The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects. I describe 4 different propensity score methods: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. I describe balance diagnostics for examining whether the propensity score model has been adequately specified. Furthermore, I discuss differences between regression-based methods and propensity score-based methods for the analysis of observational data. I describe different causal average treatment effects and their relationship with propensity score analyses.

https://www.tandfonline.com/doi/pdf/10.1080/00273171.2011.568786

An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies

A review of 144 published studies of the relationship between socioeconomic status (SES) and obesity reveals a strong inverse relationship among women in developed societies. The relationship is inconsistent for men and children in developed societies. In developing societies, however, a strong direct relationship exists between SES and obesity among men, women, and children. A review of social attitudes toward obesity and thinness reveals values congruent with the distribution of obesity by SES in different societies. Several variables may mediate the influence of attitudes toward obesity and thinness among women in developed societies that result in the inverse relationship between SES and obesity. They include dietary restraint, physical activity, social mobility, and inheritance.

Socioeconomic Status and Obesity: A Review of the Literature

Prognostic models are used in medicine for investigating patient outcome in relation to patient and disease characteristics. Such models do not always work well in practice, so it is widely recommended that they need to be validated. The idea of validating a prognostic model is generally taken to mean establishing that it works satisfactorily for patients other than those from whose data it was derived. In this paper we examine what is meant by validation and review why it is necessary. We consider how to validate a model and suggest that it is desirable to consider two rather different aspects - statistical and clinical validity - and examine some general approaches to validation. We illustrate the issues using several case studies.

What do we mean by validating a prognostic model

A review of uses of health care utilization databases for epidemiologic research on therapeutics

An important problem exists in the interpretation of modern medical research data: Biological understanding and previous research play little formal role in the interpretation of quantitative results. This phenomenon is manifest in the discussion sections of research articles and ultimately can affect the reliability of conclusions. The standard statistical approach has created this situation by promoting the illusion that conclusions can be produced with certain "error rates," without consideration of information from outside the experiment. This statistical approach, the key components of which are P values and hypothesis tests, is widely perceived as a mathematically coherent approach to inference. There is little appreciation in the medical community that the methodology is an amalgam of incompatible elements, whose utility for scientific inference has been the subject of intense debate among statisticians for almost 70 years. This article introduces some of the key elements of that debate and traces the appeal and adverse impact of this methodology to the P value fallacy, the mistaken idea that a single number can capture both the long-run outcomes of an experiment and the evidential meaning of a single result. This argument is made as a prelude to the suggestion that another measure of evidence should be used--the Bayes factor, which properly separates issues of long-run behavior from evidential strength and allows the integration of background knowledge with statistical findings.

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Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy

Twisk JW. 301 pages. New York: Cambridge Univ Pr; 2003. ISBN 0521525802. $40.00. Order phone 845-353-7500. Field of medicine: Epidemiology and biostatistics. Format: Softcover book. Audience: Physician researchers, epidemiologists, and analysts of biomedical data. Purpose: To provide a cogent nontechnical introduction to the analysis of clinical and epidemiologic longitudinal studies. Content: In longitudinal studies, the outcome variable is measured in the same individual on several different occasions so that the development of a certain outcome can be studied over time and be related to development of other variables. The book's chapters on continuous, binary, and categorical and count outcomes begin by reviewing traditional approaches to longitudinal (panel) data. Those approaches include comparing changes and repeated-measures analysis of variance. The book focuses on generalized estimating equations models, random coefficient models, and other extensions of ordinary regression to repeated-measures data. Those sophisticated methods have greater statistical power, interpretability, and ability to handle missing data than do traditional approaches. The book also includes chapters on missing data, tracking, sample size, and other aspects of study design. Highlights: Twisk uses autoregressive (Markov) models and models of changes to isolate longitudinal (within-subject) effects and carefully explains modeling strategies. By repeatedly analyzing the same data set, he compares the computer output from different model types to illustrate their similarities and differences. I used the book as the text in an ongoing longitudinal data study group, and the group found it understandable, stimulating, and practical. The chapter on software contains the statistical code (in SAS software [SAS Institute, Inc., Cary, North Carolina], Stata software [Stata Corp., College Station, Texas], and S-Plus software [MathSoft, Inc., Seattle, Washington]) and corresponding computer output from those statistical programs. We used data sets obtained from the author and replicated many analyses by comparing the generated code with the book's presented computer output. Limitations: There were discrepancies between some of the computer output and the statistical code used to generate it. Including the data sets in the book or making them available on a Web site would have been helpful. Ambiguities, such as those in Figures 5.3 and 5.5, could be eliminated by more detailed legends. Related reading: Kleinbaum and Klein's Logistic Regression: A Self Learning Text, 2nd edition (Springer, 2002), includes clear introductions to logistic regression and longitudinal data analysis but is restricted to binary outcomes. Brown and Prescott's Applied Mixed Models in Medicine (Wiley, 1999) is a well-written, intermediate text. It presents random coefficient models with examples analyzed in SAS software. Diggle and colleagues' Analysis of Longitudinal Data, 2nd edition (Oxford, 2002), the standard advanced comprehensive reference work, includes excellent figures and detailed examples in a development that emphasizes statistical theory. Reviewer: Leonard E. Braitman, PhD, Albert Einstein Healthcare Network, Philadelphia, Pennsylvania, for the Longitudinal Data Study Group; e-mail, lbraitman@att.net.

Applied Longitudinal Data Analysis for Epidemiology: A Practical Guide

Focusing on Jasmer and colleagues' study in this issue, the authors discuss the use of propensity scores to adjust for overt biases in treatment assignment in nonrandomized trials.

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Rare outcomes, common treatments: analytic strategies using propensity scores.

A probability model expresses the relation between the presence of clinical findings (input or independent variables) and the probability that a clinical state will occur (the dependent variable); for example, it expresses the probability that a disease is present or will develop or the probability that an outcome state will be reached. Probability models are developed by using selected study groups. Although these models are most often used to make predictions for groups of patients, they can also predict clinical states for individual patients. The following seven criteria provide a basis for the critical appraisal of probability models. In particular, physicians can use these criteria to decide when a specific probability model should be used to make a prediction in an individual patient. Five of the criteria are concerned with the applicability of a model to a particular patient: 1) the comparability of the patient and the study group used to develop the model; 2) the congruence between the clinical state of interest to patient and physician and the model's outcome; 3) the availability of all input variables where and when the prediction is to be made; 4) the usefulness of a quantitative estimate of the predicted clinical state; and 5) the degree of uncertainty in the probability estimate. The other two criteria are concerned with how well the probability model "works": 6) the fit of probabilities calculated from the model to the outcomes actually observed and 7) the model's ability to discriminate between outcome states relative to chance and to other, more traditional, prediction methods. We illustrate the use of these criteria by applying them, in the form of questions, to a convenient, tabular version of a model that estimates a patient's chances of surviving for 10 years after having definitive surgical therapy for primary cutaneous melanoma.

Predicting Clinical States in Individual Patients

Obesity and caloric intake: The national Health and Nutrition Examination Survey of 1971–1975 (HANES I)

Excerpt A paper reporting a trial of a new treatment or diagnostic test is difficult to interpret when its conclusions are based on a small number of subjects. The statistical descriptors known as ...

Leonard E. Braitman

Papers

Applied Longitudinal Data Analysis for Epidemiology: A Practical Guide

Rare outcomes, common treatments: analytic strategies using propensity scores.

Predicting Clinical States in Individual Patients

Obesity and caloric intake: The national Health and Nutrition Examination Survey of 1971–1975 (HANES I)

Confidence Intervals Extract Clinically Useful Information from Data