Interpreting regression models in clinical outcome studies.

Measuring the outcome of an intervention is central to the practice of evidence based medicine, and most research papers evaluating patient outcomes now incorporate some form of patient-based metric, such as questionnaires or performance tests. Once an outcome has been defined, researchers typically want to know if any other factors can influence the result. This is typically assessed with regression analysis. Regression analysis 1 determines the relationship of an independent variable (such as bone mineral density) on a dependent variable (such as ageing) with the statistical assumption that all other variables remain fixed. The calculation of the relationship results in a theoretical straight line, and the correlation coefficient (r) measures how closely the observed data are to the theoretical straight line that we have calculated. In such a linear model, we can judge how well the line fits the data ('goodness of fit') by calculating the coefficient of determination (or square of the regression line, R 2). R 2 is a measure of the percentage of total variation in the dependant variable that is accounted for by the independent variable. An R 2 of 1.0 indicates that the data perfectly fit the linear model. Any R 2 value less than 1.0 indicates that at least some variability in the data cannot be accounted for by the model (e.g., an R 2 of 0.5 indicates that 50% of the variability in the outcome data cannot be explained by the model). Given these statistical tools, we can use the regression equation to predict the value of the dependent variable based on the known value of independent variable. Since many variables may contribute to the outcome (dependent variable), further statistical analysis can be achieved with multiple regression analysis. These models are essentially the same as simple regression analysis, except that the multiple regression analysis equation describes the interrelationship of many variables and allows us to evaluate the joint effect of these variables on the outcome variable in question. Poitras et al 2 report an interesting study this month that aims to predict length of stay and early clinical function following joint arthroplasty. Multiple linear regression analyses produced an equation based on the timed-up-and-go test, which was associated with length of stay. In addition, models based on the pre-operative WOMAC function sub-score produced the best model for describing early post-operative function (as calculated by the Older American Resources and Services ALD score). As such …