Semiparametric transformation model for competing risks data with cure fraction
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Modelling and analysis of competing risks data with long-term survivors is an important area of research in recent years. For example, in the study of cancer patients treated for soft tissue sarcoma, patient may die due to different causes. Considerable portion of the patients may remain cancer free after the treatment. Accordingly, it is important to incorporate long-term survivors in the analysis of competing risks data. Motivated by this, we propose a new method for the analysis of competing risks data with long term survivors. The new method enables us to estimate the overall survival probability without estimating the cure fraction. We formulate the effects of covariates on sub-distribution (cumulative incidence) functions using linear transformation model. Estimating equations based on counting process are developed to find the estimators of regression coefficients. The asymptotic properties of the estimators are studied using martingale theory. An extensive Monte Carlo simulation study is carried out to assess the finite sample performance of the proposed estimators. Finally, we illustrate our method using a real data set.
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