What is the basic form of the logistic regression model?

logit(px) = ln(px/1-px) = alpha +betax

What is the logit of a probability of an outcome given some level of X?

It is equal to the log odds of that outcome occuring .

Logit and log odds can be used interchangeably.

Probability of an event happening at some given level of X.

What is alpha is logistic regression?

Log odds of an outcome when x = 0.

What is a+ beta in logistic regression?

Log odds of outcome when x = 1.

What is beta in logistic regression?

Log odds RATIO of an outcome comparing when X = 1 to when X = 0.

What is a regression model?

Statistical process for estimating the relationship between the dependent variable and one or more independent variables.

What are the two purposes of a multivariate logistic regression model?

To predict a probability of an outcome based on multiple variables at a time.

To understand an association between exposure and outcome while adjusting for confounding and mediation.

(Same as stratifying a table simultaneously by more than one variable)

What is the form of a multivariate logistic regression model?

ln(p/1-p) = alpha + b1x1 + b2x2 +b3x3…bkxk

What is the difference between bivariate and multivariate logistic regression?

Bivariate:

Beta is the log odds ratio of an outcome with a one unit change in X

Multivariate:

Beta is log odds ratio of the outcome associated with a one unit change in X1 HOLDING ALL OTHER Xs IN THE MODEL CONSTANT.

Beta2 is the log odds ratio of the outcome associated with a one unit change in X2 HOLDING ALL OTHER Xs CONSTANT.

How do we hold variables constant in logistic regression?

We do NOT have X =1; this is not meaningful.

Having X = 0 is not great, either.

We have fixed value of other variables except the one you want. It can be ANY value as long as the value is the same. Anyway, it cancels out. We are left with the beta of what we are interested in ONLY. Even alpha cancels out.

We want the pooled OR pooled bc the model is assuming the association between log OR and exposure variable of interest if same at every level of X (the MH pooled OR instead of X = 1 or X = 0).

What does the Breslow-Day test of homogeneity show you?

Tests for homogeneity across computed OR across stata.

If not significant, then they are likely confounders.

What does Wald Chi Square test of association show you?

Shows if explanatory models in a mutlivariate logistic regression are significant.

How do we know if a variable if a confounder?

Two things to see:

See if adding confounder changes OR between exposure and outcome by more than 10%.

See if confounder is associated with outcome after adjusting for other variables according to WALD STATISTIC. So at least one level of confounder associated with outcome after adjusting for other variables.

Both of these answers should be yes but the first takes precedence. You want to see your MAIN RELATIONSHIP.

How would you write out logistic regression model for effect measure modification?

ln(p/1-p) = alpha +B1X1 + B2X2 + B3(X1*X2)

This is a relative measure of association.

What is statistical interaction?

Occurs when joint effect of an exposure and a third variable on an outcome deviate from what is expected on the basis of their independent effects on the outcome.

You may observe more or less of an association when looking at the variables together versus one at a time.

Give an example of statistical interaction with:

CHD and SBP with effect modification by BMI

lb(p/1-p) CHD = alpha +B1(SBP) + B2(BMI) + B3(SBP*BMI)

How is the interaction term meaningful?

You need to add it to the original beta in the model for the log odds to be meaningful.

Also look at the statistical significance. If not statistically significant, do not include in the model.