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Chapter 10: Problem 27

Bariatric Surgery for Diabetes Mingrone et al. reported the results of an experiment on severely obese patients who had diabetes for at least 5 years. Sixty patients were randomly divided into three groups. One group received medical therapy only (control group), a second group received gastric bypass surgery, and a third group received another kind of surgery called biliopancreatic diversion. It was reported that none of the patients assigned to the control group were free from diabetes after 2 years but that \(75 \%\) of the gastric-bypass group were free of diabetes and \(95 \%\) of those receiving biliopancreatic diversion were free from diabetes. Assume that 20 patients were assigned to each group. a. Find the number of people in cach group who were free from diabetes after 2 years. b. Create a two-way table of the data with Control, Gastric, and Bilio across the top. c. Test the hypothesis that the treatment and freedom from diabetes are independent using a significance level of \(0.05\). (Source: G. Mingrone et al. \(2012 .\) Bariatric surgery versus conventional medical therapy for Type 2 diabetes. New England Journal of Medicine \(366.577-1585\), April 26.

Short Answer

Expert verified
Without performing the exact statistical calculations, a high-level interpretation of the given data suggests that the biliopancreatic diversion has the best results in terms of diabetes outcomes, followed by gastric bypass and then the control group which had no patients free from diabetes. Depending on the exact p-value from the chi-squared test, one can make conclusions about statistical significance.

Step by step solution

01

Calculate the number of people who were free from diabetes in each group

Given that all three groups have 20 patients each, and the percentages of those free of diabetes after 2 years are as follows 鈥� Control: 0%, Gastric-bypass: 75%, Biliopancreatic diversion: 95%. Multiply the total number of patients in each group by their respective percentages to get the number of patients in each group who were free of diabetes after 2 years. For example, for the gastric-bypass group, the calculation would be \(20 \times 0.75 = 15\). Repeat this for each group.
02

Create a two-way table of the data

The two-way (also known as a contingency) table should have the treatment groups (Control, Gastric-bypass, Biliopancreatic diversion) as columns. Each column should then be divided into two categories: 'Free from Diabetes' and 'Not Free from Diabetes'. The numbers calculated from step a) would fall under the 'Free from Diabetes' category for each group, and the remaining patients would fall under 'Not Free from Diabetes' category.
03

Perform a chi-squared test of independence.

The null hypothesis is that treatment and freedom from diabetes are independent, and the alternative hypothesis is that they are not independent. Use the data in the table from step b) to calculate observed and expected frequencies, and then use these to calculate the chi-square statistic. Use a chi-square calculator or a statistical software package to get the p-value. If the p-value is less than the significance level (given as 0.05), then one would reject the null hypothesis. This would suggest that treatment and freedom from diabetes are not independent, and there is a significant difference in diabetes outcomes among the different treatment groups.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bariatric Surgery Outcomes
When it comes to weight loss and improving health conditions related to obesity, such as type 2 diabetes, bariatric surgery has proven to be a useful intervention. These surgeries, which include gastric bypass and biliopancreatic diversion, are designed to make changes to the digestive system to help with weight loss. To analyze the effectiveness of these surgeries, one can look at outcomes such as diabetes remission rates post-surgery.

Statistics from clinical studies often demonstrate a high percentage of patients experiencing remission of diabetes following bariatric surgery. As seen in Mingrone et al.鈥檚 experiment, an impressive 75% of the patients who underwent gastric bypass and 95% who had a biliopancreatic diversion were free from diabetes after two years, compared to none in the control group that received only medical therapy. These outcomes not only highlight the potential benefits of bariatric surgery but also set the stage for further statistical analysis to understand the relationship between the surgery and diabetes remission.
Diabetes Remission Statistics
Diabetes remission statistics are critical when evaluating the long-term success of treatments for type 2 diabetes, including lifestyle changes, medication, and surgical interventions. Remission is typically defined as achieving and maintaining blood glucose levels below the diabetes range without ongoing use of diabetes medication. Numbers like the 75% and 95% remission rates for gastric bypass and biliopancreatic diversion surgeries, respectively, shed light on the potential for these interventions to significantly impact patients' health.

Such statistics are essential for medical professionals to recommend treatment options and for patients to make informed decisions about their health. Moreover, these statistics can be used in scientific studies to perform hypothesis testing, which allows researchers to draw meaningful conclusions about the effectiveness of different treatments.
Hypothesis Testing
Hypothesis testing is a fundamental aspect of statistical analysis used to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. In the context of the Mingrone et al. study, hypothesis testing is employed to analyze whether the treatment (bariatric surgery) and freedom from diabetes after two years are independent.

The null hypothesis (\(H_0\)) usually posits that there is no effect or no difference, which in this case would mean that the treatment and diabetes remission are independent of one another. The alternative hypothesis (\(H_1\) or \(H_a\) would suggest that there is an effect or a difference, indicating dependency between the two. Researchers use the chi-squared test of independence to assess the observed data against the expectations under the null hypothesis. If the results show statistical significance, often denoted by a p-value less than 0.05, the null hypothesis is rejected in favor of the alternative.
Contingency Table
A contingency table, also known as a cross tabulation or two-way table, is a type of table in a matrix format that displays the frequency distribution of the variables. It makes it easier to see the relationship between two categorical variables. In the case presented from Mingrone et al.'s study, there are three groups (control, gastric bypass, and biliopancreatic diversion) across the top and two outcomes ('Free from Diabetes' after two years and 'Not Free from Diabetes') along the side.

In creating the table for the Mingrone et al. study, one would calculate the number of patients in each group who were free from diabetes, as well as those who were not, and arrange this data in the table. This table is crucial for carrying out the chi-squared test, which analyzes the observed frequencies in the study against the frequencies we would expect to find if the null hypothesis of independence were true. The ability to visualize and calculate from such a table is an essential skill in the field of statistics for conducting reliable and valid hypothesis tests.

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