How do we find the odds?

P/1-P

How do we find the probability?

O/1+O

What are the assumptions for linear regression?

L: Linearity between Y and X; for linear regression to show association (direction and magnitude) between X and Y, the RL needs to be linear

I: Independence

Outcome of one observation is not dependent on another

N: Normality

For any fixed value of the independent value, the dependent variable is normally distributed

E: Error

Errors have homoscedasticity

Residuals have constant variance at any valueof X

(Expected and observed value of y differnece)

Why do we use logistic regression with binary variables?

Change in proportion with each one unit change in X is non-linear.

What is the linear model and what does each expression mean?

Yi = B0 + BiXi + Ei

Yi = independent variable (outcome)

B0 = Population y-intercept (alpha)

Bi = slope coefficient (beta) average change in Y when X changes in one unit

Xi= independent variable

Ei = random error term

Linear component =

B0 + BiXi

What is the logistic regression model and what does each expression mean?

Ln(P/1-P) = B0 +BiXi+ B2X2+…

Outcomes is Ln(p/1-p)

Log odds of binary varaible

Independent variable denoted by x

Alpha is the log odds of outcomes when x = 0

Beta: change in log odds with one unit change in x when w = 1 versus x = 0

What is another form for logistic regression model?

P = (e^alpha+betax)/ 1 +(e^alpha + betax)

This is because probability = O/1 + O

Why do we use logistic regression instead of 2 by 2 tables?

2 by 2 tables rely on both dependent and independent variable being binary. Not possible when one is continous.

How do we control for confounder in logistic regression model?

Remove them.

Ex: ln(p/1-p) = (-2.83) + 1.07x1 + 0.79x2 + 0.05x3

X2 and X3 are gender and alcohol abuse

X1 is HIV status

Estimate association for HIV status and death, controlling for gender and alcohol abuse.

Take e ^ beta of HIV status ONLY.

e^1.07 = 2.9153.

The odds of death for those with HIV positive is 2.9 times those without positive status, controlling for gender and alcohol abuse.

What is relationship between MH method and logistic regression?

MH methods is THE SAME as multivariate logistic regression controlling for other variables.

What is the basic form of the logistic regression model?

ln(p/1-p) = alpha +betax