Abstract
Data with censoring is common in many areas of science and the associated statistical models are generally estimated with the method of maximum likelihood combined with a model selection criterion such as Akaike’s information criterion. This manuscript demonstrates how the information theoretic minimum message length principle can be used to estimate statistical models in the presence of type I random and fixed censoring data. The exponential distribution with fixed and random censoring is used as an example to demonstrate the process where we observe that the minimum message length estimate of mean survival time has some advantages over the standard maximum likelihood estimate.
Highlights
In Type I random censoring we observe for each item i either the true survival time Ti = ti or the censoring time Ci = ci, where capital letters are used to denote random variables
The main contributions of this manuscript are to: (i) introduce the minimum message length (MML) principle of inductive inference and demonstrate how the Wallace–Freeman MML approximation can used to infer exponential models with type I censored data; (ii) show that the MML estimate of the mean lifetime has some advantages over the usual maximum likelihood estimate for small samples and that it converges to the maximum likelihood estimate for large sample sizes, (iii) incorporate the proposed codelengths for censored exponential distributions into MML finite mixture models allowing for inference of all parameters as well as the number of mixture classes; and (iv) compare the MML principle to the closely related minimum description length principle
Information theoretic universal models for the exponential distribution, including those corresponding to MML codes, are known [4], this is the first time MML has been applied to censored data
Summary
Tn) is of key interest in many areas of science and is commonly done by maximizing the likelihood and dropping terms relevant to C only This manuscript examines inference of models in the presence of censored data under the minimum message length (MML) framework. We demonstrate how MML can be used to infer models under fixed censoring as well as type I random censoring. MML analysis of the exponential distribution is not new (see, for example, [1,4]), the MML principle has not been applied to any kind of survival data with censoring to date. The main contributions of this manuscript are to: (i) introduce the MML principle of inductive inference and demonstrate how the Wallace–Freeman MML approximation can used to infer exponential models with type I censored data; (ii) show that the MML estimate of the mean lifetime has some advantages over the usual maximum likelihood estimate for small samples and that it converges to the maximum likelihood estimate for large sample sizes, (iii) incorporate the proposed codelengths for censored exponential distributions into MML finite mixture models allowing for inference of all parameters as well as the number of mixture classes; and (iv) compare the MML principle to the closely related minimum description length principle
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