The response functions for competing risks

The competing risks data consist of a pair (T,δ) where T≧0 can be interpreted as the failure time and δ as the identifier of the risk causing the failure. In many practical situations, the main interest lies in studying the inter-relationships between the probability structures of the failure time under various risks. Here, we consider two risks and propose the Junctional relationships between the probability structure of (T,δ=1) and (T,δ=2) by time-dependent scale and shape shifts. Also, a model which raptures the relative aging of a unit under the two risks is proposed. The necessary theory for confidence estimation of these shift functions is developed. These techniques are illustrated through several data sets available in the literature.     

On a recent generalization of gamma distribution

In this paper, we investigate a generalized gamma distribution recentIy developed by Agarwal and Kalla (1996). Also, we show that such generalized distribution, like the ordinary gamma distribution, has a unique mode and, unlike the ordinary gamma distribution, may have a hazard rate (mean residual life) function which is upside-down bathtub (bathtub) shaped.     

Childhood mortality spatial distribution in Ethiopia

The risk of a child dying before completing five years of age is highest in Sub-Saharan African countries. But Child mortality rates have shown substantial decline in Ethiopia. For this study, the 2000, 2005 and 2011 Ethiopian Demographic Survey (EDHS) was used. Generalized linear mixed model with spatial covariance structure was adapted. The model allowed for spatial correlation, and leads to the more realistic estimate for under-five mortality risk factors. The analysis showed that the risk of under-five mortality shows decline in years. But, some regions showed increase in years. The study highlights the need to implement better education for family planning and child care to improve the under-five mortality situation in some administrative areas.     

Likelihood‐based Inference with Missing Data Under Missing‐at‐Random

Likelihood‐based inference with missing data is challenging because the observed log likelihood is often an (intractable) integration over the missing data distribution, which also depends on the unknown parameter. Approximating the integral by Monte Carlo sampling does not necessarily lead to a valid likelihood over the entire parameter space because the Monte Carlo samples are generated from a distribution with a fixed parameter value. We consider approximating the observed log likelihood based on importance sampling. In the proposed method, the dependency of the integral on the parameter is properly reflected through fractional weights. We discuss constructing a confidence interval using the profile likelihood ratio test. A Newton–Raphson algorithm is employed to find the interval end points. Two limited simulation studies show the advantage of the Wilks inference over the Wald inference in terms of power, parameter space conformity and computational efficiency. A real data example on salamander mating shows that our method also works well with high‐dimensional missing data.     

Simplified Likelihood Based Goodness-of-fit Tests for the Weibull Distribution

The aim of this paper is to present new likelihood based goodness-of-fit tests for the two-parameter Weibull distribution. These tests consist in nesting the Weibull distribution in three-parameter generalized Weibull families and testing the value of the third parameter by using the Wald, score, and likelihood ratio procedures. We simplify the usual likelihood based tests by getting rid of the nuisance parameters, using three estimation methods. The proposed tests are not asymptotic. A comprehensive comparison study is presented. Among a large range of possible GOF tests, the best ones are identified. The results depend strongly on the shape of the underlying hazard rate.     

Subject-specific odds ratios in binomial GLMMs with continuous response

In a regression context, the dichotomization of a continuous outcome variable is often motivated by the need to express results in terms of the odds ratio, as a measure of association between the response and one or more risk factors. Starting from the recent work of Moser and Coombs (Stat Med 23:1843–1860, 2004) in this article we explore in a mixed model framework the possibility of obtaining odds ratio estimates from a regression linear model without the need of dichotomizing the response variable. It is shown that the odds ratio estimators derived from a linear mixed model outperform those from a binomial generalized linear mixed model, especially when the data exhibit high levels of heterogeneity.     

Detection of a changepoint,a mean-shift accompanied with a trend change,in short time-series with autocorrelation

In this study, a changepoint model, which can detect either a mean shift or a trend change when accounting for autocorrelation in short time-series, was investigated with simulations and a new method is proposed. The changepoint hypotheses were tested using a likelihood ratio test. The test statistic does not follow a known distribution and depends on the length of the time-series and the autocorrelation. The results imply that it is not possible to detect autocorrelation and that the estimate of the autocorrelation parameter is biased. It is therefore recommended to use critical values from the empirical distribution for a fixed autocorrelation.     

Partial logistic relevance vector machines in survival analysis

The use of relevance vector machines to flexibly model hazard rate functions is explored. This technique is adapted to survival analysis problems through the partial logistic approach. The method exploits the Bayesian automatic relevance determination procedure to obtain sparse solutions and it incorporates the flexibility of kernel-based models. Example results are presented on literature data from a head-and-neck cancer survival study using Gaussian and spline kernels. Sensitivity analysis is conducted to assess the influence of hyperprior distribution parameters. The proposed method is then contrasted with other flexible hazard regression methods, in particular the HARE model proposed by Kooperberg et al. [16]. A simulation study is conducted to carry out the comparison. The model developed in this paper exhibited good performance in the prediction of hazard rate. The application of this sparse Bayesian technique to a real cancer data set demonstrated that the proposed method can potentially reveal characteristics of the hazards, associated with the dynamics of the studied diseases, which may be missed by existing modeling approaches based on different perspectives on the bias vs. variance balance.     

Partial orders with respect to continuous covariates and tests for the proportional hazards model

Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against ordered alternatives like monotone hazard ratio and monotone ratio of cumulative hazards. Here we propose a natural extension of these partial orders to the case of continuous and potentially time varying covariates, and develop tests for the proportional hazards assumption against such ordered alternatives. The work is motivated by applications in biomedicine and economics where covariate effects often decay over lifetime. The proposed tests do not make restrictive assumptions on the underlying regression model, and are applicable in the presence of time varying covariates, multiple covariates and frailty. Small sample performance and an application to real data highlight the use of the framework and methodology to identify and model the nature of departures from proportionality.     

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n^−1/2 for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests.