Asymptotic Properties of Likelihood Ratio Statistics in Competing Risks Model Under Interval Random Censoring

This paper is concerned with testing for the equality of failure rates in a competing risks model with two risks. Three testing procedures are investigated, namely Score test, Likelihood Ratio test and Wald test. Wald test has been considered to be the most powerful in multivariate linear regression analysis.1 However in our application, Wald test is the most efficient one when the failure rate of the second failure type is strictly smaller than the first failure type, otherwise the Score or the Likelihood Ratio test is preferred. This phenomenon is illustrated by data from a mechanical-switch life test.2 The results has been extended to a k-competing risks model. A simulation study is also given to examine the performance of the three tests.

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A competing risks model with binary time varying covariates for estimation of breast cancer risks in BRCA1 families

Statistical Methods in Medical Research ◽

10.1177/09622802211008945 ◽

2021 ◽

pp. 096228022110089

Author(s):

Yun-Hee Choi ◽

Hae Jung ◽

Saundra Buys ◽

Mary Daly ◽

Esther M John ◽

...

Keyword(s):

Breast Cancer ◽

Ovarian Cancer ◽

Competing Risks ◽

Brca1 Mutation ◽

Prophylactic Surgery ◽

Time Varying ◽

Cancer Risks ◽

Competing Risks Model ◽

Time Varying Covariates ◽

Risk Reducing

Mammographic screening and prophylactic surgery such as risk-reducing salpingo oophorectomy can potentially reduce breast cancer risks among mutation carriers of BRCA families. The evaluation of these interventions is usually complicated by the fact that their effects on breast cancer may change over time and by the presence of competing risks. We introduce a correlated competing risks model to model breast and ovarian cancer risks within BRCA1 families that accounts for time-varying covariates. Different parametric forms for the effects of time-varying covariates are proposed for more flexibility and a correlated gamma frailty model is specified to account for the correlated competing events.We also introduce a new ascertainment correction approach that accounts for the selection of families through probands affected with either breast or ovarian cancer, or unaffected. Our simulation studies demonstrate the good performances of our proposed approach in terms of bias and precision of the estimators of model parameters and cause-specific penetrances over different levels of familial correlations. We applied our new approach to 498 BRCA1 mutation carrier families recruited through the Breast Cancer Family Registry. Our results demonstrate the importance of the functional form of the time-varying covariate effect when assessing the role of risk-reducing salpingo oophorectomy on breast cancer. In particular, under the best fitting time-varying covariate model, the overall effect of risk-reducing salpingo oophorectomy on breast cancer risk was statistically significant in women with BRCA1 mutation.

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