Kolmogorov-Smirnov and Cramér-von Mises tests for the k-sample problem with left-truncated and right-censored data
Clinical Snapshot
PICO Framework
| P — Population | Statistical datasets with left-truncated and right-censored survival data (illustrated with unemployment duration data) |
| I — Intervention | Novel k-sample Kolmogorov-Smirnov and Cramér-von Mises statistical tests with bootstrap resampling |
| C — Comparator | Classical log-rank test for survival analysis |
| O — Outcomes | Test performance characteristics, asymptotic behaviour, finite sample performance via simulation |
Bottom Line
This methodological study develops novel statistical tests for comparing multiple groups when survival data are subject to both left truncation and right censoring - a common scenario in health services research and epidemiology. The Kolmogorov-Smirnov and Cramér-von Mises tests offer alternatives to the log-rank test with potentially better performance under certain conditions. While primarily of interest to biostatisticians and researchers, these methods could enhance analysis of Australian administrative health datasets, pharmaceutical post-market surveillance, and longitudinal cohort studies where complex censoring patterns occur. The bootstrap implementation makes the tests practically feasible, though computational expertise is required. Clinical researchers should collaborate with statisticians when considering these methods for survival analysis in complex datasets.
Key Findings
P Value: Not reported in abstract - simulation-based p-value distributions
Effect Size: Not applicable - methodological study
Primary Outcome: Development of k-sample Kolmogorov-Smirnov and Cramér-von Mises tests for complex censored data
Nnt Or Sensitivity: Test power and Type I error rates assessed via simulation
Confidence Interval: Bootstrap-derived confidence intervals for test statistics
Clinical Application
Requires statistical software implementation and expertise in survival analysis Relevant for Australian health services research, pharmaceutical outcomes research, and epidemiological studies using administrative datasets Researchers and biostatisticians analysing survival data with complex censoring patterns
Abstract
k-Sample versions of the Kolmogorov-Smirnov and Cramér-von Mises tests are proposed for data subject to left truncation and right censoring. Their asymptotic behaviour is studied and a bootstrap resampling plan is proposed to approximate the null distribution of the new tests. The performance of the tests with finite sample sizes is investigated in a simulation study, where the classical log-rank test is also considered. An illustration with a real dataset regarding unemployment times is discussed.
References
- 1.Lago, A., Pardo-Fernández, J. C., & de Uña-Álvarez, J. (2026). Kolmogorov-Smirnov and Cramér-von Mises tests for the k-sample problem with left-truncated and right-censored data. Lifetime Data Analysis. https://doi.org/10.1006/jmva.1998.1806
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