A semiparametric approach to hazard estimation with randomly right-censored observations

Thesis/Dissertation · Tue Dec 31 23:00:00 EST 1991

OSTI ID:7042540

Kouassi, D A

One method for estimating a hazard function h(t) is to assume that it is a member of a known parametric family and can be expressed as h(t;[theta]), where [theta] is an unknown parameter. Usually, [theta] is estimated by the maximum likelihood method. Its estimator [cflx [theta]] is used in h(t;[cflx [theta]]) to obtain a parametric estimator of h(t). h(t) can be estimated nonparametrically by a kernel estimator [cflx h](t). The idea proposed in this dissertation is to fit a combination of parametric and nonparametric estimators, h[sub [alpha]](t;[cflx [theta]]) + (1 [minus] [alpha])[cflx h](t), where the weight [alpha][element of][0,1] is unknown, and is to be estimated from the data. If [cflx [alpha]] is an estimator of the weight, then the proposed semiparametric hazard estimator is h[sub [alpha]](t;[cflx [theta]]). [cflx [alpha]] is expected to be close to one when the parametric model prevails, and close to zero otherwise. Let c[sub n] be a sequence of positive numbers such that c[sub n] [yields] 0 and n1/2c[sub n] [yields] [infinity] as n [yields] [infinity]. [cflx [alpha]] is 1 + 0[sub p](n[minus]1/2c[sub n][sup [minus]1]) if the parametric model holds; otherwise of order O[sub p](n[sup [minus]1/2]). h[sub [alpha]](t;[cflx [theta]]) is integratedly weakly consistent for the true hazard function h(t) regardless of the validity of the parametric model. For finite sample sizes [cflx [alpha]] behaves as expected. [cflx [alpha]] increases with the proportion of censored observations. The jackknife procedure is an adequate means for estimating the mean square error (MSE) of h[sub [alpha]](t;[cflx [theta]]). The effect of sensoring on the MSE is investigated. The proposed hazard estimator is used to estimate the hazard function of head and neck cancer patients treated with a drug referred to as drug A.

• Research Organization: Temple Univ., Philadelphia, PA (United States)
• OSTI ID: 7042540
• Country of Publication: United States
• Language: English

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ANTINEOPLASTIC DRUGS
DISEASES
DRUGS
MATHEMATICAL MODELS
NEOPLASMS
PARAMETRIC ANALYSIS
PROBABILISTIC ESTIMATION
RANDOMNESS
RISK ASSESSMENT
STATISTICAL MODELS
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