Nonparametric estimation of the joint and conditional survival functions of the time to an event of interest and associated integrated covariate processes

Nonparametric estimation of the joint and conditional survival functions of the time to an event of interest and associated integrated covariate processes | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 4 December 2025 V2 Latest version Share on Nonparametric estimation of the joint and conditional survival functions of the time to an event of interest and associated integrated covariate processes Authors : Ashwini Joshi 0000-0002-9087-2798 [email protected] , Dario Gasbarra , and Sangita Kulathinal Authors Info & Affiliations https://doi.org/10.22541/au.175822739.96310819/v2 187 views 121 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract During the treatment of chronic diseases, a covariate process may exhibit a response over the treatment period and may also be associated with the event of interest. The integrated covariate process commonly known as the area under the response curve, over a specific treatment interval is a widely used measure of a cumulative treatment response in medical research. Our interest is in the sur- vival probability that the time to the event is larger than a fixed time t and the cumulative response up to that time is larger than a fixed value y. Because the cumulative response grows with time, the latter event of the survival probability may realise at the random time when the integrated process crosses y. A common censoring mechanism may censor both these random times. In fact, our setting gives rise to a different type of censoring mechanism of the bivariate event times. In order to handle the censoring and to use all available information, we study inverse-probability of censoring weighted estimators of the survival probability. The estimators and their efficiency differ according to the use of the informa- tion in estimation of the censoring distribution. We also give a pooled estimator of the bivariate survival function in a stratified analysis. Further, we study the conditional survival function of the time to the event given the history of the covariate process and discuss its use in the medical decision making. We suggest jackknife method for estimating variances for all the proposed estimators. The proposed estimators can be easily generalised to more than one covariate pro- cesses. We illustrate our methodology using two sets of data on the age-related macular degeneration of eye disease; one from a clinical trial and the other from a real-world study. Supplementary Material File (integrated_response_distribution_authorea_3dec_2025.pdf) Download 624.90 KB Information & Authors Information Version history V1 Version 1 18 September 2025 V2 Version 2 04 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords bivariate survival function decision making integrated covariate process inverse probability of censoring weights treatment regime Authors Affiliations Ashwini Joshi 0000-0002-9087-2798 [email protected] View all articles by this author Dario Gasbarra View all articles by this author Sangita Kulathinal View all articles by this author Metrics & Citations Metrics Article Usage 187 views 121 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Ashwini Joshi, Dario Gasbarra, Sangita Kulathinal. Nonparametric estimation of the joint and conditional survival functions of the time to an event of interest and associated integrated covariate processes. Authorea . 04 December 2025. DOI: https://doi.org/10.22541/au.175822739.96310819/v2 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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