JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1027 10.6339/21-JDS1027 Statistical Data Science Additive-Multiplicative Rates Model for Recurrent Event Data with Intermittently Observed Time-Dependent Covariates LyuTianmeng1 LuoXianghua23 SunYifeiys3072@cumc.columbia.edu4∗ Novartis Pharmaceuticals Corporation, East Hanover, NJ, U.S.A. Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN, U.S.A. Biostatistics Core, Masonic Cancer Center, University of Minnesota, Minneapolis, MN, U.S.A. Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, NY, U.S.A. Corresponding author. Email: ys3072@cumc.columbia.edu. 20214112021194615633 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.

318202112102021 2021 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2021 Open access article under the CC BY license.

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.

 additive-multiplicative rates model kernel smoothing recurrent events semiparametric method time-dependent covariates National Institutes of HealthR03MH112895National Institutes of HealthP30CA077598Lyu 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). References Andersen PK, Gill RD (1982). Cox’s regression model for counting processes: A large sample study. The Annals of Statistics, 10(4): 1100–1120. Andersen PK, Liestøl K (2003). Attenuation caused by infrequently updated covariates in survival analysis. Biostatistics, 4(4): 633–649. Boscardin WJ, Taylor JM, Law N (1998). Longitudinal models for aids marker data. Statistical Methods in Medical Research, 7(1): 13–27. Bycott P, Taylor J (1998). A comparison of smoothing techniques for cd4 data measured with error in a time-dependent cox proportional hazards model. Statistics in Medicine, 17(18): 2061–2077. 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