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unit 8 pt 2 - 5 Multivariate analysis Analysis Unit 8...

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Unit 8: Confounding and effect (measure) and effect (measure) modification Part 2 Dr. Borenstein 5 M lti i t l i A l i 5. Multivariate analysis: Analysis Stratified analysis does not allow for simultaneous adjustment of many variables because cell sizes get too small and are unstable Most often, we adjust for many confounders at once Variables such as age, gender, race, and education are often incorporated into a model with the exposure to establish the independent effect of the exposure after adjusting for other variables Multivariate analysis is a tool to adjust for multiple Multivariate analysis is a tool to adjust for multiple variables simultaneously. M lti i t l i ’d Multivariate analysis, con’d Involves modeling the relation between E and D by means of a mathematical equation In the equation, the outcome (D) is considered the dependent variable The exposure(s) of interest, other strong The exposure(s) of interest, other strong risk factors for the D and one or more PCF are considered independent (predictor, are considered independent (predictor, explanatory) variables. Before including a variable in a Before including a variable in a model, We conduct stratified PCF-E and PCF-D and also stratified M-H crude and adjusted analysis to discern if each variable should be introduced into the mathematical model. Multivariate analysis equation Multivariate analysis equation (general form) Y = α + β 1 X 1 + β 2 X 2 + . . . + β n X n + + γ X X +… + X 1 X 2 β =coefficients from mathematical model X=independent variable Y=outcome (state you wish to predict) Outcome = intercept + exposure (X 1 )+ confounder (X 2 ) + … + confounder(X n ) + + interaction term (effect-modification) for + … + interaction term (effect-modification) for exposure X1 * confounder X2 M lti l i d l Multiple regression model Outcome = continuous (BP cholesterol level Ab titers) Y = α + β 1 X 1 + β 2 X 2 + . . . + β n X n Outcome = continuous (BP, cholesterol level, Ab titers) The coefficients of each independent (X) variable are directly interpretable in relation to the outcome The presence of each variable in the model means that we know their relation to Y independent of the other variables Commonly used for cross-sectional data, cohort data looking at baseline or longitudinal change (also incorporates random effects) Many variations of the multiple regression model
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L i ti i d l Logistic regression model Outcome = natural log odds of disease Outcome natural log odds of disease Log (odds of disease)= α + β 1 X 1 + β 2 X 2 +..+ β n X n Coefficients ( β ) can be directly converted to the odds ratio, which describes the independent association of that parameter with the outcome Commonly used for case-control (frequency or unmatched) and cross-sectional data. Can be used for cohort data if time to event is not used for cohort data if time to event is not important and can adjust for follow-up time.
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