Evaluation of a Non-Parametric Penalized Kaplan–Meier Estimator Under Interval-Censored Survival Data

Interval-censored survival data arise frequently in biomedical and epidemiological studies where event times are observed only within observation intervals. Classical non-parametric estimators, such as the Kaplan–Meier (KM) estimator under imputation and the Turnbull estimator, often suffer from instability, irregular fluctuations, and overfitting when sample sizes are small or when the prevalence rate is low. Recent methodological developments, which include smoothed and penalized approaches, have been proposed to improve stability and reduce estimation error in such settings. This study evaluates and benchmarks the finite-sample performance of a nonparametric penalized likelihood KM estimator under interval-censored data. The method is compared with the classical KM estimator using four imputation strategies, that is, midpoint, regression, uniform, and multiple imputation. From a symmetry perspective, midpoint and uniform imputation preserve interval symmetry through deterministic and probabilistic mechanisms, respectively, whereas regression and multiple imputation intentionally introduce structural asymmetry to reflect data-driven risk heterogeneity and distributional uncertainty. To assess and benchmark the performance of the penalized KM estimator, an extensive Monte Carlo (MC) simulation study was conducted across varying sample sizes and prevalence rates using error-based metrics. The MC simulation results revealed that the nonparametric penalized KM estimator consistently outperforms the classical KM estimator in small samples across all prevalence rates. The gains are more pronounced under low prevalence rates where the penalized KM estimator is superior for small to relatively moderate samples of $n\approx$ 40–100. Among the imputation techniques, regression and multiple imputation generally exhibited superior performance. Real data application further confirms these findings, demonstrating that the nonparametric penalized KM estimator yields more stable and accurate survival curves than the classical KM estimator in small samples.