Due to concerns about the safety of bariatric weight loss surgery, in 2006 the Centers of Medicare and Medicaid Services (CMS) restricted coverage of bariatric surgery to hospitals designated as Centers for Excellence. Did the CMS restriction improve the outcomes of bariatric surgery for Medicare patients? Among the 1847 Medicare patients in the study having surgery in the 18 months preceding the restriction, 270 experienced overall complications, whereas in the 1639 patients having bariatric surgery in the 18 months following the restriction, 170 experienced overall complications

(a) What are the sample proportions of Medicare patients who experienced overall complications from bariatric surgery before and after the CMS restriction? Let pi be the sample proportion with complications before the restriction, and p2 be the sample proportion with complications after the restriction Enter your answers rounded to four decimal places.)

The objective is to test if the restrictions applied by the CMS reduce the proportion of patients that suffer overall complications after bariatric surgery.

The study variables are:

X₁: Number of patients that suffered overall complications after bariatric surgery before the CMS restrictions

n₁= 1847

x₁= 270

X₂: Number of patients that suffered overall complications after bariatric surgery after the CMS restrictions

n₂= 1639

x₂= 170

The hypotheses are:

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

There is no signification level determined, so I've chosen α: 0.05

(a) What are the sample proportions of Medicare patients who experienced overall complications from bariatric surgery before and after the CMS restriction on coverage? Enter your answers in decimal form, rounded to four decimal places.

Sample proportions

'p₁= 270/1847= 0.14618≅ 0.1462

'p₂= 170/1639= 0.1037

(b) Find the pooled proportion (rounded to four decimal places), the z statistic (rounded to two decimal places), and the P?value (rounded to four decimal places)

Pooled sample proportion

[tex]'p= \frac{x_1+x_2}{n_1+n_2}= \frac{270+170}{1847+1639} = 0.1262[/tex]

[tex]Z_{H_0}= \frac{('p_1-'p_2)-(p_1-p_2)}{\sqrt{'p(1-'p)*`[\frac{1}{n_1} + \frac{1}{n_2}] } }[/tex]

[tex]Z_{H_0}= \frac{(0.1462-0.1037)-0}{\sqrt{(0.1262*0.8738)*`[\frac{1}{1847} + \frac{1}{1639}] } }[/tex]

[tex]Z_{H_0}[/tex]= 3.77

The p-value is one tailed to the right as the test.

P(Z>3.77)= 1 - P(Z≤3.77)= 1 - 0.9999= 0.0001

The p-value is less than the significance level so the decision is to reject the null hypothesis.

(c)Select which statement best describes the evidence from the test you just conducted.

1. The test conducted did not reveal anything substantial.

2. There is little evidence the two proportions are different.

3. There is strong evidence the two proportions are different.

There is enough evidence to say that the proportion of patients that suffered overall complications after bariatric surgery decreased after the restrictions of the CMS.

4. There is no evidence the two proportions are different.

(d) Is this an observational study or an experiment?

1. This is an experiment.

2. This is an observational study.

(e)Can we conclude that the CMS restriction has reduced the proportion of overall complications?

1.No. We cannot determine cause and effect in observational studies.

2.Yes. The experiment gives strong evidence to support this conclusion.

(f) Improved outcomes may be due to several factors such as the use of lower? risk bariatric procedures increased surgeon experience, or healthier patients receiving the surgery. What types of variables are these, and how do they affect the types of conclusions that you can make?

1. These are explanatory variables, and they strengthen the case that the decline in complications is due to the restrictions.

2. These are explanatory variables, and they weaken the case that the decline in complications is due to the restrictions.

3. These are lurking variables, and they strengthen the case that the decline in complications is due to the restrictions.

4. These are lurking variables, and they weaken the case that the decline in complications is due to the restrictions.

Lurking or confusion variables are those factors that affect the response variable other than the explanatory variable determined by the investigator.

In experimental studies, these variables are controlled so that they do not affect the conclusions on the results. Any of these variables that are left without control affect the experiment and reduces the validity of the experiment.

(g) In a second study, a control group, consisting of non-Medicare patients obtained before and after the restrictions on coverage, was obtained. When compared with this control group, no significant evidence was found that the CMS restriction reduced the proportion of overall complications for the Medicare group. Explain in simple language how comparison with a control group could help reduce the effects of some of the variables described in part (c). Select the best explanation.

1. The reason for a comparative control group is to eliminate lurking variables (as much as possible). We can (safely) assume that both groups experienced the same exposure to newer methods, increased surgeon experience, etc. This allows us to focus on the factor of interest–the imposition of the restrictions and whether those restrictions improved results.

2. The reason for a comparative control group is to create more explanatory variables. It will allow us to focus on the factor of interest in the study.

3. The reason for a comparative control group is to make lurking variables. It will allow us to focus on the other factors of interest in the study.

4. The reason for a comparative control group is to get rid of explanatory variables (as much as possible). It will allow us to spread the focus from the factor of interest in the study to other components in the study.

I hope it helps!