Lifetime Data Analysis

, 16:118

A martingale residual diagnostic for longitudinal and recurrent event data


  • Entisar Elgmati
    • Department of Mathematics and StatisticsNewcastle University
  • Daniel Farewell
    • Department of Primary Care and Public HealthCardiff University
    • Department of Mathematics and StatisticsNewcastle University

DOI: 10.1007/s10985-009-9129-1

Cite this article as:
Elgmati, E., Farewell, D. & Henderson, R. Lifetime Data Anal (2010) 16: 118. doi:10.1007/s10985-009-9129-1


One method of assessing the fit of an event history model is to plot the empirical standard deviation of standardised martingale residuals. We develop an alternative procedure which is valid also in the presence of measurement error and applicable to both longitudinal and recurrent event data. Since the covariance between martingale residuals at times t0 and t > t0 is independent of t, a plot of these covariances should, for fixed t0, have no time trend. A test statistic is developed from the increments in the estimated covariances, and we investigate its properties under various types of model misspecification. Applications of the approach are presented using two Brazilian studies measuring daily prevalence and incidence of infant diarrhoea and a longitudinal study into treatment of schizophrenia.


CovarianceDynamic covariateEvent historyFrailtyMisspecification

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© Springer Science+Business Media, LLC 2009