Comparison of methods for analyzing recurrent events data: application to the Emergency Department Visits of Pediatric Firearm Victims

Prediction of Multiple Recurrent Events: A Comparison of Extended Cox Models in Bladder Cancer

Recurrence of bladder cancer can occur repeatedly in the same patient after treatment of the primary tumor. Models predicting the risk of a next recurrence may inform individualized decision-making on surveillance frequency. We aimed to assess the usefulness of extensions of the Cox proportional hazards model for repeated events in this context. We analyzed 531 Dutch patients with bladder cancer (1990-2012) with information on 7 prespecified predictors at the time of diagnosis of the primary and recurrent tumors. We considered 3 aspects of model variants: how to model time to the repeated events (calendar time, gap time, elapsed time); the number of preceding events (predictor, stratum variable); and the within-subject correlation (ignored in a simple Cox model, robust standard errors in a variance-correction model, random effect in a frailty model). First to fourth recurrences of bladder cancer occurred in 313, 174, 103, and 66 patients, respectively, with median calendar follow-up times of 1.1, 2.5, 3.8, and 4.5 years, respectively. We focused on gap time in the detailed analyses, allowing for clinically meaningful predictions. Variance-correction models may be useful if predictor selection is part of the model development. Frailty models may be useful when within-subject correlation is strong.

T2238C ANP gene variant and risk of recurrent acute coronary syndromes in an Italian cohort of ischemic heart disease patients

BACKGROUND

The role of C2238/atrial natriuretic peptide (ANP) minor allele, at the T2238C ANP gene variant, as a predisposing risk factor for acute cardiovascular events, has been previously reported. We aimed at evaluating, by a retrospective approach, the long-term impact of C2238/ANP-minor allele carrier status toward the risk of recurrent acute coronary syndromes (re-ACS) in an Italian cohort of ischemic heart disease patients.

METHODS

A total of 379 patients (males = 80.5%; mean age = 62.5 ± 9.2 years) presenting with ACS were retrospectively analyzed. Mean follow-up was 5.1 ± 3.5 years (range 1-26 years). Occurrence of new episodes of unstable angina, non-ST-segment elevation myocardial infarction and STE myocardial infarction over the years was recorded and compared between subjects not carrying and carrying C2238/ANP-minor allele.

RESULTS

At univariate analysis, C2238/ANP-minor allele carrier status and treatment with beta-blocker, aspirin and statin were associated with risk of re-ACS. Multivariate analysis confirmed that hypercholesterolemia (P < 0.0001) and C2238/ANP-minor allele carrier status (P < 0.05) were both significantly and independently associated with increased risk of re-ACS. Both treatments with beta-blocker and with statin were significantly associated with reduced risk of re-ACS (P = 0.01 and P < 0.01, respectively). Age above 55 years was associated with recurrence of ACS in C2238/ANP-minor allele carriers (hazard ratio 1.427, 95% confidence interval 1.066-1.911, P = 0.017). Kaplan-Meier curves confirmed highest risk of new events occurrence in C2238/ANP-minor allele carriers (P = 0.035).

CONCLUSIONS

The present results demonstrate that C2238/ANP-minor allele carrier status is an independent risk factor for ACS recurrence in an Italian cohort of ischemic heart disease patients over the long term, and they support the role of C2238/ANP-minor allele as a negative prognostic factor in coronary artery disease patients.

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.

Boston Violence Intervention Advocacy Program: a qualitative study of client experiences and perceived effect

OBJECTIVES

This study intended to explore clients' experiences and provide a contextual basis for understanding their perceptions of the effectiveness of the Boston Medical Center (BMC) Violence Intervention Advocacy Program (VIAP).

METHODS

This was an exploratory, qualitative study conducted in an urban, Level I trauma center from July 1, 2011 to February 24, 2012. Emergency department (ED) patients older than 18 years with penetrating trauma, and who were enrolled in the VIAP, were eligible. Two trained, qualitative interviewers who were not part of the VIAP obtained consent and conducted in-depth, semistructured interviews. Interviews were audiotaped, transcribed, deidentified, coded, and analyzed. Thematic content analysis consistent with grounded theory was used to identify themes related to client experiences with VIAP, life circumstances, challenges to physical and emotional healing postinjury, services provided by VIAP, and perceptions of VIAP's effectiveness.

RESULTS

Twenty subjects were interviewed. Most were male, African American, and younger than 30 years of age, reflecting the overall program's clientele. Most subjects perceived their advocates as caring adults in their lives and cited aspects of the peer support model that helped establish trusting relationships. Major challenges to healing were fear and safety, trust, isolation as a coping mechanism, bitterness, and symptoms of posttraumatic stress disorder (PTSD). Every subject noted important services provided by VIAP advocates. Most subjects explicitly stated that they had positive experiences with the VIAP and perceived advocates' roles as a positive influence, providing client-centered advocacy, education, and support.

CONCLUSIONS

This study provides insight into the lives of 20 BMC VIAP clients and contextualizes their unique challenges. Participants described positive, life-changing behaviors on their journey to healing through connections to caring, supportive adults. Information gained from this study will help the VIAP to further support its clients. However, future research is needed to identify best practices for ED-based violence intervention programs and to measure community-wide efficacy in different settings.

The revolving door phenomenon revisited: time to readmission in 17’145 [corrected] patients with 37'697 hospitalisations at a German psychiatric hospital

Objective

Despite the recurring nature of the disease process in many psychiatric patients, individual careers and time to readmission rarely have been analysed by statistical models that incorporate sequence and velocity of recurrent hospitalisations. This study aims at comparing four statistical models specifically designed for recurrent event history analysis and evaluating the potential impact of predictor variables from different sources (patient, treatment process, social environment).

Method

The so called Andersen-Gil counting process model, two variants of the conditional models of Prentice, Williams, and Peterson (gap time model, conditional probability model), and the so called frailty model were applied to a dataset of 17’415 patients observed during a 12 years period starting from 1996 and leading to 37’697 psychiatric hospitalisations. Potential prognostic factors stem from a standardized patient documentation form.

Results

Estimated regression coefficients over different models were highly similar, but the frailty model best represented the sequentiality of individual treatment careers and differing velocities of disease progression. It also avoided otherwise likely misinterpretations of the impact of gender, partnership, historical time and length of stay. A widespread notion of psychiatric diseases as inevitably chronic and worsening could be rejected. Time in community was found to increase over historical time for all patients. Most important protective factors beyond diagnosis were employment, partnership, and sheltered living situation. Risky conditions were urban living and a concurrent substance use disorder.

Conclusion

Prognostic factors for course of diseases should be determined only by statistical models capable of adequately incorporating the recurrent nature of psychiatric illnesses.

Empirical comparison of methods for analyzing multiple time-to-event outcomes in a non-inferiority trial: a breast cancer study

BACKGROUND

Subjects with breast cancer enrolled in trials may experience multiple events such as local recurrence, distant recurrence or death. These events are not independent; the occurrence of one may increase the risk of another, or prevent another from occurring. The most commonly used Cox proportional hazards (Cox-PH) model ignores the relationships between events, resulting in a potential impact on the treatment effect and conclusions. The use of statistical methods to analyze multiple time-to-event events has mainly been focused on superiority trials. However, their application to non-inferiority trials is limited. We evaluate four statistical methods for multiple time-to-event endpoints in the context of a non-inferiority trial.

METHODS

Three methods for analyzing multiple events data, namely, i) the competing risks (CR) model, ii) the marginal model, and iii) the frailty model were compared with the Cox-PH model using data from a previously-reported non-inferiority trial comparing hypofractionated radiotherapy with conventional radiotherapy for the prevention of local recurrence in patients with early stage breast cancer who had undergone breast conserving surgery. These methods were also compared using two simulated examples, scenario A where the hazards for distant recurrence and death were higher in the control group, and scenario B. where the hazards of distant recurrence and death were higher in the experimental group. Both scenarios were designed to have a non-inferiority margin of 1.50.

RESULTS

In the breast cancer trial, the methods produced primary outcome results similar to those using the Cox-PH model: namely, a local recurrence hazard ratio (HR) of 0.95 and a 95% confidence interval (CI) of 0.62 to 1.46. In Scenario A, non-inferiority was observed with the Cox-PH model (HR = 1.04; CI of 0.80 to 1.35), but not with the CR model (HR = 1.37; CI of 1.06 to 1.79), and the average marginal and frailty model showed a positive effect of the experimental treatment. The results in Scenario A contrasted with Scenario B with non-inferiority being observed with the CR model (HR = 1.10; CI of 0.87 to 1.39), but not with the Cox-PH model (HR = 1.46; CI of 1.15 to 1.85), and the marginal and frailty model showed a negative effect of the experimental treatment.

CONCLUSION

When subjects are at risk for multiple events in non-inferiority trials, researchers need to consider using the CR, marginal and frailty models in addition to the Cox-PH model in order to provide additional information in describing the disease process and to assess the robustness of the results. In the presence of competing risks, the Cox-PH model is appropriate for investigating the biologic effect of treatment, whereas the CR models yields the actual effect of treatment in the study.

Effect of recent diarrhoeal episodes on risk of pneumonia in children under the age of 5 years in Karachi, Pakistan

BACKGROUND

We assessed the association between the duration of diarrhoea and the risk ofpneumonia incidence among children <5 years of age.

METHODS

We analysed data from a cluster randomized controlled trial in Karachi, Pakistan, which assessed the effect of promoting hand washing with soap (antibacterial and plain) on child health. Field workers visited households with children <5 years of age weekly and asked primary caregivers if their child had diarrhoea, cough or difficulty breathing in the preceding week. We used the WHO clinical case definitions for diarrhoea and pneumonia.We used adjusted time-to-event analyses with cumulative diarrhoea prevalence over the previous 2 and 4 weeks as exposure and pneumonia as outcome. We calculated the attributable risk of pneumonia due to recent diarrhoea across the intervention groups.

RESULTS

873 households with children <5 years were visited. Children had an increased risk of pneumonia for every additional day of diarrhoea in the 2 weeks (1.06, 95% CI: 1.03-1.09) and 4 weeks (1.04, 95% CI: 1.03-1.06) prior to the week of pneumonia onset. The attributable risk of pneumonia cases due to recent exposure to diarrhoea was 6%. A lower associated pneumonia risk following diarrhoea was found in the control group: (3%) compared with soap groups (6% in antibacterial soap, 9% in plain soap).

CONCLUSION

Children <5 years of age are at an increased risk of pneumonia following recent diarrhoeal illness. Public health programmes that prevent diarrhoea may also reduce the burden of respiratory illnesses.

Statistical modelling for recurrent events: an application to sports injuries

BACKGROUND

Injuries are often recurrent, with subsequent injuries influenced by previous occurrences and hence correlation between events needs to be taken into account when analysing such data.

OBJECTIVE

This paper compares five different survival models (Cox proportional hazards (CoxPH) model and the following generalisations to recurrent event data: Andersen-Gill (A-G), frailty, Wei-Lin-Weissfeld total time (WLW-TT) marginal, Prentice-Williams-Peterson gap time (PWP-GT) conditional models) for the analysis of recurrent injury data.

METHODS

Empirical evaluation and comparison of different models were performed using model selection criteria and goodness-of-fit statistics. Simulation studies assessed the size and power of each model fit.

RESULTS

The modelling approach is demonstrated through direct application to Australian National Rugby League recurrent injury data collected over the 2008 playing season. Of the 35 players analysed, 14 (40%) players had more than 1 injury and 47 contact injuries were sustained over 29 matches. The CoxPH model provided the poorest fit to the recurrent sports injury data. The fit was improved with the A-G and frailty models, compared to WLW-TT and PWP-GT models.

CONCLUSIONS

Despite little difference in model fit between the A-G and frailty models, in the interest of fewer statistical assumptions it is recommended that, where relevant, future studies involving modelling of recurrent sports injury data use the frailty model in preference to the CoxPH model or its other generalisations. The paper provides a rationale for future statistical modelling approaches for recurrent sports injury.

Effect of prison-based opioid substitution treatment and post-release retention in treatment on risk of re-incarceration

AIMS

People who use heroin are frequently incarcerated multiple times. Reducing re-incarceration of this group is important for reducing both health risks associated with incarceration and the costs of correctional administration. Opioid substitution treatment (OST) in prisons may help to reduce re-incarceration, but research findings on this topic have been mixed. In this study, we examined the effect of OST in prison and after release on re-incarceration.

DESIGN

Longitudinal cohort study. SETTING, PARTICIPANTS AND MEASUREMENTS: Data on OST and incarceration were linked for a cohort of 375 male heroin users recruited originally in prisons in New South Wales, Australia. Data were linked for the period 1 June 1997-31 December 2006. Re-incarceration was examined using recurrent-event survival analysis models. Model 1 examined the effect of OST status at release from prison (i.e. in treatment versus out of treatment on the day of release) on re-incarceration. Model 2 considered the effect of remaining in OST after release on risk of re-incarceration.

FINDINGS

Ninety per cent of participants were re-incarcerated following their first observed release. Pre-incarceration cocaine use was associated with a 13% increase in the average risk of re-incarceration. There was no significant association between simply being in OST at the time of release and risk of re-incarceration; however, in the model taking into account post-release retention in treatment, the average risk of re-incarceration was reduced by 20% while participants were in treatment.

CONCLUSIONS

In New South Wales, Australia, opioid substitution treatment after release from prison has reduced the average risk of re-incarceration by one-fifth.

Additive and multiplicative hazards modeling for recurrent event data analysis

BACKGROUND

Sequentially ordered multivariate failure time or recurrent event duration data are commonly observed in biomedical longitudinal studies. In general, standard hazard regression methods cannot be applied because of correlation between recurrent failure times within a subject and induced dependent censoring. Multiplicative and additive hazards models provide the two principal frameworks for studying the association between risk factors and recurrent event durations for the analysis of multivariate failure time data.

METHODS

Using emergency department visits data, we illustrated and compared the additive and multiplicative hazards models for analysis of recurrent event durations under (i) a varying baseline with a common coefficient effect and (ii) a varying baseline with an order-specific coefficient effect.

RESULTS

The analysis showed that both additive and multiplicative hazards models, with varying baseline and common coefficient effects, gave similar results with regard to covariates selected to remain in the model of our real dataset. The confidence intervals of the multiplicative hazards model were wider than the additive hazards model for each of the recurrent events. In addition, in both models, the confidence interval gets wider as the revisit order increased because the risk set decreased as the order of visit increased.

CONCLUSIONS

Due to the frequency of multiple failure times or recurrent event duration data in clinical and epidemiologic studies, the multiplicative and additive hazards models are widely applicable and present different information. Hence, it seems desirable to use them, not as alternatives to each other, but together as complementary methods, to provide a more comprehensive understanding of data.

Psychosocial assessment and repetition of self-harm: the significance of single and multiple repeat episode analyses

BACKGROUND

Self-harm is a common reason for presentation to the Emergency Department. An important question is whether psychosocial assessment reduces risk of repeated self-harm. Repetition has been investigated with survival analysis using various models, though many are not appropriate for recurrent events.

METHODS

Survival analysis was used to investigate associations between psychosocial assessment following an episode of self-harm and subsequent repetition, including (i) one repeat, and (ii) recurrent repetition (≤5 repeats) using (a) an independent episodes model, and (b) a stratified episodes model based on a conditional risk set. Data were from the Multicentre Study on Self-harm in England, 2000 to 2007.

RESULTS

Psychosocial assessment following an index episode of self-harm was associated with a 51% (95% CI 42%-58%) decreased risk of a repeat episode in persons with no psychiatric treatment history, and 26% (95% CI 8%-34%) decreased risk in those with a treatment history. For recurrent repetition, assessment was associated with a 57% (95% CI 51%-63%) decreased risk of repetition assuming independent episodes, and 13% (95% CI 1%-24%) decreased risk accounting for ordering and correlation of episodes by the same person (stratified episodes model). All models controlled for age, gender, method, history of self-harm, and centre differences.

LIMITATIONS

Some missing data on psychiatric treatment for non-assessed patients.

CONCLUSIONS

Psychosocial assessment appeared to be beneficial in reducing the risk of repetition, especially in the short-term. Findings for recurrent repetition were highly dependent on model assumptions. Analyses should fully account for ordering and correlation of episodes by the same person.

Semi-parametric additive risk models: application to injury duration study

In survival analysis, the Cox model is a multiplicative model and widely used in survival analysis. However, the assumption of proportional hazards in the Cox multiplicative model is a crucial one that needs to be fulfilled for the results to be meaningful. When proportionality is a questionable assumption, an alternative but less widely used method is additive model. The additive hazards model assumes that covariates act in an additive manner on an unknown baseline hazard rate. Using the emergency department (ED) visits data, we demonstrated the additive hazards regression models and showed the differences in estimates obtained by the additive hazards models and the Cox model. In our study, the Cox model gave a higher estimate than the additive hazards model. However, both models revealed similar results with regard to covariates selected to remain in the model and the estimated survival functions based on the Cox and additive hazards models were almost identical. Since Cox and additive hazards models give different aspects of the association between risk factors and the study outcome, it seems desirable to use together to give a more comprehensive understanding of data.

Analyzing the occurrence of falls and its risk factors: some considerations

OBJECTIVE

Falls are a common problem facing elderly people and are associated with considerable mortality and morbidity. The objective of this paper is to study the application of the conditional model as an alternative for the statistical analysis of the occurrence of falls and their associated factors.

METHODS

Cohort study. We select all ninety-eight residents admitted during the year 2007 in a long-term care centre, Seville, Spain. Five models were fitted: Negative binomial, standard Cox for the first fall, standard Cox for all falls, Andersen-Gill model, and Prentice-Williams-Peterson model.

RESULTS

The crude incidence rate of falls was 26.3 per 100 person-months. The median time to fall decreases depending on the falls previously experienced, while the hazard rises. The AG's standard errors are between 1.4 and 2.7 times bigger than those estimated by Standard Cox. The major differences between marginal models were in the "Barthel 25-60" coefficient, where the conditional model attributed an HR=2.39 versus HR=3.77 estimated by the extension model.

CONCLUSION

As the risk increases depending on the falls previously suffered by an individual, the PWP-conditional model becomes an interesting alternative for obtaining unbiased and precise estimations of coefficients associated with possible risk factors of falls.