heterogeneity (e.g., varied lifestyles, genetic variations, and other unmeasurable effects) and event dependence (i.e., event incidences may change the risk of future recurrent events). Moreover, event incidences may change the disease progression so that there may exist event-varying covariate effects (the covariate effects may change after each event) and event effect (the effect of prior events on the future events). In this article, we propose a Bayesian regression model that not only accommodates correlation among recurrent events from both sources, but also explicitly characterizes the event-varying covariate effects and event effect. This model is especially useful in quantifying how the incidences of events change the effects of covariates and risk of future events. We compare the proposed model with several commonly used recurrent event models and apply our model to the motivating lipid-lowering trial (LLT) component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) (ALLHAT-LLT).

A higher sport-related reinjury risk does not mean inadequate rehabilitation: the methodological challenge of choosing the correct comparison group

Previous injury is a well-established predictor of subsequent injury in sports medicine. Some have interpreted this to mean that either our current methods of rehabilitation are inadequate or there is some permanent damage to the tissue and 100% rehabilitation is not possible. In 2011, we illustrated that these analyses and interpretations failed to account for the fact that some athletes are more prone to get injured, either physiologically, or because of their role/type of play. We suggested that the appropriate analysis would simply require using statistical methods that measured how each individual athlete's risk changed from preinjury to postinjury.In this paper, we revisit our recommendation and illustrate that it too would be flawed if the risk of injury changed over time independent of an injury ever occurring. This might be expected if general fitness were to decline over the season, or if the style of play changed between early season games and postseason championship games. Acknowledging that risk may change regardless of whether an injury occurred or not leads to three different general definitions of 100% rehabilitation: (1) a return to the baseline state, (2) a return to the immediate preinjury state and (3) a return to the state that would have been present had the initial injury never occurred. We guide the reader on how to estimate the risks for each definition and the assumptions that must be acknowledged.

Analyzing recurrent events when the history of previous episodes is unknown or not taken into account: proceed with caution

OBJECTIVE

Researchers in public health are often interested in examining the effect of several exposures on the incidence of a recurrent event. The aim of the present study is to assess how well the common-baseline hazard models perform to estimate the effect of multiple exposures on the hazard of presenting an episode of a recurrent event, in presence of event dependence and when the history of prior-episodes is unknown or is not taken into account.

METHODS

Through a comprehensive simulation study, using specific-baseline hazard models as the reference, we evaluate the performance of common-baseline hazard models by means of several criteria: bias, mean squared error, coverage, confidence intervals mean length and compliance with the assumption of proportional hazards.

RESULTS

Results indicate that the bias worsen as event dependence increases, leading to a considerable overestimation of the exposure effect; coverage levels and compliance with the proportional hazards assumption are low or extremely low, worsening with increasing event dependence, effects to be estimated, and sample sizes.

CONCLUSIONS

Common-baseline hazard models cannot be recommended when we analyse recurrent events in the presence of event dependence. It is important to have access to the history of prior-episodes per subject, it can permit to obtain better estimations of the effects of the exposures.

Mammalian Target of Rapamycin Inhibitors and Clinical Outcomes in Adult Kidney Transplant Recipients

BACKGROUND AND OBJECTIVES

Emerging evidence from recently published observational studies and an individual patient data meta-analysis shows that mammalian target of rapamycin inhibitor use in kidney transplantation is associated with increased mortality. Therefore, all-cause mortality and allograft loss were compared between use and nonuse of mammalian target of rapamycin inhibitors in patients from Australia and New Zealand, where mammalian target of rapamycin inhibitor use has been greater because of heightened skin cancer risk.

DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS

Our longitudinal cohort study included 9353 adult patients who underwent 9558 kidney transplants between January 1, 1996 and December 31, 2012 and had allograft survival ≥1 year. Risk factors for all-cause death and all-cause and death-censored allograft loss were analyzed by multivariable Cox regression using mammalian target of rapamycin inhibitor as a time-varying covariate. Additional analyses evaluated mammalian target of rapamycin inhibitor use at fixed time points of baseline and 1 year.

RESULTS

Patients using mammalian target of rapamycin inhibitors were more likely to be white and have a history of pretransplant cancer. Over a median follow-up of 7 years, 1416 (15%) patients died, and 2268 (24%) allografts were lost. There was a higher risk of all-cause mortality with time-varying mammalian target of rapamycin inhibitor use (hazard ratio, 1.47; 95% confidence interval, 1.23 to 1.76) as well as in the fixed time model analyses comparing mammalian target of rapamycin inhibitor use at baseline (hazard ratio, 1.54; 95% confidence interval, 1.22 to 1.93) and 1 year (hazard ratio, 1.63; 95% confidence interval, 1.32 to 2.01). Time-varying mammalian target of rapamycin inhibitor use was associated with higher risk of death because of malignancy (hazard ratio, 1.37; 95% confidence interval, 1.09 to 1.71). There were no statistically significant differences in the risk of all-cause (hazard ratio, 0.98; 95% confidence interval, 0.85 to 1.12) and death-censored (hazard ratio, 0.85; 95% confidence interval, 0.69 to 1.03) allograft loss between the mammalian target of rapamycin inhibitor use and nonuse groups in the time-varying model as well as the fixed time models.

CONCLUSIONS

Mammalian target of rapamycin inhibitor use was associated with a higher risk of all-cause mortality but not allograft loss.

Safety data from randomized controlled trials: applying models for recurrent events

Simple descriptive listings and inference statistics based on 2×2 tables are still the most common way of summarizing and reporting adverse events data from randomized controlled trials, although these methods do not account for differences in observation times between treatment groups. Using standard methods from survival analysis such as the Cox model or Kaplan-Meier estimates would overcome this problem but limit the analysis to the first safety-related event of each subject. As an alternative, we discuss two models for recurrent events data-the Andersen-Gill and Prentice-Williams-Peterson model-regarding their applicability to safety data from randomized controlled trials. We argue that these models can be used to estimate two different quantities: a direct treatment effect on the risk of an event (Prentice-Williams-Peterson) and a total treatment effect as sum of the direct effect and the treatment's indirect effect via the event history (Anderson-Gill). Using simulated data, we illustrate the difference between these treatment effects and analyze the performance of both models in different scenarios. Because both models are limited to the analysis of cause-specific hazards if competing risks are present, we suggest to incorporate estimates of the mean frequency of events in the analysis to additionally allow the comparison of treatment effects on absolute event probabilities. We demonstrate the application of both models and the mean frequency function to safety endpoints with an illustrative analysis of data from a randomized phase-III study. Copyright © 2016 John Wiley & Sons, Ltd.

Does Prison Crowding Predict Higher Rates of Substance Use Related Parole Violations? A Recurrent Events Multi-Level Survival Analysis

Objective

This administrative data-linkage cohort study examines the association between prison crowding and the rate of post-release parole violations in a random sample of prisoners released with parole conditions in California, for an observation period of two years (January 2003 through December 2004).

Background

Crowding overextends prison resources needed to adequately protect inmates and provide drug rehabilitation services. Violence and lack of access to treatment are known risk factors for drug use and substance use disorders. These and other psychosocial effects of crowding may lead to higher rates of recidivism in California parolees.

Methods

Rates of parole violation for parolees exposed to high and medium levels of prison crowding were compared to parolees with low prison crowding exposure. Hazard ratios (HRs) with 95% confidence intervals (CIs) were estimated using a Cox model for recurrent events. Our dataset included 13070 parolees in California, combining individual level parolee data with aggregate level crowding data for multilevel analysis.

Results

Comparing parolees exposed to high crowding with those exposed to low crowding, the effect sizes from greatest to least were absconding violations (HR 3.56 95% CI: 3.05–4.17), drug violations (HR 2.44 95% CI: 2.00–2.98), non-violent violations (HR 2.14 95% CI: 1.73–2.64), violent and serious violations (HR 1.88 95% CI: 1.45–2.43), and technical violations (HR 1.86 95% CI: 1.37–2.53).

Conclusions

Prison crowding predicted higher rates of parole violations after release from prison. The effect was magnitude-dependent and particularly strong for drug charges. Further research into whether adverse prison experiences, such as crowding, are associated with recidivism and drug use in particular may be warranted.

A Randomized Controlled Trial of Regional Citrate Versus Regional Heparin Anticoagulation for Continuous Renal Replacement Therapy in Critically Ill Adults

OBJECTIVE

To determine whether regional anticoagulation of continuous renal replacement therapy circuits using citrate and calcium prolongs circuit life and/or affects circulating cytokine levels compared with regional anticoagulation using heparin and protamine.

DESIGN

Multicenter, parallel group randomized controlled trial.

SETTING

Seven ICUs in Australia and New Zealand.

PATIENTS

Critically ill adults requiring continuous renal replacement therapy.

INTERVENTIONS

Patients were randomized to receive one of two methods of regional circuit anticoagulation: citrate and calcium or heparin and protamine.

MEASUREMENTS AND MAIN RESULTS

The primary outcome was functional circuit life measured in hours, assessed using repeated events survival analysis. In addition, we measured changes in interleukin-6, interleukin-8, and interleukin-10 blood levels. We randomized 212 subjects who were treated with 857 continuous renal replacement therapy circuits (median 2 circuits per patient [interquartile range, 1-6], 390 in citrate group vs 467 in heparin group). The groups were well matched for baseline characteristics. Patients receiving regional continuous renal replacement therapy anticoagulation with heparin and protamine were more likely to experience circuit clotting than those receiving citrate and calcium (hazard ratio, 2.03 [1.36-3.03]; p < 0.0005; 857 circuits). The median lifespan of the first study circuit in each patient was 39.2 hours (95% CI, 32.1-48.0 hr) in the citrate and calcium group versus 22.8 hours (95% CI, 13.3-34.0 hr) in the heparin and protamine group (log rank p = 0.0037, 204 circuits). Circuit anticoagulation with citrate and calcium had similar effects on cytokine levels compared with heparin and protamine anticoagulation. There were more adverse events in the group assigned to heparin and protamine anticoagulation (11 vs 2; p = 0.011).

CONCLUSIONS

Regional citrate and calcium anticoagulation prolongs continuous renal replacement therapy circuit life compared with regional heparin and protamine anticoagulation, does not affect cytokine levels, and is associated with fewer adverse events.

Effectiveness of two year balance training programme on prevention of fall induced injuries in at risk women aged 75-85 living in community: Ossébo randomised controlled trial

OBJECTIVE

To assess the effectiveness of a two year exercise programme of progressive balance retraining in reducing injurious falls among women aged 75-85 at increased risk of falls and injuries and living in the community.

DESIGN

Pragmatic multicentre, two arm, parallel group, randomised controlled trial.

SETTING

20 study sites in 16 medium to large cities throughout France.

PARTICIPANTS

706 women aged 75-85, living in their own home, and with diminished balance and gait capacities, randomly allocated to the experimental intervention group (exercise programme, n=352) or the control group (no intervention, n=354).

INTERVENTION

Weekly supervised group sessions of progressive balance training offered in community based premises for two years, supplemented by individually prescribed home exercises.

OUTCOME MEASURES

A geriatrician blinded to group assignment classified falls into one of three categories (no consequence, moderate, severe) based on physical damage and medical care. The primary outcome was the rate of injurious falls (moderate and severe). The two groups were compared for rates of injurious falls with a "shared frailty" model. Other outcomes included the rates of all falls, physical functional capacities (balance and motor function test results), fear of falling (FES-I), physical activity level, and perceived health related quality of life (SF-36). Analysis was by intention to treat.

RESULTS

There were 305 injurious falls in the intervention group and 397 in the control group (hazard ratio 0.81, 95% confidence interval 0.67 to 0.99). The difference in severe injuries (68 in intervention group v 87 in control group) was of the same order of magnitude (0.83, 0.60 to 1.16). At two years, women in the intervention group performed significantly better on all physical tests and had significantly better perception of their overall physical function than women in the control group. Among women who started the intervention (n=294), the median number of group sessions attended was 53 (interquartile range 16-71). Five injurious falls related to the intervention were recorded.

CONCLUSION

A two year progressive balance retraining programme combining weekly group and individual sessions was effective in reducing injurious falls and in improving measured and perceived physical function in women aged 75-85 at risk of falling.Trial registration ClinicalTrials.gov (NCT00545350).

The effect of oral immunomodulatory therapy on treatment uptake and persistence in multiple sclerosis

Objective:

We aimed to analyse the effect of the introduction of fingolimod, the first oral disease-modifying therapy, on treatment utilisation and persistence in an international cohort of patients with multiple sclerosis (MS).

Methods:

MSBASIS, a prospective, observational sub-study of the MSBase registry, collects demographic, clinical and paraclinical data on patients followed from MS onset ( n=4718). We conducted a multivariable conditional risk set survival analysis to identify predictors of treatment discontinuation, and to assess if the introduction of fingolimod has altered treatment persistence.

Results:

A total of 2640 patients commenced immunomodulatory therapy. Following the introduction of fingolimod, patients were more likely to discontinue all other treatments (hazard ratio 1.64, p<0.001) while more patients switched to fingolimod than any other therapy (42.3% of switches). Patients switched to fingolimod due to convenience. Patients treated with fingolimod were less likely to discontinue treatment compared with other therapies ( p<0.001). Female sex, country of residence, younger age, a high Expanded Disability Status Scale score and relapse activity were all independently associated with higher rates of treatment discontinuation.

Conclusion:

Following the availability of fingolimod, patients were more likely to discontinue injectable treatments. Those who switched to fingolimod were more likely to do so for convenience. Persistence was improved on fingolimod compared to other medications.

Analysis of Preventive Interventions for Malaria: Exploring Partial and Complete Protection and Total and Primary Intervention Effects

Event dependence, the phenomenon in which future risk depends on past disease history, is not commonly accounted for in the statistical models used by malaria researchers. However, recently developed methods for the analysis of repeated events allow this to be done, while also accounting for heterogeneity in risk and nonsusceptible subgroups. Accounting for event dependence allows separation of the primary effect of an intervention from its total effect, which is composed of its primary effect on risk of disease and its secondary effect mediated by event dependence. To illustrate these methods and show the insights they can provide, we have reanalyzed 2 trials of seasonal malaria chemoprevention (SMC) in Boussé, Burkina Faso, and Kati, Mali, in 2008–2009, as well as a trial of intermittent preventive treatment of malaria in infants in Navrongo, Ghana, in 2000–2004. SMC completely protects a large fraction of recipients, while intermittent preventive treatment in infants provides modest partial protection, consistent with the rationale of these 2 different chemopreventive approaches. SMC has a primary effect that is substantially greater than the total effect previously estimated by trials, with the lower total effect mediated by negative event dependence. These methods contribute to an understanding of the mechanisms of protection from these interventions and could improve understanding of other tools to control malaria, including vaccines.

Longitudinal studies 3: Data modeling using standard regression models and extensions

In longitudinal studies the relationship between exposure and disease can be measured once or multiple times while participants are monitored over time. Traditional regression techniques are used to model outcome data when each epidemiological unit is observed once. These models include generalized linear models for quantitative continuous, discrete, or qualitative outcome responses, and models for time-to-event data. When data come from the same subjects or group of subjects, observations are not independent and the underlying correlation needs to be addressed in the analysis. In these circumstances extended models are necessary to handle complexities related to clustered data, and repeated measurements of time-varying predictors and/or outcomes.

A joint frailty model to estimate the recurrence process and the disease-specific mortality process without needing the cause of death

In chronic diseases, such as cancer, recurrent events (such as relapses) are commonly observed; these could be interrupted by death. With such data, a joint analysis of recurrence and mortality processes is usually conducted with a frailty parameter shared by both processes. We examined a joint modeling of these processes considering death under two aspects: 'death due to the disease under study' and 'death due to other causes', which enables estimating the disease-specific mortality hazard. The excess hazard model was used to overcome the difficulties in determining the causes of deaths (unavailability or unreliability); this model allows estimating the disease-specific mortality hazard without needing the cause of death but using the mortality hazards observed in the general population. We propose an approach to model jointly recurrence and disease-specific mortality processes within a parametric framework. A correlation between the two processes is taken into account through a shared frailty parameter. This approach allows estimating unbiased covariate effects on the hazards of recurrence and disease-specific mortality. The performance of the approach was evaluated by simulations with different scenarios. The method is illustrated by an analysis of a population-based dataset on colon cancer with observations of colon cancer recurrences and deaths. The benefits of the new approach are highlighted by comparison with the 'classical' joint model of recurrence and overall mortality. Moreover, we assessed the goodness of fit of the proposed model. Comparisons between the conditional hazard and the marginal hazard of the disease-specific mortality are shown, and differences in interpretation are discussed.

Data generation for the Cox proportional hazards model with time-dependent covariates: a method for medical researchers

The proliferation of longitudinal studies has increased the importance of statistical methods for time-to-event data that can incorporate time-dependent covariates. The Cox proportional hazards model is one such method that is widely used. As more extensions of the Cox model with time-dependent covariates are developed, simulations studies will grow in importance as well. An essential starting point for simulation studies of time-to-event models is the ability to produce simulated survival times from a known data generating process. This paper develops a method for the generation of survival times that follow a Cox proportional hazards model with time-dependent covariates. The method presented relies on a simple transformation of random variables generated according to a truncated piecewise exponential distribution and allows practitioners great flexibility and control over both the number of time-dependent covariates and the number of time periods in the duration of follow-up measurement. Within this framework, an additional argument is suggested that allows researchers to generate time-to-event data in which covariates change at integer-valued steps of the time scale. The purpose of this approach is to produce data for simulation experiments that mimic the types of data structures applied that researchers encounter when using longitudinal biomedical data. Validity is assessed in a set of simulation experiments, and results indicate that the proposed procedure performs well in producing data that conform to the assumptions of the Cox proportional hazards model.

Concordance measures in shared frailty models: application to clustered data in cancer prognosis

Frailty models are gaining interest in prognostic studies, especially because of the spread of multicenter studies. However, little research has been performed to extend prognostic tools to frailty models, including discrimination measures. As previously performed for the Harrell's c-index, we extended two different discrimination measures (the model-based concordance probability estimation of Gönen and Heller and the nonparametric Uno's c-index) to take into account cluster membership. We calculate measures at three levels: between-group, where only patients with different frailties are compared, within-group, where only patients sharing the same frailty are compared, and overall. We performed simulations to study the impact of group size and the number of groups on these measures. Results showed that the two measures can be extended to frailty models while remaining independent from censoring distribution, provided that the group size is sufficient. We apply the extended measures to two real datasets, a meta-analysis and a large multicenter trial.

Heterogeneity and event dependence in the analysis of sickness absence

BACKGROUND

Sickness absence (SA) is an important social, economic and public health issue. Identifying and understanding the determinants, whether biological, regulatory or, health services-related, of variability in SA duration is essential for better management of SA. The conditional frailty model (CFM) is useful when repeated SA events occur within the same individual, as it allows simultaneous analysis of event dependence and heterogeneity due to unknown, unmeasured, or unmeasurable factors. However, its use may encounter computational limitations when applied to very large data sets, as may frequently occur in the analysis of SA duration.

METHODS

To overcome the computational issue, we propose a Poisson-based conditional frailty model (CFPM) for repeated SA events that accounts for both event dependence and heterogeneity. To demonstrate the usefulness of the model proposed in the SA duration context, we used data from all non-work-related SA episodes that occurred in Catalonia (Spain) in 2007, initiated by either a diagnosis of neoplasm or mental and behavioral disorders.

RESULTS

As expected, the CFPM results were very similar to those of the CFM for both diagnosis groups. The CPU time for the CFPM was substantially shorter than the CFM.

CONCLUSIONS

The CFPM is an suitable alternative to the CFM in survival analysis with recurrent events, especially with large databases.

Risk of repeated febrile episodes during chemotherapy-induced granulocytopenia in children with cancer: a prospective single center study

BACKGROUND

Febrile neutropenia (FN) is a possible complication of antineoplastic chemotherapy. Aim of the study was to estimate the risk of developing fever at the beginning of any neutropenic period based on the previous history of FN.

PROCEDURE

The conditional frailty model was used to estimate the risk of developing fever during neutropenia separately for children with acute leukaemia/non-Hodgkin lymphoma (AL/NHL), or solid tumour (ST). The total number of previous FN episodes (PFNE), age, gender, type of tumour, calendar year of granulocytopenic period, phase of treatment, and granulocyte count were included in the model.

RESULTS

A total of 901 granulocytopenic periods was observed in 223 children: 306 in 66 AL/NHL and 595 in 157 ST. Fever developed in 328 cases: 125 in 53 AL/NHL and 203 in 92 ST. The PFNE variable was not significantly associated to the risk of fever [hazard ratio (HR) of 0.87, 95% confidence interval (CI) of 0.62-1.22 in children with AL/NHL, and HR of 0.98, 95% CI of 0.70-1.37 in those with ST]. The hazard of FN was significantly affected by the phase of treatment in AL/NHL (P<0.01), and by the level of neutropenia at onset in ST (P<0.01).

CONCLUSIONS

Previous history of FN does not increase the risk of further febrile episodes in any new subsequent granulocytopenic period. The aggressiveness of chemotherapy and the level of neutropenia at onset are the most important risk factors in children with AL/NHL and with ST respectively.