A comparison of three methods of estimating the logistic regression coefficients

A Sampling experiment performed using data collected for a large clinical trial shows that the discriminant function estimates of the logistic regression coefficients for discrete variables may be severely biased. The simulations show that the mixed variable location model coefficient estimates have bias which is of the same magnitude as the bias in the coefficient estimates obtained using conditional maximum likelihood estimates but require about one-tenth of the computer time.     

Comparing several experimental groups with a control in the multivariate case

This paper presents a multivariate extension of Dunnett's test for comparing simultaneously k treatment group means with a single control group mean. A test based on Hotelling T²statistics is presented and approximate critical values are evaluated for the case of equal numbers of observations in each group, for the .05 and .01 levels of significance, for 1 to 5 variates, for 1 to 10 treatment groups, and for varying degrees of freedom. The accuracy of the procedure for generating approximate critical values is assessed via simulation studies conducted for selected cases and an example is presented using real data.     

A generating algorithm for linear trend-free and nearly linear trend-free block designs

The theory and properties of trend-free (TF) and nearly trend-free (NTF) block designs are wel1 developed. Applications have been hampered because a methodology for design construction has not been available.

This article begins with a short review of concepts and properties of TF and NTF block designs. The major contribution is provision of an algorithm for the construction of linear and nearly linear TF block designs. The algorithm is incorporated in a computer program in FORTRAN 77 provided in an appendix for the IBM PC or compatible microcomputer, a program adaptable also to other computers. Three sets of block designs generated by the program are given as examples.

A numerical example of analysis of a linear trend-free balanced incomplete block design is provided.     

Ridge Regression: Degrees of Freedom in the Analysis of Variance

It appears to be common practice with ridge regression to obtain a decomposition of the total sum of squares, and assign degrees of freedom, according to established least squares theory. This discussion notes the obvious fallacies of such an approach, and introduces a decomposition based on orthogonality, and degrees of freedom based on expected mean squares, for non-stochastic k.     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

Posterior analysis,prediction and reliability in three-parameter weibull distributions

The paper develops Bayesian analysis in the context of samples from three-parameter Weibull distributions and shows how to tackle the problems of prediction and estimation of reliability curves. As Johnson, Kotz and Balakrishnan ( 1994 ) mentioned, the prediction problems for the three-parameter Weibull model seem to be unresolved and is certainly worth looking into (p.671). Posterior analysis organized around Gibbs sampling is shown to perform well. An application to stock returns is used to illustrate the potential of the approach.     

Multiple deletion measures and conditional influence in regression model

The joint effect of the deletion of the ith and jih cases is given by Gray and Ling (1984), they discussed the influence measures for influential subsets in linear regression analysis. The present paper is concerned with multiple sets of deletion measures in the linear regression model. In particular we are interested in the effects of the jointly and conditional influence analysis for the detection of two influential subsets.     

A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.     

Penalized inverse probability weighted estimators for weighted rank regression with missing covariates

Abstract

In this article, we study the variable selection and estimation for linear regression models with missing covariates. The proposed estimation method is almost as efficient as the popular least-squares-based estimation method for normal random errors and empirically shown to be much more efficient and robust with respect to heavy tailed errors or outliers in the responses and covariates. To achieve sparsity, a variable selection procedure based on SCAD is proposed to conduct estimation and variable selection simultaneously. The procedure is shown to possess the oracle property. To deal with the covariates missing, we consider the inverse probability weighted estimators for the linear model when the selection probability is known or unknown. It is shown that the estimator by using estimated selection probability has a smaller asymptotic variance than that with true selection probability, thus is more efficient. Therefore, the important Horvitz-Thompson property is verified for penalized rank estimator with the covariates missing in the linear model. Some numerical examples are provided to demonstrate the performance of the estimators.