Chapter 23, Problem 23.24E

(a)

To determine

To find: The sample proportions of Medicare patients who experienced overall complications from bariatric surgery before and after the CMS restriction on coverage.

To test: Whether there is evidence that the proportions of overall complications are different before and after the CMS restriction or not.

Answer to Problem 23.24E

The sample proportions of Medicare patients who experienced overall complications from bariatric surgery before the CMS restriction on coverage is 0.146.

The sample proportions of Medicare patients who experienced overall complications from bariatric surgery after the CMS restriction on coverage is 0.104.

The conclusion is that, there is evidence that the proportions of overall complications are different before and after the CMS restriction.

Explanation of Solution

Given info:

In the survey, out of 1,847 Medicare patient 270 patients experienced overall complications and out of 1,639 Medicare patients having bariatric surgery 170 patients experienced overall complications

Calculation:

The sample proportion of Medicare patients who experienced overall complications from before bariatric surgery is,

$\begin{array}{c}{\widehat{p}}_{\text{Before}}=\frac{\text{Number of patients experienced overall complications}}{\text{Total number of patients}}\\ =\frac{270}{1,847}\\ =\text{0}\text{.146}\end{array}$

Thus, the sample proportion of Medicare patients who experienced overall complications from before bariatric surgery is 0.146.

The sample proportion of Medicare patients who experienced overall complications from after bariatric surgery is,

$\begin{array}{c}{\widehat{p}}_{\text{After}}=\frac{\text{Number of patients experienced overall complications}}{\text{Total number of patients}}\\ =\frac{170}{1,639}\\ =\text{0}\text{.104}\end{array}$

Thus, the sample proportion of Medicare patients who experienced overall complications from after bariatric surgery is 0.104.

PLAN:

Check whether or not there is evidence that the proportions of overall complications are different before and after the CMS restriction.

Let $p_1$ denote as the proportion of complications before the CMS restriction and $p_2$ is denoted as the proportion of complications after the CMS restriction.

State the test hypotheses.

Null hypothesis:

$H_0:p_{\text{1}}=p_{\text{2}}$

Alternative hypothesis:

$H_a:p_{\text{1}}\ne p_{\text{2}}$

SOLVE:

Test statistic and P-value:

Software procedure:

Step by step procedure to obtain test statistic and P-value using the MINITAB software:

• Choose Stat > Basic Statistics > 2 Proportions.
• Choose Summarized data.
• In First sample, enter Trials as 1,847 and Events as 270.
• In Second sample, enter Trials as 1,639 and Events as 170.
• Choose Options.
• Choose Pooled proportions.
• In Confidence level, enter 95.
• In Alternative, select not equal.
• Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

From the MINITAB output, the value of the z-statistic is 3.77 and the P-value is 0.000.

CONCLUDE:

The P-value is 0.000 and the significance level is 0.05.

Here, the P-value is less than the significance level.

That is, $0.000\left(=P\text{-value}\right)<0.05\left(=\alpha \right)$.

Therefore, by the rejection rule, it can be concluded that there is evidence to reject $H_0$ at $\alpha =0.05$.

Thus, there is evidence that the proportions of overall complications are different before and after the CMS restriction.

(b)

To determine

To check: Whether the given study is an observational study or an experiment.

To check: Whether the CMS restriction has reduced the proportion of overall complications.

Answer to Problem 23.24E

The given study is experiment study.

Yes, the CMS restriction has reduced the proportion of overall complications.

Explanation of Solution

Observational study:

If the individuals under the study are just observed and measured based on certain characteristics without modifying them, then the study is termed as observational study.

Experimental Study:

If some treatments are applied on the individuals in order to observe the effectiveness of the treatments then the study is termed as experimental study.

The analysis is designed to compare the treatments. The selected patients are considered to be the experimental units which are randomly assigned to Medicare patients who experienced overall complications from before and after bariatric surgery. This implies that the study is experimental.

Justification:

The sample proportion of Medicare patients who experienced overall complications from after bariatric surgery is 10.4%, which is lesser when compared to the sample proportion (14.6%) of Medicare patients who experienced overall complications from before bariatric surgery.

(c)

To determine

To identify: The types of variables.

To check: The types of variables affect the conclusion or not.

Answer to Problem 23.24E

The variables “use of lower-risk bariatric procedures”, “increased surgeon experience”, or “healthier patients receiving the surgery” are considered as lurking variables.

Yes, the conclusion is affected by the types of variables.

Explanation of Solution

The given variables “use of lower-risk bariatric procedures”, “increased surgeon experience”, or “healthier patients receiving the surgery” are considered as lurking variables. These variables may affect the proportion of overall complications.

Hence, there is the chance for CMS restriction to reduce the proportion of overall complications by including the lurking variables.

(d)

To determine

To explain: Comparison with a control group could help reduce the effects of some of the variables described in part (c).

Answer to Problem 23.24E

The explanation is that the control group includes non-Medicare patients obtained before and after the restrictions on coverage.

Explanation of Solution

The control group includes non-Medicare patients obtained before and after the restrictions on coverage. In other words, the non-Medicare patients received no treatments which reduces the effect of the lurking variables described in part (c).