Modified check loss for efficient estimation via model selection in quantile regression.

The check loss function is used to define quantile regression. In cross-validation, it is also employed as a validation function when the true distribution is unknown. However, our empirical study indicates that validation with the check loss often leads to overfitting the data. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. This has the effect of guarding against overfitting to some extent. The adjustment is devised to shrink to zero as sample size grows. Through various simulation settings of linear and nonlinear regressions, the improvement due to modification of the check loss by quadratic adjustment is examined empirically.

A class of generalized linear mixed models adjusted for marginal interpretability.

Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model (GLMM) by introducing latent random variables. The first approach is effective for parameter estimation, but leaves one without a formal model for the data with which to assess quality of fit or make individual-level predictions for future observations. The second approach overcomes these deficiencies, but leads to parameter estimates that must be interpreted conditional on the latent variables. To obtain marginal summaries, one needs to evaluate an analytically intractable integral or use attenuation factors as an approximation. Further, we note an unpalatable implication of the standard GLMM. To resolve these issues, we turn to a class of marginally interpretable GLMMs that lead to parameter estimates with a marginal interpretation while maintaining the desirable statistical properties of a conditionally specified model and avoiding problematic implications. We establish the form of these models under the most commonly used link functions and address computational issues. For logistic mixed effects models, we introduce an accurate and efficient method for evaluating the logistic-normal integral.

Low cancer incidence rates in Ohio Amish.

BACKGROUND: The Amish have not been previously studied for cancer incidence, yet they have the potential to help in the understanding of its environmental and genetic contributions. The purpose of this study was to estimate the incidence of cancer among the largest Amish population. METHODS: Adults from randomly selected households were interviewed and a detailed cancer family history was taken. Using both the household interview data and a search of the Ohio cancer registry data, a total of 191 cancer cases were identified between the years 1996 and 2003. RESULTS: The age-adjusted cancer incidence rate for all cancers among the Amish adults was 60% of the age-adjusted adult rate in Ohio (389.5/10(5) vs. 646.9/10(5); p < 0.0001). The incidence rate for tobacco-related cancers in the Amish was 37% of the rate for Ohio adults (p < 0.0001). The incidence rate for non-tobacco-related cancers in the Amish was 72% of the age-adjusted adult rate in Ohio (p = 0.0001). CONCLUSION: Cancer incidence is low in the Ohio Amish. These data strongly support reduction of cancer incidence by tobacco abstinence but cannot be explained solely on this basis. Understanding these contributions may help to identify additional important factors to target to reduce cancer among the non-Amish.

Judgement post-stratification for designed experiments.

In many scientific studies, information that is not easily translated into covariates is ignored in the analysis. However, this type of information may significantly improve inference. In this research, we apply the idea of judgment post-stratification to utilize such information. Specifically, we consider experiments that are conducted under a completely randomized design. Sets of experimental units are formed, and the units in a set are ranked. Estimation is performed conditional on the sets and ranks. We propose a new estimator for a treatment contrast. We improve the new estimator by Rao-Blackwellization. Asymptotic distribution theory and corresponding inferential procedures for both estimators are developed. Simulation studies quantify the superiority of the new estimators and show their desirable properties for small and moderate sample sizes. The impact of the new techniques is illustrated with data from a clinical trial.

Judgement post-stratification with imprecise rankings.

Judgement post-stratification, which is based on ideas similar to those in ranked set sampling, relies on the ability of a ranker to forecast the ranks of potential observations on a set of units. In practice, the authors sometimes find it difficult to assign these ranks. This note shows how one can borrow techniques from the literature on finite population sampling to allow a probabilistic ranking of the units in a set, thus facilitating use of these sampling plans and improving estimation. The same techniques provide one approach to estimation using a judgement post-stratified sample with multiple rankers. The technique is illustrated on allometric data relating brain weight to body weight in different species of mammals, and on a study of student performance in graduate school.