The Asymmetric Power-Student-t Model for Censored and Truncated Data.

In this paper, we propose the power Student-t regression model for censored (limited) observations which extends the Student-t censored regression model. This extension is based on the asymmetric and heavy-tailed power Student-t distribution. The score functions and expected information matrix are given as well as the process for estimating the parameters in the model is discussed by using the likelihood approach. Two simulation studies are conducted to evaluate parameter recovery and properties of the model and finally, two applications to a real data set are reported to demonstrate the usefulness of this new methodology.

Truncated Power-Normal Distribution with Application to Non-Negative Measurements.

This paper focuses on studying a truncated positive version of the power-normal (PN) model considered in Durrans (1992). The truncation point is considered to be zero so that the resulting model is an extension of the half normal distribution. Some probabilistic properties are studied for the proposed model along with maximum likelihood and moments estimation. The model is fitted to two real datasets and compared with alternative models for positive data. Results indicate good performance of the proposed model.

Asymmetric regression models with limited responses with an application to antibody response to vaccine.

We develop regression models for limited and censored data based on the mixture between the log-power-normal and Bernoulli-type distributions. A likelihood-based approach is implemented for parameter estimation and a small-scale simulation study is conducted to evaluate parameter recovery, with emphasis on bias estimation. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. A real data example, the safety and immunogenecity study of measles vaccine in Haiti, is presented to illustrate how different models can be used to fit this type of data. As shown, the asymmetric models considered seem to present the best fit for the data set under study, revealing significance of the explanatory variable sex, which is not found significant with the log-normal model.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors.

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model's goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

Mixture of normal distributions in multivariate null intercept measurement error model.

In this paper we propose the use of a multivariate null intercept measurement error model, where the true unobserved value of the covariate follows a mixture of two normal distributions. The proposed model is applied to a dental clinical trial presented in Hadgu and Koch (1999). A Bayesian approach is considered and a Gibbs Sampler is used to perform the computations.

Local influence in comparative calibration models under elliptical t-distributions.

In this paper we consider applications of local influence (Cook, 1986) to evaluate small perturbations in the model or data set in the context of structural comparative calibration (Bolfarine and Galea, 1995) assuming that the measurements obtained follow a multivariate elliptical distribution. Different perturbation schemes are investigated and an application is considered to a real data set, using the elliptical t-distribution.

Testing homogeneity in Weibull-regression models.

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.

Bayesian analysis of a multivariate null intercept errors-in-variables regression model.

Longitudinal data are of great interest in analysis of clinical trials. In many practical situations the covariate can not be measured precisely and a natural alternative model is the errors-in-variables regression models. In this paper we study a null intercept errors-in-variables regression model with a structure of dependency between the response variables within the same group. We apply the model to real data presented in Hadgu and Koch (Hadgu, A., Koch, G. (1999). Application of generalized estimating equations to a dental randomized clinical trial. J. Biopharmaceutical Statistics 9(1):161-178). In that study volunteers with preexisting dental plaque were randomized to two experimental mouth rinses (A and B) or a control mouth rinse with double blinding. The dental plaque index was measured for each subject in the beginning of the study and at two follow-up times, which leads to the presence of an interclass correlation. We propose the use of a Bayesian approach to model a multivariate null intercept errors-in-variables regression model to the longitudinal data. The proposed Bayesian approach accommodates the correlated measurements and incorporates the restriction that the slopes must lie in the (0, 1) interval. A Gibbs sampler is used to perform the computations.