1. Research Techniques Made Simple: Multivariable Analysis Marlies Wakkee Loes Hollestein Tamar Nijsten Department of Dermatology, Erasmus University Medical Center, Rotterdam, The Netherlands

2. What Is Multivariable Analysis? Multivariable analysis is a statistical technique that can be used to simultaneously explore whether multiple risk factors (referred to as independent variables) are related to a certain outcome (referred to as dependent variable).

3. Multivariable Regression Techniques Multivariable technique Dependent variable (outcome) Example of dependent variable Model parameters Statistically significant CI No. of independent variables (predictors) allowed for consideration Example of interpretation of associations Linear regressionContinuous Intima media thickness β=change in the dependent variable If the CI does not include 0 No. of subjects/10 Psoriasis: β=change in IMT of psoriasis patients compared to controls of the same age and sex (ref) Logistic regressionDichotomous Occurrence of a cutaneous melanoma Odds ratio (OR) If the CI does not include 1,0 No. of events/10 NSAID use: OR of melanoma for NSAID users compared to no NSAID users adjusted for age, gender, and sunburn Cox proportional hazard regression Time until eventTime to occurrence of a CVD Hazard ratio (HR)If the CI does not include 1,0 No. of events/10 Psoriasis: HR of a CVD for psoriasis patients compared to patients without psoriasis adjusted for other CV risk factors

4. Confounding The relationship between an independent variable, an outcome and a confounder.

5. Intermediate Variable The role of the intermediate variable in the relationship between an independent variable and an outcome.

6. Statistical Interaction The effect of an independent variable on the outcome changes over the value of another variable in the multivariable model. Additive interaction in linear regression Multiplicative interaction in logistic or Cox PH regression

7. Selection of Independent Variables for the Multivariable Model multivariable linear regression for every independent variable approximately ten subjects multiple logistic regression and proportional hazard analysis for every independent variable approximately ten events

8. Limitations of Multivariable Regression Analysis Provides information on potential associations, but a significant association does not automatically imply causality It only adjusts for measured confounding