<p>Survival analysis models allow us to analyze and predict the time until a certain event occurs. Existing nonparametric models assume that the censoring of observations is random and unrelated to the study conditions. The estimators of the survival and hazard functions assume a constant survival probability between modes, have poor interpretability for datasets with multimodal time distributions, and lead to poor-quality data descriptions. In this paper, we investigate the quality of nonparametric models on four medical datasets with informative censoring and multimodal time distribution and propose a modification to improve the description quality. Proved properties of IBS and AUPRC metrics show that the best quality is achieved at survival function with unimodal time distribution. We propose modifying the nonparametric model based on virtual events from a truncated normal distribution that allows for the suppression of informative censoring. We compared the quality of the nonparametric models on multiple random subsets of datasets of different sizes using the AUPRC and IBS metrics. According to the comparison of the quality using Welch’s test, the proposed model with virtual events significantly outperformed the existing Kaplan–Meier model for all datasets (<i>p</i>-value <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="180_2025_1610_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$<10^{-6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo><</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>). The quality increase of IBS is from 6.91 to 21.92%, and the quality increase of AUPRC is from 12.92 to 18.4%. The nonparametric models with virtual events provide a better interpretation, allow a better description of the observed data, and are stable in terms of the informativeness of censoring. The proposed method is embedded in an open-source <Emphasis FontCategory="NonProportional">survivors</Emphasis> Python library.</p>

Informative right censoring in nonparametric survival models

期刊论文
发表日期：

2025年2月25日

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Iulii Vasilev,
Mikhail Petrovskiy,
Igor Mashechkin

摘要

Survival analysis models allow us to analyze and predict the time until a certain event occurs. Existing nonparametric models assume that the censoring of observations is random and unrelated to the study conditions. The estimators of the survival and hazard functions assume a constant survival probability between modes, have poor interpretability for datasets with multimodal time distributions, and lead to poor-quality data descriptions. In this paper, we investigate the quality of nonparametric models on four medical datasets with informative censoring and multimodal time distribution and propose a modification to improve the description quality. Proved properties of IBS and AUPRC metrics show that the best quality is achieved at survival function with unimodal time distribution. We propose modifying the nonparametric model based on virtual events from a truncated normal distribution that allows for the suppression of informative censoring. We compared the quality of the nonparametric models on multiple random subsets of datasets of different sizes using the AUPRC and IBS metrics. According to the comparison of the quality using Welch’s test, the proposed model with virtual events significantly outperformed the existing Kaplan–Meier model for all datasets (p-value $<10^{-6}$ $< 10^{- 6}$ ). The quality increase of IBS is from 6.91 to 21.92%, and the quality increase of AUPRC is from 12.92 to 18.4%. The nonparametric models with virtual events provide a better interpretation, allow a better description of the observed data, and are stable in terms of the informativeness of censoring. The proposed method is embedded in an open-source survivors Python library.