The identifiability of the mixed proportional hazards competing risks model

Summary. We prove identification of dependent competing risks models in which each risk has a mixed proportional hazard specification with regressors, and the risks are dependent by way of the unobserved heterogeneity, or frailty, components. We show that the conditions for identification given by Heckman and Honoré can be relaxed. We extend the results to the case in which multiple spells are observed for each subject.     

Job stressors,coping, and psychological distress among Japanese employees: Interplay between active and non-active coping

In this study the sole and the combined effects of active and non-active forms of coping on psychological distress across various kinds of job stressors were examined. Data on job stressors, coping and psychological distress were obtained from 4487 male employees of a research institute in the automobile industry in Japan (mean age=36.27 years, SD = 7.43). A hierarchical moderated multiple regression analysis was conducted to estimate and test the significance of the main effects and their interactions. The results show that although active coping was effective in decreasing psychological distress regardless of the type of job stressor, the effectiveness was weaker in situations that require effortful coping, such as role ambiguity and insufficient authority. Furthermore, the effectiveness of active coping was influenced by the other strategies, especially in effortful coping situations. While distancing or seeking social support improved the effectiveness, restraint coping reduced it. These results suggest that the type of non-active coping that individuals combine with active coping can be critical in determining health outcomes in more complex and effortful coping situations. Consideration of the coping combinations, not merely the situational context, is important in explaining how the work environment influences employees' psychological distress.     

Robustness of the Multiple Correlation Coefficient When Sampling From a Mixture of Two Multivariate Normal Populations

The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis H_o : ρ_1·2…p = 0 versus H_a:ρ_1·2…p > 0, given the mixture model.     

Analysis of a long-term study of neurotic disorder, with insights into the process of non-response

Summary.  The paper studies the non-response process in a long-term study of neurotic dis-order by comparing the analysis based on the responses that were collected by the established practice of interviewing the subjects, at dates arranged in advance (appointments), with the analysis of the nearly complete set of responses that were collected by an extensive effort that involved attempts to interview without seeking a prior agreement. The method of multiple imputation is applied, and its properties are explored in a setting that is not perfectly suited for its application: a relatively small sample size, ordinal score outcomes and the likelihood that the outcomes are missing not at random.     

Bayesian projection of the acquired immune deficiency syndrome epidemic

Short-term projections of the acquired immune deficiency syndrome (AIDS) epidemic in England and Wales have been regularly updated since the publication of the Cox report in 1988. The key approach for those updates has been the back-calculation method, which has been informally adapted to acknowledge various sources of uncertainty as well as to incorporate increasingly available information on the spread of the human immunodeficiency virus (HIV) in the population. We propose a Bayesian formulation of the back-calculation method which allows a formal treatment of uncertainty and the inclusion of extra information, within a single coherent composite model. Estimation of the variably dimensioned model is carried out by using reversible-jump Markov chain Monte Carlo methods. Application of the model to data for homosexual and bisexual males in England and Wales is presented, and the role of the various sources of information and model assumptions is appraised. Our results show a massive peak in HIV infections around 1983 and suggest that the incidence of AIDS has now reached a plateau, although there is still substantial uncertainty about the future.     

Asymptotically valid single-stage multiple-comparison procedures

We establish general conditions for the asymptotic validity of single-stage multiple-comparison procedures (MCPs) under the following general framework. There is a finite number of independent alternatives to compare, where each alternative can represent, e.g., a population, treatment, system or stochastic process. Associated with each alternative is an unknown parameter to be estimated, and the goal is to compare the alternatives in terms of the parameters. We establish the MCPs’ asymptotic validity, which occurs as the sample size of each alternative grows large, under two assumptions. First, for each alternative, the estimator of its parameter satisfies a central limit theorem (CLT). Second, we have a consistent estimator of the variance parameter appearing in the CLT. Our framework encompasses comparing means (or other moments) of independent (not necessarily normal) populations, functions of means, quantiles, steady-state means of stochastic processes, and optimal solutions of stochastic approximation by the Kiefer–Wolfowitz algorithm. The MCPs we consider are multiple comparisons with the best, all pairwise comparisons, all contrasts, and all linear combinations, and they allow for unknown and unequal variance parameters and unequal sample sizes across alternatives.     

Large-scale multiple testing under dependence

Summary.  The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two-state hidden Markov model. We propose oracle and asymptotically optimal data-driven procedures that aim to minimize the false non-discovery rate FNR subject to a constraint on the false discovery rate FDR. It is shown that the performance of a multiple-testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses, and hence conventional FDR procedures that ignore this structural information are inefficient. Both theoretical properties and numerical performances of the procedures proposed are investigated. It is shown that the procedures proposed control FDR at the desired level, enjoy certain optimality properties and are especially powerful in identifying clustered non-null cases. The new procedure is applied to an influenza-like illness surveillance study for detecting the timing of epidemic periods.     

A Note on Stagewise Regression

Suppose one estimates the coefficient β₂ in E[Y] = β₀ + β₁ X ₁ + β₂ X ₂ by stagewise regression. That is, first the model E[Y] ≌ β₀ + β₁ X ₁ is fit using simple linear regression followed by a simple linear regression of the residuals from this model on X ₂ to yield the estimator β₂. The ratio of the squared t statistic for the estimate b ₂ from multiple regression to the squared t statistic for β₂ is greater than or equal to 1.0 and is shown to be a convenient function of correlation coefficients among Y, X ₁, and X ₂. Examination of stagewise regression can provide useful insights when introducing concepts of multiple regression.     

Some Deficiencies of Using Moment Generating Functions

Dissatisfaction is expressed with the well-known definitions of partial and multiple correlation. Partial correlation is defined here as the ordinary correlation between two random variables after their linear dependence on the partialed-out variables has been subtracted. This leads to familiar results; it also clarifies the auto-regressivelike assumptions required for the partial autocorrelations to have a cut-off property. Multiple correlation is similarly considered.     

The average area under correlated receiver operating characteristic curves: a nonparametric approach based on generalized two-sample Wilcoxon statistics

It is well known that, when sample observations are independent, the area under the receiver operating characteristic (ROC) curve corresponds to the Wilcoxon statistics if the area is calculated by the trapezoidal rule. Correlated ROC curves arise often in medical research and have been studied by various parametric methods. On the basis of the Mann–Whitney U-statistics for clustered data proposed by Rosner and Grove, we construct an average ROC curve and derive nonparametric methods to estimate the area under the average curve for correlated ROC curves obtained from multiple readers. For the more complicated case where, in addition to multiple readers examining results on the same set of individuals, two or more diagnostic tests are involved, we derive analytic methods to compare the areas under correlated average ROC curves for these diagnostic tests. We demonstrate our methods in an example and compare our results with those obtained by other methods. The nonparametric average ROC curve and the analytic methods that we propose are easy to explain and simple to implement.