Approximate maximum likelihood estimation for logistic regression with covariate measurement error

In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)‐InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC‐InterAct Study under a sensitivity analysis framework.     

Maximum likelihood estimation of ordered multinomial parameters

The pool adjacent violator algorithm Ayer et al. (1955, The Annals of Mathematical Statistics, 26, 641-647) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972, Statistical Inference under Order Restrictions, Wiley, New York). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of 'ordered' multinomial parameters p(i)= (p(1i),p(2i),.,p(mi)) for 1 相似文献   

Semiparametric maximum likelihood for measurement error model regression

This paper presents an EM algorithm for semiparametric likelihood analysis of linear, generalized linear, and nonlinear regression models with measurement errors in explanatory variables. A structural model is used in which probability distributions are specified for (a) the response and (b) the measurement error. A distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood. For various types of extra information about the measurement error distribution, the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of (a) and (b) if the true x were available. Simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption. The approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution.     

Semiparametric maximum likelihood for nonlinear regression with measurement errors

This article demonstrates semiparametric maximum likelihood estimation of a nonlinear growth model for fish lengths using imprecisely measured ages. Data on the species corvina reina, found in the Gulf of Nicoya, Costa Rica, consist of lengths and imprecise ages for 168 fish and precise ages for a subset of 16 fish. The statistical problem may therefore be classified as nonlinear errors-in-variables regression with internal validation data. Inferential techniques are based on ideas extracted from several previous works on semiparametric maximum likelihood for errors-in-variables problems. The illustration of the example clarifies practical aspects of the associated computational, inferential, and data analytic techniques.     

Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation

We derive the nonparametric maximum likelihood estimate (NPMLE) of the cumulative incidence functions for competing risks survival data subject to interval censoring and truncation. Since the cumulative incidence function NPMLEs give rise to an estimate of the survival distribution which can be undefined over a potentially larger set of regions than the NPMLE of the survival function obtained ignoring failure type, we consider an alternative pseudolikelihood estimator. The methods are then applied to data from a cohort of injecting drug users in Thailand susceptible to infection from HIV-1 subtypes B and E.     

Penalized gaussian process regression and classification for high-dimensional nonlinear data

The model based on Gaussian process (GP) prior and a kernel covariance function can be used to fit nonlinear data with multidimensional covariates. It has been used as a flexible nonparametric approach for curve fitting, classification, clustering, and other statistical problems, and has been widely applied to deal with complex nonlinear systems in many different areas particularly in machine learning. However, it is a challenging problem when the model is used for the large-scale data sets and high-dimensional data, for example, for the meat data discussed in this article that have 100 highly correlated covariates. For such data, it suffers from large variance of parameter estimation and high predictive errors, and numerically, it suffers from unstable computation. In this article, penalized likelihood framework will be applied to the model based on GPs. Different penalties will be investigated, and their ability in application given to suit the characteristics of GP models will be discussed. The asymptotic properties will also be discussed with the relevant proofs. Several applications to real biomechanical and bioinformatics data sets will be reported.     

Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form

The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data.     

Semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles

We consider semiparametric regression for periodic longitudinal data. Parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect. The within-subject correlation is modeled using subject-specific random effects and a random stochastic process with a periodic variance function. We use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function, whose estimator is shown to be a periodic cubic smoothing spline. We use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components. We show that all model parameters can be easily obtained by fitting a linear mixed model. A common problem in the analysis of longitudinal data is to compare the time profiles of two groups, e.g., between treatment and placebo. We develop a scaled chi-squared test for the equality of two nonparametric time functions. The proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations.     

Unified maximum likelihood estimates for closed capture-recapture models using mixtures

Agresti (1994, Biometrics 50, 494-500) and Norris and Pollock (1996a, Biometrics 52, 639-649) suggested using methods of finite mixtures to partition the animals in a closed capture-recapture experiment into two or more groups with relatively homogeneous capture probabilities. This enabled them to fit the models Mh, Mbh (Norris and Pollock), and Mth (Agresti) of Otis et al. (1978, Wildlife Monographs 62, 1-135). In this article, finite mixture partitions of animals and/or samples are used to give a unified linear-logistic framework for fitting all eight models of Otis et al. by maximum likelihood. Likelihood ratio tests are available for model comparisons. For many data sets, a simple dichotomy of animals is enough to substantially correct for heterogeneity-induced bias in the estimation of population size, although there is the option of fitting more than two groups if the data warrant it.