Category: Covariate adjustment (June 22, 2007). Covariate adjustment is the use of statistical methods (most notably analysis of covariance or ANCOVA) to correct for an imbalance in an important prognostic variable between a treatment/exposure group and a control group. You can find the theme and closely related categories and other resources at the bottom of this page.

Stats: A simple application of propensity scores (April 26, 2006). In many research studies, you do not have the opportunity to randomly assign an exposure variable. The influence of the exposure variable on the outcome variable can sometimes produce misleading results because there may be other covariates which are important predictors of the outcome which are also imbalanced across the levels of exposure. A propensity score model creates a new composite variable, the propensity score, which helps you identify pairs or groups of variables with similar covariate patterns. The use of stratification or matching on the propensity score removes the effect of covariate imbalance and allows for a fair and unbiased comparison of the exposure group with the control group.

Stats: Adjusted odds ratios (January 20, 2005) Someone asked me today how to compute an adjusted odds ratio. He has a case control study where cases represent cancer patients. He also has various Single Nucleotide Polymorphisms (SNPs). These would be coded as 0-1 depending on whether the SNP was present or absent. He also has demographic information, such as age, sex, smoking status, and so forth.

Stats: Adjusting a variable for age and sex (October 26, 2006). Someone asked me how to adjust bone mineral density (BMD) for age and sex. I presume that BMD changes as children grow (or as adults age) and that BMD is different for men and women. If you did not adjust for age and sex, then are statistical comparison that you make between a treatment group and control group could be biased by a differential in the sex ratio and/or average age between the two groups.

Stats: Adjusting for a baseline measurement (February 28, 2005). Someone asked me today about how to analyze a two group experiment with a baseline value. This is common research design. Researchers will assess all patients at the beginning of the study. They then randomly assign half of these patients to receive an intervention and half to be in a control group. Then they take a second measurement of the same outcome. The measurement at the beginning of the study, the baseline value, helps improve the research design by removing some of the variation in the data. There are four common approaches for analyzing this data, two good and two bad.

Stats: Adjusting for covariate imbalance (May 20, 2005). Here's a graph I want to insert in my book. It illustrates how to adjust for covariate imbalance. The data comes from the Data and Story Library, lib.stat.cmu.edu/DASL/DataArchive.html, and shows the housing prices of 117 homes in Albuquerque, New Mexico in 1993. The data set also includes variables that might influence the sales price of the home such as the size in square feet, the age in years, and whether the house was custom built.

Stats: Moderator variables (February 15, 2005). I've always disliked the excessive use of detailed terminology, but when someone asked me about moderator variables, I had to look up the details. Basically, a moderator variable is one that interacts with the exposure or treatment variable. It effectively forces you to qualify your findings.

Stats: More on propensity score models (June 26, 2006). Several months ago, I set out to develop some good examples of how to use propensity scores to adjust for covariate imbalance in an observational study. I was consulting with someone recently about this very issue and she brought some additional references to my attention. I then dug a bit further and found some additional references as well.

Stats: Propensity scores (March 10, 2006). When I have time, I want to describe the use of propensity scores and show some examples. Propensity scores offer a simple and effective way to correct for covariate imbalance in an observational study.

Stats: Re-weighting the data (January 25, 2005). A recent article, Two Statistical Paradoxes in the Interpretation of Group Differences: Illustrated with Medical School Admission and Licensing Data. Wainer H, Brown LM. The American Statistician 2004: 58(2); 117-23, shows how a simple re-weighting of the data can lead to a fairer comparison between two groups.

Stats: Stepwise regression to screen for covariates (November 25, 2005). Someone wrote asking about how best to use stepwise regression in a research problem where there were a lot of potential covariates. A covariate is a variable which may affect your outcome but which is not of direct interest. You are interested in the covariate only to assure that it does not interfere with your ability to discern a relationship between your outcome and your primary independent variable (usually your treatment or exposure variable).

Stats: Testing baseline imbalance in a randomized study (January 19, 2005). Randomization will roughly balance out the covariates between the treatment group and the control group because of the law of large numbers. Once in a while, though, an important amount of covariate imbalance will creep into a randomized study. Just as a flip of 100 coins will not always yield exactly 50 heads and 50 tails, a randomized study will not always yield perfect covariate imbalance. When such an imbalance occurs, it is called a chance bias or accidental bias. It can seriously affect the quality of your analysis.

Stats: Using APR-DRGs for risk adjustment (May 24, 2006). The 3M company, famous for Post-It notes, among other things, has a division for health information systems. One of their products is software that produces classifications called "All patient Refined Diagnosis Related Groups" or APR-DRGs. These APR-DRGs are computed from information typically collected as part of the billing process. Patients in a common APR-DRG represent a reasonably homogenous set of patients with respect to type of condition and severity of disease.

Theme and closely related categories:

Other resources:

Illustrative example: Are sex and death related? David Batty. BMJ 1998: 316(7145); 1671a-. [Full text]

Illustrative example: Are sex and death related? Study failed to adjust for an important confounder [letter; comment]. David Batty. British Medical Journal 1998: 316(7145); 1671; discussion 1672. [Full text]

Illustrative example: Effect of male age on fertility: evidence for the decline in male fertility with increasing age. M. A. Hassan, S. R. Killick. Fertil Steril 2003: 79 Suppl 32-9. [Medline]

Illustrative example: Maternal smoking and Down syndrome: the confounding effect of maternal age. C. L. Chen, T. J. Gilbert, J. R. Daling. Am J Epidemiol 1999: 149(5); 442-6.

Illustrative example: META-ANALYSIS Dose-specific Meta-Analysis and Sensitivity Analysis of the Relation between Alcohol Consumption and Lung Cancer Risk. Jeffrey E. Korte, Paul Brennan, S. Jane Henley, Paolo Boffetta. Am. J of Epidemiology 2002: 155(6); 496-506.

Illustrative example: Patient volume, staffing, and workload in relation to risk-adjusted outcomes in a random stratified sample of UK neonatal intensive care units: a prospective evaluation. Tucker J, UK Neonatal Staffing Study Group. Lancet 2002: 35999-107. [Medline]

Illustrative example: Sex and death: are they related? Findings from the Caerphilly cohort study. GD Smith, S Frankel, J Yarnell. British Medical Journal 1997: 315(7123); 1641-1644. [Medline] [Abstract] [Full text]

Illustrative example: Sexual intercourse and risk of ischaemic stroke and coronary heart disease: the Caerphilly study. S. Ebrahim, M. May, Y. Ben Shlomo, P. McCarron, S. Frankel, J. Yarnell, G. Davey Smith. J Epidemiol Community Health 2002: 56(2); 99-102. [Medline]

Illustrative example: Socioeconomic status and health in blacks and whites: the problem of residual confounding and the resiliency of race. J. S. Kaufman, R. S. Cooper, D. L. McGee. Epidemiology 1997: 8(6); 621-8.

Interesting article: Assessing non-consent bias with parallel randomized and nonrandomized clinical trials. S. M. Marcus. J Clin Epidemiol 1997: 50(7); 823-8. [Medline]

Interesting article: Baseline imbalance in randomised controlled trials. C Roberts, DJ Torgerson. British Medical Journal 1999: 319(7203); 185. [Medline] [Full text] [PDF]

Interesting article: Causal Knowledge as a Prerequisite for Confounding Evaluation: An Application to Birth Defects Epidemiology. Miguel A. Hernán, Sonia Hernández-Díaz2, Martha M. Werler2 and Allen A. Mitchell2. Am. J of Epidemiology 2002: 155(2); 176-184.

Interesting article: Characteristics of good causation studies. S. Daya. Semin Reprod Med 2003: 21(1); 73-84. [Medline]

Interesting article: Choosing covariates in the analysis of clinical trials. M. L. Beach, P. Meier. Controlled Clinical Trials 1989: 10(4 Suppl); 161S-175S.

Interesting article: Clinical trials in acute myocardial infarction: Should we adjust for baseline characteristics? Ewout W. Steyerberg, Patrick M.M. Bossuyt, Kerry L. Lee. American Heart Journal 2000: 139(5); 745-751.

Interesting article: A comparison of direct adjustment and regression adjustment of epidemiologic measures. T. C. Wilcosky, L. E. Chambless. J Chronic Dis 1985: 38(10); 849-56.

Interesting article: Conditions for confounding of the risk ratio and of the odds ratio. J. F. Boivin, S. Wacholder. American Journal Epidemiology 1985: 121(1); 152-8. [Medline]

Interesting article: Covariate imbalance and conditional size: dependence on model-based adjustments. S. E. Maxwell. Stat Med 1993: 12(2); 101-9. [Medline]

Interesting article: Covariate imbalance and random allocation in clinical trials. S. J. Senn. Stat Med 1989: 8(4); 467-75. [Medline]

Interesting article: How do risk factors work together? Mediators, moderators, and independent, overlapping, and proxy risk factors. H. C. Kraemer, E. Stice, A. Kazdin, D. Offord, D. Kupfer. Am J Psychiatry 2001: 158(6); 848-56. Interesting article: Identifiability, exchangeability, and epidemiological confounding. S. Greenland, J. M. Robins. Int J Epidemiol 1986: 15(3); 413-9.

Interesting article: The impact of covariate imbalance on the size of the logrank test in randomized clinical trials. N. Kinukawa, T. Nakamura, K. Akazawa, Y. Nose. Stat Med 2000: 19(15); 1955-67. [Medline]

Interesting article: Look before You Leap: Stratify before You Standardize. Bernard C.K. Choi. American Journal of Epidemiology 1999: 149(12); 1087-1095.

Interesting article: Mediators and moderators of treatment effects in randomized clinical trials. H. C. Kraemer, G. T. Wilson, C. G. Fairburn, W. S. Agras. Arch Gen Psychiatry 2002: 59(10); 877-83.

Interesting article: Presenting statistical uncertainty in trends and dose-response relations. S Greenland, KB Michels, JM Robins, C Poole, WC Willett. AJE 1999: 149(12); 1077-86.

Interesting article: Properties of simple randomization in clinical trials. J. M. Lachin. Control Clin Trials 1988: 9(4); 312-26. [Medline]

Interesting article: Research Methods: Why Covariance? A Rationale for Using Analysis of Covariance Procedures in Randomized Studies. Matthew J. Taylor. Journal of Early Intervention 1993: 17(4); 455-466.

Interesting article: Statistical properties of randomization in clinical trials. J. M. Lachin. Control Clin Trials 1988: 9(4); 289-311. [Medline]

Interesting article: A summary statistic for measuring change from baseline. R. M. Donahue. J Biopharm Stat 1997: 7(2); 287-99. [Medline]

Interesting article: Suspended judgment. Significance tests of covariate imbalance in clinical trials. C. B. Begg. Control Clin Trials 1990: 11(4); 223-5. [Medline]

Interesting article: Testing for imbalance of covariates in controlled experiments. T. Permutt. Stat Med 1990: 9(12); 1455-62. [Medline]

Interesting article: The use of percentage change from baseline as an outcome in a controlled trial is statistically inefficient: a simulation study. A. J. Vickers. BMC Med Res Methodol 2001: 1(1); 6. [Medline] [Abstract] [Full text] [PDF]

Interesting article: What random assignment does and does not do. M. S. Krause, K. I. Howard. J Clin Psychol 2003: 59(7); 751-66. [Medline]

[Return to full topic list] [Read current weblog entries]

This webpage was written by Steve Simon on 2007-06-22, edited by Steve Simon, and was last modified on 2008-07-08. Send feedback to ssimon at cmh dot edu or click on the email link at the top of the page.