Comparison of Parameter Estimates for One Special Model of Survival Curves for Sample with Interval Censoring
Anton Korobeynikov
Saint Petersburg State University
Introduction: In practice time to event data can rarely be observed directly. Usually, one can only know some time interval where observation lies in, thus data became censored. The mixed case interval censoring is one of the most important models of censoring seen in the practical applications. It is well-known that significant loss of information about underlying distribution due to censoring can lead to almost arbitrary large-sample behaviour of parameter estimates including inconsistency, etc.
Parameter Estimates: We consider the problem of parameter estimation for one special survival curve model [1] with incomplete data due to censoring. In particular, we propose new parameter estimator based on the non-parametric estimate of distribution function (which itself turns out to be Hellinger-consistent [2]). The computation procedure is described as well. Large sample properties of this new estimator such as consistency, efficiency, robustness in presence of outliers are studied by the means of Monte-Carlo simulations. All these properties are compared with the same properties of the ordinary maximum likelihood estimates.
Conclusions: It was found that compared to the maximum likelihood estimates proposed estimates have slightly bigger variance. However, they possess better robustness properties when sample contains significant amount of outliers.
References:
[1] Bart, A.G. Analysis of Medical and Biological Systems (The Inverse Functions Approach). St. Petersburg, St. Petersburg University Press (2003, In Russian).
[2] Schick, A. and Yu, Q. Consistency of the GMLE With Mixed Case Interval Censored Data. Scand. J. Stat., 27 (2000), 45-55.
