This paper provides an overview of problems in multivariate modeling of epidemiologic data, and examines some proposed solutions. Special attention is given to the task of model selection, which involves selection of the model form, selection of the variables to enter the model, and selection of the form of these variables in the model. Several conclusions are drawn, among them: a) model and variable forms should be selected based on regression diagnostic procedures, in addition to goodness-of-fit tests; b) variable-selection algorithms in current packaged programs, such as conventional stepwise regression, can easily lead to invalid estimates and tests of effect; and c) variable selection is better approached by direct estimation of the degree of confounding produced by each variable than by significance-testing algorithms. As a general rule, before using a model to estimate effects, one should evaluate the assumptions implied by the model against both the data and prior information.

Modeling and variable selection in epidemiologic analysis.

http://faculty.econ.ucdavis.edu/faculty/cameron/research/je97preprint.pdf

An R-squared measure of goodness of fit for some common nonlinear regression models

We congratulate Drs. Kang and Schafer (KS henceforth) for a careful and thought-provoking contribution to the literature regarding the so-called “double robustness” property, a topic that still engenders some confusion and disagreement. The authors’ approach of focusing on the simplest situation of estimation of the population mean μ of a response y when y is not observed on all subjects according to a missing at random (MAR) mechanism (equivalently, estimation of the mean of a potential outcome in a causal model under the assumption of no unmeasured confounders) is commendable, as the fundamental issues can be explored without the distractions of the messier notation and considerations required in more complicated settings. Indeed, as the article demonstrates, this simple setting is sufficient to highlight a number of key points.

As noted eloquently by Molenberghs (2005), in regard to how such missing data/causal inference problems are best addressed, two “schools” may be identified: the “likelihood-oriented” school and the “weighting-based” school. As we have emphasized previously (Davidian, Tsiatis and Leon, 2005), we prefer to view inference from the vantage point of semi-parametric theory, focusing on the assumptions embedded in the statistical models leading to different “types” of estimators (i.e., “likelihood-oriented” or “weighting-based”) rather than on the forms of the estimators themselves. In this discussion, we hope to complement the presentation of the authors by elaborating on this point of view.

Throughout, we use the same notation as in the paper.

/pdf/comment-demystifying-double-robustness-a-comparison-of-57p5hklcrh.pdf

Comment: Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data

The Sarbanes‐Oxley Act (2002) required the U.S. Comptroller General to study the potential effects of requiring mandatory audit firm rotation. The General Accounting Office (GAO) concludes in its recently released study of mandatory audit firm rotation that “mandatory audit firm rotation may not be the most efficient way to strengthen auditor independence” (GAO 2003, Highlights). However, the GAO also suggests that mandatory audit firm rotation could be necessary if the Sarbanes‐Oxley Act's requirements do not lead to improved audit quality (GAO 2003, 5). We examine the relation between audit firm tenure and fraudulent financial reporting. Comparing firms cited for fraudulent reporting from 1990 through 2001 with both a matched set of non‐fraud firms and with the available population of non‐fraud firms, we find that fraudulent financial reporting is more likely to occur in the first three years of the auditor‐client relationship. We fail to find any evidence that fraudulent financial reporting is more lik...

Audit Firm Tenure and Fraudulent Financial Reporting

Generalized additive models have the form η(x) = α + σ fj (x j ), where η might be the regression function in a multiple regression or the logistic transformation of the posterior probability Pr(y = 1 | x) in a logistic regression. In fact, these models generalize the whole family of generalized linear models η(x) = β′x, where η(x) = g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions fj (xj ) nonparametrically, using a scatterplot smoother as a building block. We demonstrate the models in two different analyses: a nonparametric analysis of covariance and a logistic regression. The procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis. A variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions: these include confidence curves, degrees of freedom estimates, and approximat...

Generalized Additive Models: Some Applications

Logistic regression-type models are used in many applications. Some examples include the classical dose-response experiment, prospective and retrospective studies of disease incidence (with and without matching), and the analysis of ordinal data. In most instances, the model is fitted by the method of maximum likelihood, which, like least squares, is sensitive to atypical observations. An alternative to maximum likelihood is proposed and illustrated by examples.

Resistant fits for some commonly used logistic models with medical application.

The recent introduction of complex multivariate statistical models in matched case-control studies is a mixed blessing. Their use can lead to a better understanding of the way in which many variables contribute to the risk of disease. On the other hand, these powerful methods can obscure salient features in the data that might have been detected by other, less sophisticated methods. This shortcoming is due to a lack of support methodology for the routine use of these models. Satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model. Goodness of fit must be examined if inferences are to be trusted. This paper is concerned with the analysis of matched case-control studies with logistic models. Analogies of these models to linear regression models are emphasized. In particular, basic concepts such as analysis of variance, multiple correlation coefficient, one-degree-of-freedom tests, and residual analysis are discussed. The fairly new field of regression diagnostics is also introduced. All procedures are illustrated on a study of bladder cancer in males.

https://www.jstor.org/stable/pdfplus/2530907.pdf

Daryl Pregibon

Papers

Resistant fits for some commonly used logistic models with medical application.

Data analytic methods for matched case-control studies.