An alternative to the product limit method: the multistate approach

Editorial Note

The plan for this special volume of the Journal of Statistical Research started with Professor Dr. M. Ataharul Islam as one of the editors. Unfortunately, Professor Islam has passed away during the preparation of this volume on December 6, 2020. To honor Professor Islam’s contribution to the statistical community we have published this significant methodological work of Islam from 27 years back, originally published in the Journal of Royal Statistical Society, Series D (The Statistician). Permission to re-publish the article in JSR has been granted by the Royal Statistical Society and the John Wiley & Sons, Inc. The original reference to the publication is here: M. Ataharul Islam: AN ALTERNATIVE TO THE PRODUCT LIMIT METHOD: THE MULTISTATE APPROACH, The Statistician 43, 237–245, 1994.


A multistate alternative to the product limit method is developed. The approach proposed takes into account the censored and uncensored survivorship functions separately. The methods are useful in situations of informative censoring. This approach can be used for unequal probabilities of death for uncensored and censored states. The product limit estimates can be shown to be a special case of the proposed alternative if probabilities of death for uncensored and censored states are assumed to be equal.

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