Assignment Instructions:

Solve the questions below using short answer responses and algebra.

1. In a 5-year cohort study conducted in Fulton County, Georgia, involving seniors 70 years of age or older, one research question concerned evaluating the relationship of social support network on risk of mortality. A logistic regression model was fit to describe the relationship between social support network and odds of death.

Consider the following variables:

DEATH: coded 0 for no death and 1 for death

SSN (social support network): coded ordinally 0 (weak), 1, 2, 3, 4, 5 (strong)

AGE: continuous variable 

SEX: coded 0 for female and 1 for male

COMORB: coded 0 for no serious comorbidities and 1 for ≥ 1comorbidities

1A. State the general form of the expression for the logistic regression model that contains all of the covariates.

 = B0 + β1 death + β2SSN + β3age + β4sex + β5Comorb

1B. State the expression for the logistic model that includes an interaction term for the variables SSN and SEX.

1C. Using the expression from part 1A, state the expression for the odds ratio comparing a person with SSN=5 compared to SSN=2, adjusting for AGE, SEX, and COMORB.

1D. State the null hypothesis for the interaction term in part 1B.

1E. Assume we reject the null hypothesis in part 1D. Using the expression from part 1B, state the expressions for the odds ratios comparing a person with SSN=4 to a person with SSN=2.