Cox regression with missing covariate data using a modified partial likelihood method

Missing covariate values is a common problem in survival analysis. In this paper we propose a novel method for the Cox regression model that is close to maximum likelihood but avoids the use of the EM-algorithm. It exploits that the observed hazard function is multiplicative in the baseline hazard function with the idea being to profile out this function before carrying out the estimation of the parameter of interest. In this step one uses a Breslow type estimator to estimate the cumulative baseline hazard function. We focus on the situation where the observed covariates are categorical which allows us to calculate estimators without having to assume anything about the distribution of the covariates. We show that the proposed estimator is consistent and asymptotically normal, and derive a consistent estimator of the variance–covariance matrix that does not involve any choice of a perturbation parameter. Moderate sample size performance of the estimators is investigated via simulation and by application to a real data example.     

On the robustness of the generalized fused lasso to prior specifications

Using networks as prior knowledge to guide model selection is a way to reach structured sparsity. In particular, the fused lasso that was originally designed to penalize differences of coefficients corresponding to successive features has been generalized to handle features whose effects are structured according to a given network. As any prior information, the network provided in the penalty may contain misleading edges that connect coefficients whose difference is not zero, and the extent to which the performance of the method depend on the suitability of the graph has never been clearly assessed. In this work we investigate the theoretical and empirical properties of the adaptive generalized fused lasso in the context of generalized linear models. In the fixed \(p\) setting, we show that, asymptotically, adding misleading edges in the graph does not prevent the adaptive generalized fused lasso from enjoying asymptotic oracle properties, while forgetting suitable edges can be more problematic. These theoretical results are complemented by an extensive simulation study that assesses the robustness of the adaptive generalized fused lasso against misspecification of the network as well as its applicability when theoretical coefficients are not exactly equal. Our contribution is also to evaluate the applicability of the generalized fused lasso for the joint modeling of multiple sparse regression functions. Illustrations are provided on two real data examples.     

Stochastically optimal bootstrap sample size for shrinkage-type statistics

In nonregular problems where the conventional \(n\) out of \(n\) bootstrap is inconsistent, the \(m\) out of \(n\) bootstrap provides a useful remedy to restore consistency. Conventionally, optimal choice of the bootstrap sample size \(m\) is taken to be the minimiser of a frequentist error measure, estimation of which has posed a major difficulty hindering practical application of the \(m\) out of \(n\) bootstrap method. Relatively little attention has been paid to a stronger, stochastic, version of the optimal bootstrap sample size, defined as the minimiser of an error measure calculated directly from the observed sample. Motivated by this stronger notion of optimality, we develop procedures for calculating the stochastically optimal value of \(m\). Our procedures are shown to work under special forms of Edgeworth-type expansions which are typically satisfied by statistics of the shrinkage type. Theoretical and empirical properties of our methods are illustrated with three examples, namely the James–Stein estimator, the ridge regression estimator and the post-model-selection regression estimator.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

Predictive Inference for Big,Spatial, Non‐Gaussian Data: MODIS Cloud Data and its Change‐of‐Support

Remote sensing of the earth with satellites yields datasets that can be massive in size, nonstationary in space, and non‐Gaussian in distribution. To overcome computational challenges, we use the reduced‐rank spatial random effects (SRE) model in a statistical analysis of cloud‐mask data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board NASA's Terra satellite. Parameterisations of cloud processes are the biggest source of uncertainty and sensitivity in different climate models’ future projections of Earth's climate. An accurate quantification of the spatial distribution of clouds, as well as a rigorously estimated pixel‐scale clear‐sky‐probability process, is needed to establish reliable estimates of cloud‐distributional changes and trends caused by climate change. Here we give a hierarchical spatial‐statistical modelling approach for a very large spatial dataset of 2.75 million pixels, corresponding to a granule of MODIS cloud‐mask data, and we use spatial change‐of‐Support relationships to estimate cloud fraction at coarser resolutions. Our model is non‐Gaussian; it postulates a hidden process for the clear‐sky probability that makes use of the SRE model, EM‐estimation, and optimal (empirical Bayes) spatial prediction of the clear‐sky‐probability process. Measures of prediction uncertainty are also given.     

Differences by gender, ethnicity, and acculturation in the efficacy of the keepin' it REAL model prevention program

This study examined whether the efficacy of keepin' it REAL, a model program for substance use prevention in schools, was moderated by gender, ethnicity, and acculturation. Gender differences in program efficacy may arise through boys' higher risk of drug use, inadequate attention to girls' developmental issues, or cultural factors like polarized gender expectations. Data came from a randomized trial in 35 Phoenix, Arizona, middle schools involving 4,622 mostly Latino 7th graders. Using multi-level mixed models and multiple imputation missing techniques, results for the total sample showed no gender differences in program effects on recent substance use, but the program was more effective in fostering boys' than girls' anti-drug norms. Subgroup analyses demonstrated several more beneficial program effects for boys than girls (less alcohol and cigarette use and stronger anti-drug norms), but only among less acculturated Latinos. There were no gender differences in program effects among more acculturated Latinos, nor among non-Latino whites.     

Effects of a single-lesson tobacco prevention curriculum on knowledge, skill identification and smoking intention

One in five students report experimenting with tobacco before the age of 13 and most prevention efforts take place in the school setting. This study measures the effect of a single-lesson tobacco prevention curriculum, conducted by a health education center, focusing on knowledge of tobacco, ability to identify refusal techniques, and intent not to smoke. Data were collected, via electronic keypads, from students visiting a non-school, health education center in Michigan (n = 704 intervention and 85 comparison). Contingency table Chi-squared tests and t-tests demonstrated that a single lesson can improve general knowledge and ability to identify appropriate refusal techniques. Improvement in intent not to smoke was not significant because both groups had very high intent prior to implementation. Similar to results from other programs, multivariate logistic regression of gender, general knowledge, and skill identification revealed that only the skill variable was associated with intent not to smoke at pretest. Recommendations are given for further research and for designing more effective curricula or programs.     

Intergenerational class mobility in contemporary Britain: political concerns and empirical findings

In Britain in recent years social mobility has become a topic of central political concern, primarily as a result of the effort made by New Labour to make equality of opportunity rather than equality of condition a focus of policy. Questions of the level, pattern and trend of mobility thus bear directly on the relevance of New Labour's policy analysis, and in turn are likely be crucial to the evaluation of its performance in government. However, politically motivated discussion of social mobility often reveals an inadequate grasp of both empirical and analytical issues. We provide new evidence relevant to the assessment of social mobility - in particular, intergenerational class mobility - in contemporary Britain through cross-cohort analyses based on the NCDS and BCS datasets which we can relate to earlier cross-sectional analyses based on the GHS. We find that, contrary to what seems now widely supposed, there is no evidence that absolute mobility rates are falling; but, for men, the balance of upward and downward movement is becoming less favourable. This is overwhelmingly the result of class structural change. Relative mobility rates, for both men and women, remain essentially constant, although there are possible indications of a declining propensity for long-range mobility. We conclude that under present day structural conditions there can be no return to the generally rising rates of upward mobility that characterized the middle decades of the twentieth century - unless this is achieved through changing relative rates in the direction of greater equality or, that is, of greater fluidity. But this would then produce rising rates of downward mobility to exactly the same extent - an outcome apparently unappreciated by, and unlikely to be congenial to, politicians preoccupied with winning the electoral 'middle ground'.     

Do hostile sexual beliefs affect men's perceptions of sexual-interest messages?

This study tested the distorted cognitions component of Hall and Hirschman's (1991) quadripartite model of sexual aggression. Men (N = 107) with and without hostile sexual beliefs viewed erotic slides with a female partner who provided one of four patterns of feedback: clear disinterest, token disinterest, compliant interest, and clear interest. Hostile men reported fewer differences between women, were unresponsive to their partner's perceived embarrassment, and reported a consistent positive mood regardless of her feedback. Conversely, nonhostile men were more responsive to feedback, mirrored the partner's embarrassment, and experienced a less positive mood when she communicated clear disinterest in the erotica. These findings support the distorted cognitions component of the quadripartite model of sexual aggression. The authors also discuss the strengths and limitations of this study's methodology.