Suppose researchers are interested in the relationship betwe

Suppose researchers are interested in the relationship between periodontal disease and hypertension. In their particular analysis, the researchers have decided through confirmed medical records to use dichotomous variables (Y/N) for both outcome and predictor. In order to best address the relationship in their dataset, the researchers have included a few variables in their final multiple regression model. The following is a computerized output for the model that they intend to use in their analysis.

Analysis of Maximum Likelihood Estimates

Parameter

DF

Estimate

Standard
Error

Wald
Chi-Square

Pr > ChiSq

Intercept

1

-6.8430

0.4746

207.8959

<.0001

Periodontal Disease

1

1

-0.2250

0.1544

2.1227

0.1451

BMIcontinuous

1

0.0635

0.0115

30.3765

<.0001

Agecontinuous

1

0.0891

0.00475

351.7248

<.0001

Alcoholic Drinks/Day

2

1

0.5619

0.1657

11.5042

0.0007

Cigarettes/Day

2

1

0.4279

0.2138

4.0056

0.0454

A) Write out the final model in symbols using the beta coefficients provided above.

B) Which of the variables included in the model significantly impact the outcome?

C) Suppose the relationship between periodontal disease and hypertension was significant in the bivariate linear regression model that preceded this. What can be said about the relationship between the outcome and exposure when factoring in the other variables?

Analysis of Maximum Likelihood Estimates
Parameter		DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept		1	-6.8430	0.4746	207.8959	<.0001
Periodontal Disease	1	1	-0.2250	0.1544	2.1227	0.1451
BMIcontinuous		1	0.0635	0.0115	30.3765	<.0001
Agecontinuous		1	0.0891	0.00475	351.7248	<.0001
Alcoholic Drinks/Day	2	1	0.5619	0.1657	11.5042	0.0007
Cigarettes/Day	2	1	0.4279	0.2138	4.0056	0.0454

Solution

(a) Model equation:

These are the binary logic regression estimates for the Parameters in the model. The logistic regression model models the log odds of a positive response as a linear combination the predictor variables.

log [p/(1-p)] = -6.8430 -0.2250 (Periodontal Disease) + 0.0635 (BMIcontinuous) + 0.0891 (Agecontinuous) + 0.5619 (Alcoholic Drinks/Day) + 0.4279 (Cigarettes/Day)

(b) Age and BMI are the most significant variables (age being the highest) though the other two variables, namely alocohlic drinks/day and Ciggarettes/day also significantly impact the outcome.

(c) In this multivariate regression model, by the inclusion of other variables as factors, the relationship between periodontal disease and hypertension comes out to be insignificant.