Statistics and Its Interface

Volume 12 (2019)

Number 3

Adjusted-crude-incidence analysis of multiple treatments and unbalanced samples on competing risks

Pages: 423 – 437



Sangbum Choi (Department of Statistics, Korea University, Seoul, South Korea)

Chaewon Kim (School of Industrial Management Engineering, Korea University, Seoul, South Korea)

Hua Zhong (Division of Biostatistics, Department of Population Health, New York University School of Medicine, New York, N.Y., U.S.A.)

Eun-Seok Ryu (Department of Computer Engineering, Gachon University, Gyeonggi-do, South Korea)

Sung Won Han (School of Industrial Management Engineering, Korea University, Seoul, South Korea)


In this paper, we discuss adjusted cumulative incidence in multiple treatment groups with unbalanced samples. In a nonrandomized experiment or an observational study, the observed data may be unbalanced in covariates when multiple treatments are administered differently based on patients’ characteristics. In the case of multiple survival outcomes, clinical researchers are often interested in estimating the cumulative incidence within a specific treatment group, and this approach is subject to a potential bias with unbalanced samples. Using extensive simulation analyses, we demonstrate that a naïve approach to the estimation of a cumulative incidence curve may yield misleading results, unless patients’ characteristics are fully considered. To achieve an unbiased estimation from unbalanced data, we propose an adjusted cumulative incidence based on the inverse probability of a treatment weighting. In a series of simulations, the proposed method shows robust performance when estimating cumulative incidence under various scenarios, including balanced and unbalanced samples. Lastly, we explain how to apply the proposed method using an example based on real data.


competing risks, cumulative incidence, inverse probability of treatment weighting, Kaplan–Meier, survival analysis

This research was supported by a grant from the National Research Foundation of Korea (NRF-2017R1E1A1A03070507, NRF-2017R1C1B1004817) and by a Korea University Grant (K1719881, K1607341, K1822881).

Received 13 April 2017

Published 4 June 2019