Datafrom the study wereusedto constructa logistic regression model.Answer the following questions using the model details and parameter estimates given below.

Model:Logit (PrD = 1/PrD = 0) = o + 1AGE+ 2ALCOHOL + 3VITAMIND+4RETREAT

Where:

D=1 fordeath, D=0 for nodeath

AGE=1 for patients older than 55 years,AGE=0 forpatients aged less than or equal to 55 years

ALCOHOL=1 for alcohol abuse, ALCOHOL=0 for normal or no alcohol consumption

VITAMIND=1deficient (<=20ng/ml),VITAMIND=0normal (>20ng/ml)

RETREAT=1retreatment cancer case, 0=first cancer episode

Analysis of Maximum Likelihood Estimates

Parameter

DF

Estimate

Standard

Error

Wald

Chi-Square

Pr>ChiSq

Intercept

1

-3.7196

0.3201

135.0050

<.0001

Age

1

-0.0397

0.2708

0.0214

0.8836

Alcohol

1

0.7678

0.4451

2.9756

0.0845

VitaminD

1

1.3466

0.3839

12.3019

0.0005

Retreat

1

2.2415

0.3495

41.1221

<.0001

Calculate the estimatedriskofdeathfor a60 year oldwith normal alcohol consumption whowas vitamin D deficientandwasafirst cancer episodepatient.

Write the equation using coefficientsfor the odds ratio ofdeathcomparing someone whohasvitamin D deficiencyto someone whohas normalvitamin D levels, adjusted forage, alcoholabuse, andcancer treatment history.

Calculate the odds ratiofor the equation

interpret the odds ratio

If there were an interaction term between vitamin D deficiency and age in this model and the beta coefficient for the interaction term was 0.175, what would the odds ratio for of death comparing people who do and do not have vitamin D deficiencyfor persons older than 55 years?Assume all other beta coefficients have the same values as in the output above.[3points]

interpret the odds ratio calculated.