Regression Analysis

Regression models the relationship between an outcome (dependent) variable and one or more predictor (independent) variables. Linear regression handles continuous outcomes (the slope = change per unit predictor); logistic handles binary outcomes (yields odds ratios); Cox handles time-to-event outcomes (yields hazard ratios). It lets you predict, and adjust for confounders.

A simple selector: start from the outcome you want to model, and its data type points you to one of three regressions — each producing a different effect measure (slope, odds ratio or hazard ratio). Adding predictors lets the model adjust for confounders.

Identify the outcome first. A continuous outcome means a linear model whose coefficient is the change per unit predictor. A yes/no outcome means a logistic model reporting odds ratios. A “time until something happens” outcome means a Cox model reporting hazard ratios. An “adjusted” estimate is one holding the other modelled predictors constant.

Regression is how observational EM research strips out confounding to estimate an independent association, and how risk scores are built. Reading the output — which model, which effect measure, what was adjusted for — tells you whether an “association” is robust or an artefact of the variables left out.

• Linear → continuous outcome → slope (β)
• Logistic → binary outcome → odds ratio
• Cox → time-to-event → hazard ratio

Serial lactate monitoring in sepsis (Ann Emerg Med / observational cohort, 243 patients) — because the outcome was binary (in-hospital death), the authors used multivariable logistic regression. After adjustment, the lack of serial lactate monitoring was independently associated with mortality, adjusted OR 2.09 (95% CI 1.12–3.89). The binary outcome is exactly why the effect measure is an odds ratio. Adjusted associations are still observational — residual confounding can remain, so an OR from regression does not prove that monitoring itself saved lives.

• Reading a regression coefficient as proof of causation — correlation ≠ causation.
• Extrapolating the model beyond the range of data it was fitted on.
• Overfitting (too many predictors for the sample) or ignoring unchecked model assumptions (linearity, proportional hazards).