Fuzzy midpoint–based imputation methods for non-parametric survival estimation with interval-censored data

Résumé

The analysis of failure time data frequently encounters situations in which the exact time of event occurrence is unknown but is known to lie within a specified interval, resulting in interval-censored data. In practice, classical approaches such as the nonparametric Kaplan–Meier (KM) estimator are commonly employed, with unobserved event times imputed using Midpoint imputation. However, Midpoint imputation implicitly imposes a symmetric structure on the unobserved event times, which may fail to reflect underlying data asymmetry. Moreover, the resulting Midpoint imputed KM survival curves do not adequately capture within-interval uncertainty and often yield stepwise and potentially biased survival estimates. This study investigates fuzzy logic–based imputation as an alternative framework for estimating survival functions under interval censoring, offering a more flexible representation of uncertainty that accommodates both symmetric and asymmetric event-time distributions. A Monte Carlo simulation study was conducted to evaluate five fuzzy midpoint-based imputation methods, namely, the Fuzzy Centroid, Fuzzy α-Cut, Fuzzy Arithmetic, Fuzzy Fully Random Variable, and Fuzzy Weighted Average against the traditional Midpoint imputation approach. Statistical performance evaluation metrics were used to assess method performance across varying sample sizes and prevalence rates. For empirical validation, the ACTG181 and Breast Cancer clinical datasets were analyzed using bootstrap resampling. The results indicate that the Fuzzy α-Cut, Fuzzy Arithmetic, and Fuzzy Fully Random Variable imputation methods consistently outperform the classical Midpoint approach, producing smoother and more reliable survival curves. This improvement is partly attributable to their ability to relax strict symmetry assumptions imposed by the classical Midpoint imputation, particularly in small-sample settings. In contrast, the Fuzzy Centroid and Fuzzy Weighted Average methods exhibited performance comparable to that of the classical Midpoint imputation.

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