Comparison of Methods for Analyzing Recurrent Events Data: Application to the Emergency Department Visits of Pediatric Firearm Victims

https://doi.org/10.1016/j.aap.2006.07.009Get rights and content

Abstract

In many medical conditions subjects can experience recurrent incidents. A common feature for the recurrent events data and multi-stage failure time observations is that the events are naturally ordered and occur in a certain sequence over time. To analyze such data, conventional methods based on either the frequency of events or the time to the first event or overall survival time is often inefficient and unsophisticated. If data have repeated events over a period with censored failure time in longitudinal studies, more complex analytic approaches are needed to obtain accurate estimates and efficient inferences, because adjustment is necessary for existing correlation between recurrent failure times within a subject. For analyzing different kinds of recurrent event data we review the existing models—multiple failure time models and frailty models, which allow use of all the available information to accurately estimate the relative risks of recurrences in a given dataset. Using the Pediatric Firearm Victim's Emergency Department Visit Study, the results from the proposed models are compared, and applicability and appropriateness of each model are discussed.

Introduction

In many medical conditions subjects can experience recurrent incidents. A common feature for the recurrent events data is that the events are naturally ordered and occur in a certain sequence over time. Examples of such data include tumor recurrences, epileptic seizures, asthma attacks, migraines, infectious episodes, myocardial infarctions, injuries, and admissions to hospital. To analyze such data in both observational studies and randomized clinical trials, many investigators estimate and compare the event rates using less than optimal statistical approaches. Conventional analysis is based on either the frequency of events using the chi-square test or the time to the first event or overall survival time using the Cox proportional hazards model (Cox, 1972). Such conventional methods are inefficient because they do not consider the duration of treatment, and do not take into account all the available information in the data, and so often produce misleading conclusions. If data have repeated events over a period with censored failure time in longitudinal studies, even more complex analytic approaches are needed to obtain accurate estimates and efficient inferences, because adjustment is necessary for existing correlation between recurrent failure times within a subject.

To obtain efficient inference procedures for a covariate effect over time, we propose to utilize multiple failure time models, which take into account the underlying correlation between recurrence times. We also propose to apply the frailty model, which has been used mainly for family data (Guo, 1993, Hougaard et al., 1992, Pickles et al., 1994, Thomas et al., 1990, Yashin and Iachine, 1995), but not often for recurrent event data (Aalen et al., 1995). Multiple failure time models and frailty models allow use of all the available information to accurately estimate the relative risk of recurrence. We focus on applying and examining the multiple failure time models and the frailty model to recurrent event data of pediatric firearm victims.

The main aim of this article is to show the differences in estimates and interpretation obtained by several approaches for recurrent events data analysis and to provide an insight into the choice of appropriate models according to a given recurrent event data and research objectives. In our study we consider one particular application, namely the Emergency Department (ED) Visits of the Pediatric Firearm Victims. In this study, clearly some difference between subjects is expected. Each subject has a number of ED visits and contributes several observations, which will be dependent if there is inter-subject variation. Using the Pediatric Firearm Victim's ED Visit Study, the results from the proposed models are compared, and applicability and appropriateness of each model to this type of data are discussed. To provide accurate parameter estimation of recurrence time distribution, we utilize available methodologies discussed in Section 3: the multiple failure time models as extension of the Cox proportional hazards model with Markov assumption, conditional approach, marginal approach, and random effects approach.

Four additional sections comprise this paper. In Section 2, a description of the Pediatric Firearm Victim's ED Visit Study is provided. In Section 3, the methods for analysis of recurrent event data are reviewed. In Section 4, these methods are applied to the Pediatric Firearm Victim's ED Visit Study. Section 5 contains a discussion, and applicability and appropriateness of each model are discussed.

Section snippets

Clinical background

Fatal and non-fatal firearm-related injuries remain an important public health issue (Miller et al., 2001, Miller et al., 2002). Estimated non-fatal firearm injury rate is 119 per 100,000 person-years for age 15–24 years olds. In Wisconsin in 2003, intentional firearm injury is the leading cause of death among African American males aged 12–18, with an estimated rate of 58 fatalities per 100,000 person-years (http://webappa.cdc.gov/cgi-bin/broker.exe, accessed 6/22/2006). Treatment of

Methods for analysis of recurrent failure times

The multiple failure time models as extension of the Cox proportional hazards model considered in this paper are (I) Cox proportional hazards model without extension; (II) the Anderson and Gill model (Anderson and Gill, 1982); (III) the Prentice, Williams, and Peterson conditional model (Prentice et al., 1981); (IV) the Wei, Lin, and Weissfeld marginal model (Wei et al., 1989); and (V) the random effects frailty model (Clayton and Cuzick, 1985, Hougaard, 1987, Hougaard, 1995). In all models we

Applications of the models to the ED visit data

In this section, we demonstrate the adaptation of the multiple failure time and frailty models to the ED visit data. The ED revisit is defined as the recurrent event. A subject's kth failure or the kth level represents the kth revisit to the ED. Since a subject's risk of the ED revisit might differ with the level k, a different baseline hazard function was used for each level k, where k = 1, 2, …, K. In this study we focus only on the first four revisits (K = 4), for which sufficient information

Discussion

Among naturally ordered recurrent events correlation between recurrent failure times within a subject exists. For an example, one can suppose that subjects who experience more frequent episodes of violent injury, the sooner the subsequent violent injury will occur. To obtain accurate estimates and efficient inferences in such study, a variety of models for the recurrent event data analysis were examined. The main aim of this paper was to show the differences in estimates and interpretation

References (39)

  • R. Henderson et al.

    Effect of frailty on marginal regression estimates in survival analysis

    J. R. Stat. Soc. B

    (1999)
  • P. Hougaard et al.

    Measuring the similarities between the lifetime of adult Danish twins born between 1881–1930

    J. Am. Stat. Assoc.

    (1992)
  • P. Hougaard

    Analysis of Multivariate Survival Data

    (2000)
  • P. Hougaard

    Modelling multivariate survival

    Scand. J. Stat.

    (1987)
  • P. Hougaard

    Frailty models for survival data

    Lifetime Data Anal.

    (1995)
  • C.R. Kaufmann et al.

    A population-based study of trauma recidivism

    Trauma

    (1998)
  • P.J. Kelly et al.

    Survival analysis for recurrent event data: an application to childhood infectious diseases

    Stat. Med.

    (2000)
  • K.W. Kizer et al.

    Hospitalization charges, costs and income for firearm-related injuries at a university trauma center

    JAMA

    (1995)
  • J.P. Klein

    Semiparametric estimation of random effects using the Cox model based on the EM algorithm

    Biometrics

    (1992)
  • Cited by (0)

    View full text