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Journal of Data Science


Additive-Multiplicative Rates Model for Recurrent Event Data with Intermittently Observed Time-Dependent Covariates
Volume 19, Issue 4 (2021), pp. 615–633
Pub. online: 4 November 2021      Type: Statistical Data Science     
Received
31 August 2021
Accepted
12 October 2021
Published
4 November 2021

Abstract

Regression methods, including the proportional rates model and additive rates model, have been proposed to evaluate the effect of covariates on the risk of recurrent events. These two models have different assumptions on the form of the covariate effects. A more flexible model, the additive-multiplicative rates model, is considered to allow the covariates to have both additive and multiplicative effects on the marginal rate of recurrent event process. However, its use is limited to the cases where the time-dependent covariates are monitored continuously throughout the follow-up time. In practice, time-dependent covariates are often only measured intermittently, which renders the current estimation method for the additive-multiplicative rates model inapplicable. In this paper, we propose a semiparametric estimator for the regression coefficients of the additive-multiplicative rates model to allow intermittently observed time-dependent covariates. We present the simulation results for the comparison between the proposed method and the simple methods, including last covariate carried forward and linear interpolation, and apply the proposed method to an epidemiologic study aiming to evaluate the effect of time-varying streptococcal infections on the risk of pharyngitis among school children. The R package implementing the proposed method is available at www.github.com/TianmengL/rectime.

Supplementary material

 Supplementary Material
The supplementary material includes the R code that implements the proposed methods. It also includes an example file to illustrate how to simulate data and estimate model parameters using the provided code files.

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Keywords
additive-multiplicative rates model kernel smoothing recurrent events semiparametric method time-dependent covariates

Funding
Lyu and Luo were partially supported by the U.S. National Institutes of Health (R03MH112895). Luo was also supported by the U.S. National Institutes of Health (P30CA077598).

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