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

Authors

  • Ying Xu,

    Corresponding author
    1. Scientific Development Division, Singapore Clinical Research Institute, Nanos #02-01, Singapore, Singapore
    • Centre for Quantitative Medicine, Office of Clinical Sciences, Duke-NUS Graduate Medical School, Singapore, Singapore
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  • Yin Bun Cheung,

    1. Centre for Quantitative Medicine, Office of Clinical Sciences, Duke-NUS Graduate Medical School, Singapore, Singapore
    2. Scientific Development Division, Singapore Clinical Research Institute, Nanos #02-01, Singapore, Singapore
    3. Department of International Health, FI-33014 University of Tampere, Tampere, Finland
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  • K. F. Lam,

    1. Department of Statistics and Actuarial Science, Meng Wah Complex, The University of Hong Kong, Hong Kong, China
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  • Paul Milligan

    1. Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, WC1E 7HT, UK
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Corresponding author: e-mail: tina.xu@scri.edu.sg, Phone: +65 6508 8334, Fax: +65 6508 8317

Abstract

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

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