Nonparametric Quantile Estimation with Correlated Failure Time Data

Abstract

In biomedical studies, correlated failure time data arise often. Although point and confidence interval estimation for quantiles with independent censored failure time data have been extensively studied, estimation for quantiles with correlated failure time data has not been developed. In this article, we propose a nonparametric estimation method for quantiles with correlated failure time data. We derive the asymptotic properties of the quantile estimator and propose confidence interval estimators based on the bootstrap and kernel smoothing methods. Simulation studies are carried out to investigate the finite sample properties of the proposed estimators. Finally, we illustrate the proposed method with a data set from a study of patients with otitis media.

Local polynomial estimation of a conditional mean function with dependent truncated data

“…See Doukhan (1994), page 99, for more details. Also, α-mixing has been used in applications with clustered survival data; see, for instance, Cai and Kim (2003).…”

Asymptotic normality in conditional wavelet density with left-truncated α-mixing observations

“…Besides, since wp / n → 1, (23) follows from (27) and (28). As to (24), according to Lemma A2 we have Lemma A3 (Yang [33], Theorem 2.2) Let >2, >0, EZ i = 0 and E|Z i | + <∞.…”

Conditional quantile estimation with truncated, censored and dependent data

“…See [7, p. 99], for more details. We mention that α-mixing has been used in applications with clustered survival data; see, for instance, Cai and Kim [5].…”