Non-Linear Regression

Abstract

Objectives 1. Regression with log-link is useful for studying the relative change in an outcome variable. 2. In a log-link regression model, the antilog of each coefficient represents the independent association of that covariate with the relative change in the outcome variable, holding all other variables constant. 3. Logistic regression is useful for studying associations for a binary outcome variable. 4. In a logistic regression model, the antilog of each coefficient represents the odds ratio of that covariate with the outcome variable, holding all other variables in the model constant. 5. In log-link and logistic regression models, the null hypothesis for a covariate is that the antilog of the coefficient for that covariate equals 1.0. 19.1 Regression for Ratios In the previous chapter, we studied linear regression models, which assume the general form: Mean outcome = b 0 + b 1 * (predictor1) * b 2 × (predictor2) + b 3 * (predictor3)… By definition, linear regression models specify a linear relationship between the outcome variable and the predictor variables in a model. In linear regression, each one-unit difference in a predictor variable is linked with some constant difference in the outcome variable. For example, the linear regression model in the previous chapter linked each 1 ng/ml higher 25-hydroxyvitamin D level with a 0.01 pg/ml lower IL-6 level. In many instances, the assumption of a linear relationship between two factors is reasonable. However, there are certain circumstances in which nonlinear relationships might be expected. For example, the HIV viral load, a measure of HIV disease severity, grows exponentially with time in untreated patients, such that each week the viral load