Asymptotic convergence in distribution of the area bounded by prevalence-weighted Kaplan–Meier curves using empirical process modelling

@article{Heuser2018AsymptoticCI,
  title={Asymptotic convergence in distribution of the area bounded by prevalence-weighted Kaplan–Meier curves using empirical process modelling},
  author={Aaron Heuser and Minh Huynh and Joshua C. Chang},
  journal={Royal Society Open Science},
  year={2018},
  volume={5}
}
The Kaplan–Meier product-limit estimator is a simple and powerful tool in time to event analysis. An extension exists for populations stratified into cohorts where a population survival curve is generated by weighted averaging of cohort-level survival curves. For making population-level comparisons using this statistic, we analyse the statistics of the area between two such weighted survival curves. We derive the large sample behaviour of this statistic based on an empirical process of product… 

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References

SHOWING 1-10 OF 27 REFERENCES
Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data.
TLDR
Results from small-sample simulation studies indicate that these statistics compare favorably with the log-rank procedure even under the proportional hazards alternative, and may perform better than it under the crossing hazards alternative.
Weighted Kaplan‐Meier Statistics: Large Sample and Optimality Considerations
SUMMARY We propose a cumulative weighted difference in the Kaplan-Meier estimates as a test statistic for equality of distributions in the two-sample censored data survival analysis problem. For
A simple nonparametric estimator of the bivariate survival function under univariate censoring
SUMMARY In the presence of univariate censoring, the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at-risk probability to the survival function of
Using Weighted Kaplan‐Meier Statistics in Nonparametric Comparisons of Paired Censored Survival Outcomes
TLDR
Simulations presented over a range of potential dependence in the paired censored survival data demonstrate substantial power gains associated with taking into account the dependence structure, and highlight the need for accounting for dependence in this popular family of tests.
The asymptotic properties of nonparametric tests for comparing survival distributions
The asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary, and possibly
Asymptotic properties of Kaplan-Meier estimator for censored dependent data
Effects of frailty in survival analysis
  • O. Aalen
  • Mathematics
    Statistical methods in medical research
  • 1994
TLDR
It is emphasized that the frailty phenom enon may be modelled in many different ways, and a stochastic process approach is discussed as an alternative to the common proportional frailty model.
Life table methods for heterogeneous populations: Distributions describing the heterogeneity
Taking account of heterogeneity between the individuals in population based mortality studies is important. A systematic way of describing heterogeneity is by an unobserved quantity called frailty,
A comparison between Kaplan-Meier and weighted Kaplan-Meier methods of five-year survival estimation of patients with gastric cancer.
TLDR
This study aimed to compare estimations of Kaplan-Meier and Weighted Kaplan- Meier as an alternative method to deal with the problem of heavy-censoring and decreases bias of survival probabilities by providing appropriate weights and presents more accurate understanding.
Nonparametric Estimation from Incomplete Observations
Abstract In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample
...
...