Abstract: Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a con tinuous right-skewed distribution for positive values. We review methods pro posed in the literature for analyzing data with excess zeros. A two-part logit-log normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.
Abstract: : In this paper, we discussed classical and Bayes estimation procedures for estimating the unknown parameters as well as the reliability and hazard functions of the flexible Weibull distribution when observed data are collected under progressively Type-II censoring scheme. The performances of the maximum likelihood and Bayes estimators are compared in terms of their mean squared errors through the simulation study. For the computation of Bayes estimates, we proposed the use of Lindley’s approximation and Markov Chain Monte Carlo (MCMC) techniques since the posteriors of the parameters are not analytically tractable. Further, we also derived the one and two sample posterior predictive densities of future samples and obtained the predictive bounds for future observations using MCMC techniques. To illustrate the discussed procedures, a set of real data is analysed.
Abstract: Motivated by a situation encountered in the Well Elderly 2 study, the paper considers the problem of robust multiple comparisons based on K independent tests associated with 2K independent groups. A simple strategy is to use an extension of Dunnett’s T3 procedure, which is designed to control the probability of one or more Type I errors. However, this method and related techniques fail to take into account the overall pattern of p-values when making decisions about which hypotheses should be rejected. The paper suggests a multiple comparison procedure that does take the overall pattern into account and then describes general situations where this alternative approach makes a practical difference in terms of both power and the probability of one or more Type I errors. For reasons summarized in the paper, the focus is on 20% trimmed means, but in principle the method considered here is relevant to any situation where the Type I error probability of the individual tests can be controlled reasonably well.
Abstract: We study a new five-parameter model called the extended Dagum distribution. The proposed model contains as special cases the log-logistic and Burr III distributions, among others. We derive the moments, generating and quantile functions, mean deviations and Bonferroni, Lorenz and Zenga curves. We obtain the density function of the order statistics. The parameters are estimated by the method of maximum likelihood. The observed information matrix is determined. An application to real data illustrates the importance of the new model.
Abstract: : Normally, one may think that the distribution of closed birth interval of any specific order may be the same as the distribution of most recent closed birth interval of the same order. But it is not true. Here the distinction between the distribution of a specific order of usual closed birth interval and most recent closed birth interval of the same order is examined. In this context, firstly we demonstrate the distinction between the most recent closed birth interval and usual closed birth interval empirically by considering a real data set. Further, the distinction between these distributions is demonstrated theoretically, by taking certain hypothetical values of fertility parameters involved in the stochastic model proposed for the purpose.
Abstract: A total of 1094 HIV patients were involved in a cohort study (from January-December 2010) with follow-up in their CD4 cell transition counts and grouped according to their immunological states into five(5) states developed by Guiseppe Di Biase et al (2007). The five states (5) considered were: State one (CD4 > 500 cells/mm3 ), State two (350 < CD4 500 cells /mm3 ) State three(200 < CD4 350 cells/mm3 ), State four(CD4 200 cells/mm3 ), State five(Death). These states de ne the seriousness of the sickness based on the epidemiological states of the patients CD4 cell counts. We use the non-stationary Markov chain model for the prediction. The estimation of the non-stationary probabilities were done using the exponential smoothing technique. The result of the prediction showed a gradual decrease of the CD4 cells as we move from Jan-Dec. Furthermore, the result showed that the patients in the study cannot survive death from the month Dec. 2011, if they are not subjected to therapy, using highly active antiretrovirals (HAART). The results also showed that the model can be used for the testing of the drug e efficacy administered to patients within a given period.
Abstract: Early phase clinical trials may not have a known variation (σ) for the response variable. In the light of applying t-test statistics, several procedures were proposed to use the information gained from stage-I (pilot study) to adaptively re estimate the sample size for managing the overall hypothesis test. We are interested in choosing a reasonable stage-I sample size (m) towards achieving an accountable overall sample size (stage-I and later). Conditional on any specified m, this paper replaces σ by the estimated σ (from stage-I with sample size m) to use the conventional formula under normal distribution assumption to re-estimate an overall sample size. The estimated σ, re-estimated overall sample size and the collective information (stage-I and later) would be incorporated into a surrogate normal variable which undergoes hypothesis test based on standard normal distribution. We plot the actual type I&II error rates and the expected sample size against m in order to choose a good universal stage-I sample size (𝑚∗ ) to start
Abstract: Traditional loss reserves models focus on the mean of the conditional loss distribution. If the factors driving high claims differ systematically from those driving medium to low claims, alternative models that differentiate such differences are required. We propose quantile regression model loss reserving as the model offers potentially different solutions at distinct quantiles so that the effects of risk factors are differentiated at different points of the conditional loss distribution. Due to its nonparametric nature, quantile regression is free of the model assumptions for traditional mean regression models, including homogeneous variance across risk factors and symmetric and light tails, etc. These model assumptions have posed a great barrier in applications as they are often not met in the claim data. Using two sets of run-off triangle claim data from Israel and Queensland, Australia, we present the quantile regression approach that illustrates the sensitivity of claim size to risk factors, namely the trend pattern and initial claim level, in different quantiles. Trained models are applied to predict future claims in the lower run-off triangle. Findings suggest that reliance on standard loss reserves techniques gives rise to misleading inferences and that claim size is not homogeneously driven by the same risk factors across quantiles.
Abstract: Analysis of footprint data is important in the tire industry. Estimation procedures for multiple change points and unknown parameters in a segmented regression model with unknown heteroscedastic variances are developed for analyzing such data. Our approaches include both likelihood and Bayesian, with and without continuity constraints at the change points. A model selection procedure is also proposed to choose among competing models for fitting a middle segment of the data between change points. We study the performance of the two approaches and apply them to actual tire data examples. Our Maximization–Maximization–Posterior (MMP) algorithm and the likelihood–based estimation are found to be complimentary to each other.
Abstract: The generalized gamma model has been used in several applied areas such as engineering, economics and survival analysis. We provide an extension of this model called the transmuted generalized gamma distribution, which includes as special cases some lifetime distributions. The proposed density function can be represented as a mixture of generalized gamma densities. Some mathematical properties of the new model such as the moments, generating function, mean deviations and Bonferroni and Lorenz curves are provided. We estimate the model parameters using maximum likelihood. We prove that the proposed distribution can be a competitive model in lifetime applications by means of a real data set.