Use the following for 1-4 A cross-sectional study[1] of 1046 consecutive admissi

Question

Use the following for 1-4

A cross-sectional study[1] of 1046 consecutive admissions of adults with coronary arterial disease (CAD) at a Turkish hospital. Of interest was whether gender was associated with other factors related to CAD in this population. One such factor was the presence of peripheral artery disease at admission. The data are summarized as a 2x2 table below.

Peripheral Artery Disease

Yes

No

Men

44

582

Women

9

411

Which variable is the disease and which is the exposure in this example? Compute the conditional probabilities of disease on exposure in each exposure group. Write a sentence comparing these probabilities (a significance test is not required).

In a similar 2x2 array, show the expected cell counts for each cell. Are the assumptions concerning sample size for the chi-square test of independence satisfied in this analysis?

Considering your answer to question 2, proceed with an appropriate test of significance (either the chi-square test for independence or an appropriate test for small samples). State your null and alternative hypotheses, the value of your test statistic, the p-value and your conclusion in the context of the research.

Another variable of interest was the procedure participants underwent for CAD at their hospital admission. The data are summarized below. Perform a single test of significance for whether the proportions for men and women given each treatment are homogeneous. State your null and alternative hypotheses, the value of your test statistic, the p-value and your conclusion in the context of the research.

Procedure

Normal+medical treatment

PTCA+stent

Surgical treatment

Men

331

177

118

Women

296

73

51

[1] Atik, Derya, et al. "The significance of gender in patients administered coronary angiography with respect to smoking, peripheral arterial disease, diabetes mellitus and the procedure used." Journal of evaluation in clinical practice (2014)

Peripheral Artery Disease

Yes

No

Men

44

582

Women

9

411

Explanation / Answer

1.

Disease Variable : Yes / No

Exposure Variaable : Male / Female

H0:  gender was no associated with the other factors related to CAD in the population.

H1: gender was associated with the other factors related to CAD in the population.

Let the los be alpha 5%

Chisquare contribution is

Degrees of freedom: 1

Test Statistic, X^2: 12.4744
Critical X^2: 3.841456
P-Value: 0.0004

Here P-value < alpha 0.05, we reject H0

Thus, we conclude that gender was associated with the other factors related to CAD in the population.

2.

H0:  gender was no associated with the other factors related to CAD in the population.

H1: gender was associated with the other factors related to CAD in the population.

The expected frequenices are

The chisquare contribution is

Degrees of freedom: 2

Test Statistic, X^2: 32.4694
Critical X^2: 5.991471
P-Value: 0.0000

Here P-value < alpha 0.05, we reject H0

Thus, we conclude that gender was associated with the other factors related to CAD in the population.

Yes No Total Men 31.719 594.281 626 Women 21.281 398.719 420 Total 53 993 1046

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