Non-parametric hazard function estimation using the Kaplan–Meier estimator

Abstract

Estimation of the hazard function when the data are censored is an important problem in medical research. In this article, we propose a simple non-parametric estimator of the hazard function. Its asymptotic properties are derived, and numerical comparisons with other existing estimators are made. The proposed estimator is shown to be at least as good as the other estimators from both the theoretical and the numerical points of view.

A local linear estimation of conditional hazard function in censored data

“…from which we may considerλ n (t|x) as a local linear-type extension to conditional hazard function of the estimator suggested by Kim et al (2005).…”

“…In fact, they applied kernel method to both the response and the covariates, and used a local polynomial regression method in estimation. On the other hand, Kim et al (2005) suggested a nonparametric estimation of unconditional hazard function using the Kaplan-Meier estimator (cf. Kaplan & Meier, 1958).…”

“…Local linear regression techniques were also applied by Fan and Gijbels (1994) and Spierdijk (2008) for such data. Our proposed estimator is motivated by ideas of Fan et al (1996) and Kim et al (2005). In particular, Fan et al (1996) introduced a double kernel approach in estimating time series model with covariates.…”

“…Wong (1983, 1984) and Watson and Leadbetter (1964) studied parametric and nonparametric estimators, Singpurwalla and Wong (1983) suggested kernel estimators, and Patil, Wells, and Marron (1994) showed that all estimators of the nonparametric hazard function suggested so far can be classified into two types. Recently, Kim et al (2005) proposed a nonparametric estimator using the jump size of the Kaplan-Meier estimator and derived its asymptotic properties.…”

“…The estimator suggested in this paper is motivated by the ideas of Fan, Yao, and Tong (1996) and Kim, Bae, Choi, and Park (2005). The asymptotic distribution of the proposed estimator is derived, and some numerical results are also provided.…”