biostats lecture 6

correlation

• relationship (association) between 2 variables: X and Y

• no direction

• x ← → Y

regression

• one way relationship (association) of ONE variable (Y) with usually multiple variables (Xs): how Y is associatied Xs

• directional

• X’s → Y

• there is one Y but can have multiple Xs

• direction assiciation is an assumption based on theory and temproral

theory

• regression direction

• biologically, X causes Y

• smoking causes lung cancer

temporal

• regression direction

• X occured before Y

• thalidomide use leads to birth defects

dependent variable (Y)

• outcome variable of interest

• for a regression model, there is only ONE

independent variables (Xs)

• variables that are assumed to affect/predict the outcome Y

• in a regression, there can be multiple

risk factors

• attributes or characteristics that affect the occurence of the outcome

• smoking is a __ for lung cancer

• does not have to reduce risk: it needs to affect (either increase or decrease) the occurence of the outcome

confounding factors

• a variable that influences both the occurence of the outcome AND the likelihood of getting the treatment/intervention, but not in the casual pathway between them

• is a risk facotr, but a risk factor may not be one of these

purpose of regression analysis

• priamrily, in obervational studies, controlling for confounding factors to reduce bias in the estimated treatment effect

• to estimate the independent effects of multiple risk factors on an outcome

• to adjust for imbalance in baseline characteristics, when randomization did not work

• to increase precision and reduce standard errors of the estimated treatment effect, even when randomization worked well

observational

• purpose of regression analysis primarily in ___ studies, controlling for confounding factors to reduce bias in the estimated treatment effect

regression models

• depends on how the dependent variable is measures

• linear, logistic, cox’s proportional hazards

dependent

• regression model to use depends on how the __ variable is measured

continuous

• linear regression: for ___ dependent variable

binary

• logistic regression for __ dependent variable

time to event

• cox’s proportional hazards regression for ___ dependent variable

statistical inferences and interpretation from regression analysis

• step 1: first determine if there is a statistical significance )P vale, 95% CI)

• steps 2 and 3: if there is a statistical significance, then interpret the direction and magnitude of the effect

coefficient (beta coefficient)

• results of linear regression

odds ratio (OR)

• results of logistic regression

hazard ratio

• results of cox’s proportional hazards

linear regression model

• reports coefficients

• for continuous dependent variable

linear regression statistical significance

• if P value < 0.05 or 95% CI NOT include 0, then X has a statistically significant association with outcome Y

linear regression direction of effect

• if coefficient > 0, then X has a positive association with Y (as X increases, Y increases)

• if coefficient < 0, then X has a negative association with Y (as X increases, Y decreases)

linear regression magnitude of the effect

• interpretation of a coefficient

• when X changes by one unit, how much will Y change, after adjusting for other covariates

logistic regression model

• for binary dependent variable

• reports odds ratio

logistic regression statistical significance

• if P value < 0.05 or 95% CI NOT include 1, then X is associated with statistically significant difference in odds of outcome Y occuring

logistic regression direction of effect

• if OR >1, then odds of the outcome Y occuring increases with X

• if OR < 1 then odds of the outcome Y occuring decreases with X

logistic regression magnitude of effect

• if OR > 1 then (OR-1) x 100%, gives he % increase in odds of Y

• if OR < 1, then (1-OR) x 100% gives the % decrease in odds of Y