Reference no: EM131031558

Birthweight is suspected to have a confounding effect on the relationship between surfactant use and mortality of newborns. Below are two tables of the surfactant use and mortality frequency stratified by birthweight.

Birthweight < 1000
	Mortality +	Mortality -	Total
Surfactant +	177	153	330
Surfactant -	479	290	769
Total	656	443	1099

Birthweight < 1000
	Mortality +	Mortality -	Total
Surfactant +	40	508	548
Surfactant -	82	1141	1223
Total	122	1649	1771

For the strata birthweight < 1000, the crude OR = 0.70 and for the birthweight 21000, crude OR = 1.10. Compute the odds ratio using the Cochran-Mantel-Haenszel method as well as the unadjusted (or crude) method for the overall surfactant use and mortality.

1. What is the OR_Crude regardless of birthweight?

2. What is the OR_CMH taking into consideration birthweight is a potential confounder?

3. True or False: The OR_CHM estimate supports that birthweight is a confounder.

A study wants to look at the correlation between sugar consumption and the development of cavities. The table below shows the average daily intake of sugar (g) and the total number of cavities per patient over the one-year study period.

Daily Sugar Intake	Number of Cavities
25	2
80	3
120	3
10	0
50	1
30	1
110	4

4. What is the sample correlation coefficient?

5. What type of correlation does this represent?

a. Strong positive

b. Strong inverse

c. Weak inverse

d. No correlation

The investigator wants to construct a regression equation based on his current sample to be able to predict the number of cavities that a patient develops based only on their sugar Intake given the standard deviation for the daily sugar intake Is 43.25 and the standard deviation for the number of cavities is 1.41.

6. What is the slope of the line (i.e. what is bi)?

7. What is the y-intercept (i.e. what is b₀)?

8. What is the predicted number of cavities for someone who consumes on average 45 grams of sugar a day?

A small pilot study is run to compare a new drug for chronic pain to one that is currently available. Participants are randomly assigned to receive either the new drug or the currently available drug and report improvement in pain on a 5-point ordinal scale. 1= Pain is much worse, 2 = Pain is slightly worse, 3 = No change, 4 = Pain improved slightly, 5 = Pain much improved.

Use the Mann-Whitney U test to determine if the new drug is significantly better in improvement in pain with a 5% level of significance (i.e. one-sided).

New Drug:	3	5	4	3	4	2	5
Standard Drug:	3	1	4	1	2	3	2

9. What is the critical value?

10. Define Group 1 to be those who received the New Drug. What is R₁?

11. Define Group 2 to be those wo received the Standard Drug. What is R₂?

12. What is U₁?

13. What is U₂?

14. True or False: Reject the null hypothesis as the test statistic is less than the critical value.

Extra Credit:

Fourteen young asthmatic volunteers were studied to assess the short-term effects of sulfur dioxide (502) exposure under various conditions. The baseline data in the table below are presented regarding bronchial reactivity to 502 stratified by lung function (as defined by FEV1/FVC) at screening.

Lung Function Group
Group A FEV1/FVC ≤ 74%	Group B FEV1/FVC 75%-84%	Group C FEV1/FVC  ≥ 85%
20.8	7.5	9.2
4.1	11.9	2.0
13.8	10.0	2.5
	4.5	6.1
	3.1	7.5
	28.1

15. Suppose we do not wish to assume normality. What nonparametric test can be used to compare the three groups?

a. Mann-Whitney U Test

b. Sign Test

c. Wilcoxon Signed Rank Test

d. Kruskal-Wallis Test

Conduct the two-sided nonparametric test as answered in question 15.

16. What is the critical value?

17. What is the test statistic?

18. True or False: Fail to reject the null hypothesis as the test statistic does not fall within the rejection region.