5,207 research outputs found
Local partial-likelihood estimation for lifetime data
This paper considers a proportional hazards model, which allows one to
examine the extent to which covariates interact nonlinearly with an exposure
variable, for analysis of lifetime data. A local partial-likelihood technique
is proposed to estimate nonlinear interactions. Asymptotic normality of the
proposed estimator is established. The baseline hazard function, the bias and
the variance of the local likelihood estimator are consistently estimated. In
addition, a one-step local partial-likelihood estimator is presented to
facilitate the computation of the proposed procedure and is demonstrated to be
as efficient as the fully iterated local partial-likelihood estimator.
Furthermore, a penalized local likelihood estimator is proposed to select
important risk variables in the model. Numerical examples are used to
illustrate the effectiveness of the proposed procedures.Comment: Published at http://dx.doi.org/10.1214/009053605000000796 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Local partial likelihood estimation in proportional hazards regression
Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] considered the
estimation of the risk function in the proportional hazards model.
Their proposed estimator is based on integrating the estimated derivative
function obtained through a local version of the partial likelihood. They
proved the large sample properties of the derivative function, but the large
sample properties of the estimator for the risk function itself were not
established. In this paper, we consider direct estimation of the relative risk
function for any location normalization point .
The main novelty in our approach is that we select observations in shrinking
neighborhoods of both and when constructing a local version of the
partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997)
1661--1690] only concentrated on a single neighborhood, resulting in the
cancellation of the risk function in the local likelihood function. The
asymptotic properties of our estimator are rigorously established and the
variance of the estimator is easily estimated. The idea behind our approach is
extended to estimate the differences between groups. A simulation study is
carried out.Comment: Published at http://dx.doi.org/10.1214/009053606000001299 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Hazard models with varying coefficients for multivariate failure time data
Statistical estimation and inference for marginal hazard models with varying
coefficients for multivariate failure time data are important subjects in
survival analysis. A local pseudo-partial likelihood procedure is proposed for
estimating the unknown coefficient functions. A weighted average estimator is
also proposed in an attempt to improve the efficiency of the estimator. The
consistency and asymptotic normality of the proposed estimators are established
and standard error formulas for the estimated coefficients are derived and
empirically tested. To reduce the computational burden of the maximum local
pseudo-partial likelihood estimator, a simple and useful one-step estimator is
proposed. Statistical properties of the one-step estimator are established and
simulation studies are conducted to compare the performance of the one-step
estimator to that of the maximum local pseudo-partial likelihood estimator. The
results show that the one-step estimator can save computational cost without
compromising performance both asymptotically and empirically and that an
optimal weighted average estimator is more efficient than the maximum local
pseudo-partial likelihood estimator. A data set from the Busselton Population
Health Surveys is analyzed to illustrate our proposed methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000001145 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Analysis of Diabetes Data using Extended Cox Model with Frailty under Partial and Penalized partial likelihood estimation methods
Data on Diabetes were analyzed using partial likelihood (Pl) and penalized partial likelihood (Ppl) estimation methods in non-proportional hazards model with dichotomous time-varying covariates. Gamma and Inverse Gaussian frailty distributions were used to account for patient- specific unobserved heterogeneity. Four likelihood configurations were formed from the combinations of the two estimation methods and frailty distributions. These are Partial likelihood with Gamma frailty, Partial likelihood with Inverse Gaussian frailty, Penalized partial likelihood with Gamma frailty and Penalized partial likelihood with Gamma frailty. The results revealed that age and body mass index of the patients significantly increased the risk of death from diabetes, while regular exercise had significant decreased risk of death. Penalized partial likelihood estimation method generally outperformed models with Partial likelihood under all scenarios for the data and Gamma frailty provided a better fit in accounting for unobserved heterogeneity among the diabetic patients
Bayesian estimation of Cox model with non-nested random effects: an application to the ratification of ILO conventions by developing countries
We use a multivariate hazard model for the analysis of data on the timing of ratifications of different conventions. The model accounts for two random effects, one at the country level and the other at the convention level. We use a semi-parametric Bayesian approach, based on the partial likelihood. Our findings confirm the results of preceding studies that ratification behaviour varies substantially across members states and conventions. Furthermore, the results yield insights on the impact of unobserved heterogeneity on the ratification process. --gibbs sampling,partial likelihood,frailties,duration analysis
Partial Likelihood-Based Scoring Rules for Evaluating Density Forecasts in Tails
We propose new scoring rules based on partial likelihood for assessing the relative out-of-sample predictive accuracy of competing density forecasts over a specific region of interest, such as the left tail in financial risk management. By construction, existing scoring rules based on weighted likelihood or censored normal likelihood favor density forecasts with more probability mass in the given region, rendering predictive accuracy tests biased towards such densities. Our novel partial likelihood-based scoring rules do not suffer from this problem, as illustrated by means of Monte Carlo simulations and an empirical application to daily S\&P 500 index returns.
Computational Methods in Survival Analysis
Survival analysis is widely used in the fields of medical science, pharmaceutics, reliability and financial engineering, and many others to analyze positive random phenomena defined by event occurrences of particular interest. In the reliability field, we are concerned with the time to failure of some physical component such as an electronic device or a machine part. This article briefly describes statistical survival techniques developed recently from the standpoint of statistical computational methods focussing on obtaining the good estimates of distribution parameters by simple calculations based on the first moment and conditional likelihood for eliminating nuisance parameters and approximation of the likelihoods. The method of partial likelihood (Cox, 1972, 1975) was originally proposed from the view point of conditional likelihood for avoiding estimating the nuisance parameters of the baseline hazards for obtaining simple and good estimates of the structure parameters. However, in case of heavy ties of failure times calculating the partial likelihood does not succeed. Then the approximations of the partial likelihood have been studied, which will be described in the later section and a good approximation method will be explained. We believe that the better approximation method and the better statistical model should play an important role in lessening the computational burdens greatly. --
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