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Treatment In a 2018 study by Zhu et al. reported in The Lancet, researchers conducted an experiment to determine the efficacy and safety of the drug dorzagliatin in the treatment of patients with Type 2 diabetes. In this double-blind study, patients were randomly assigned to one of two treatment groups (drug or placebo) and the glucose levels of the two groups were compared after 12 weeks. If we test whether treatment group is associated with glucose level, are we doing a test of homogeneity or a test of independence?

Short Answer

Expert verified
The test being done is a test of independence.

Step by step solution

01

Understanding The Experiment

In this experiment, patients are randomly assigned to either the treatment group (where they receive the drug) or to the control group (where they receive a placebo). After 12 weeks, glucose levels between the two groups are compared. The intent is to determine if there is a difference in glucose levels between patients who receive the drug and those who receive the placebo - specifically, whether the drug has an effect on glucose levels.
02

Identifying The Type Of Test

In this context, where we are investigating the effect of the drug (the variable) on glucose levels, this would be a test of independence. We are trying to determine if the variable 'treatment or placebo' is independent of the variable 'glucose levels.' If they are independent, then the drug has no effect on glucose levels; if they are not independent, then the drug has some effect on glucose levels. This is different from a test of homogeneity, which would be interested if patients in the treatment and control groups came from the same overall population (i.e., the glucose level distribution of patients before the treatment is the same.)

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Key Concepts

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

Statistical Hypothesis Testing
Statistical hypothesis testing is a fundamental process used in statistics to determine whether 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 study by Zhu et al., the researchers used hypothesis testing to evaluate the efficacy of dorzagliatin in treating Type 2 diabetes. The null hypothesis (\( H_0 \)) in this case would assert that the drug has no effect on glucose levels, meaning treatment and glucose levels are independent. The alternative hypothesis (\( H_1 \)) contrasts by suggesting that there is a significant effect, indicating dependence. A p-value is calculated to determine the strength of evidence against the null hypothesis. If the p-value is below a predetermined significance level, often 0.05, the null hypothesis is rejected, indicating a statistically significant effect on glucose levels by the drug.

Understanding these terms and the process of hypothesis testing is crucial for interpreting the results of experiments like the one conducted. It's important for students to grasp the difference between rejecting the null hypothesis and accepting the alternative hypothesis, weighing the evidence provided by the sample data, and the inherent possibility of making an error in this decision-making process.
Double-Blind Study
A double-blind study is a type of clinical trial where neither the participants nor the researchers know who is receiving the active treatment and who is receiving the placebo. This method is used to prevent bias in research results. Bias can occur when participants have expectations about their treatment, or when researchers subconsciously influence results based on their expectations.

In the study by Zhu et al., implementing a double-blind design was essential to ensure the reliability of the findings by minimizing bias. It prevents the placebo effect, where patients might report improvements simply because they believe they are being treated, and observer bias, where researchers might interpret results more favorously if they expect the treatment to work. Explaining such concepts with simple examples, like comparing it to a 'taste test' where neither the person tasting nor the person administering the test knows the brands being compared, can help students understand the significance and implications of this study design.
Type 2 Diabetes Treatment
Type 2 diabetes is a chronic condition impacting the way the body processes blood sugar (glucose). Treatment for this condition typically involves a combination of lifestyle changes, monitoring blood sugar, and possibly medication or insulin therapy. Dorzagliatin, mentioned in the Zhu et al. study, represents a possible pharmaceutical intervention designed to improve glycemic control.

When discussing Type 2 diabetes treatments, it's valuable to educate students about the variety of treatment options and their intended effects on the body's insulin resistance and glucose production. Emphasizing the goal of maintaining normal glucose levels to prevent complications can illustrate why new treatments, like dorzagliatin, are being researched and highlight the importance of evidence-based medicine in diabetes management. This real-world application of statistics in medical research shows how the interpretation of data can directly affect health outcomes.
Randomized Control Trial
A randomized control trial (RCT) is regarded as the gold standard for testing new medical treatments. In RCTs, subjects are randomly assigned to either the experimental group receiving the treatment or the control group receiving a placebo. Randomization aims to evenly distribute any other factors that might influence the outcome, other than the treatment itself, ensuring that any effects observed are likely due to the treatment.

Explaining RCTs with an analogy can be helpful; for instance, likening it to flipping a coin to decide which soccer team kicks off the game, to ensure no team has an unfair advantage. The study by Zhu et al. utilized an RCT to have a valid comparison of the effects of the drug versus a placebo on glucose levels in Type 2 diabetes patients. Understanding RCTs allows students to appreciate the robustness of such trials when it comes to drawing conclusions about cause and effect in medical research, which is a cornerstone concept for those studying experimental design and statistics.

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Most popular questions from this chapter

In the study referenced in exercise \(10.33\), researchers also collected data on use of apps to monitor diet and calorie intake. The data are reported in the table. Test the hypothesis that diet app use and gender are associated. Use a \(0.05\) significance level. $$ \begin{array}{ccc} \text { Use } & \text { Male } & \text { Female } \\ \hline \text { Yes } & 43 & 241 \\ \hline \text { No } & 50 & 84 \\ \hline \end{array} $$

In a 2009 study reported in the New England Journal of Medicine, Boyer et al. randomly assigned children aged 6 months to 18 years who had nonlethal scorpion stings to receive an experimental antivenom or a placebo. "Good" results were no symptoms after four hours and no detectable plasma venom. $$ \begin{array}{|lccc|} \hline & \text { Antivenom } & \text { Placebo } & \text { Total } \\ \hline \text { No Improvement } & 1 & 6 & 7 \\ \hline \text { Improvement } & 7 & 1 & 8 \\ \hline \text { Total } & 8 & 7 & 15 \\ \hline \end{array} $$ The alternative hypothesis is that the antivenom leads to improvement. The p-value for a one-tailed Fisher's Exact Test with these data is \(0.009\). a. Suppose the study had turned out differently, as in the following table. $$ \begin{array}{|lcc|} \hline & \text { Antivenom } & \text { Placebo } \\ \hline \text { Bad } & 0 & 7 \\ \hline \text { Good } & 8 & 0 \\ \hline \end{array} $$ Would Fisher's Exact Test have led to a p-value larger or smaller than 0.009? Explain. b. Suppose the study had turned out differently, as in the following table. $$ \begin{array}{|lcc|} \hline & \text { Antivenom } & \text { Placebo } \\ \hline \text { Bad } & 2 & 5 \\ \hline \text { Good } & 6 & 2 \\ \hline \end{array} $$ Would Fisher's Exact Test have led to a p-value larger or smaller than 0.009? Explain. c. Try the two tests, and report the p-values. Were you right? Search for a Fisher's Exact Test calculator on the Internet, and use it.

When playing Dreidel, (see photo) you sit in a circle with friends or relatives and take turns spinning a wobbly top (the dreidel). In the center of the circle is a pot of several foil-wrapped chocolate coins. If the four-sided top lands on the Hebrew letter gimmel, you take the whole pot and everyone needs to contribute to the pot again. If it lands on hey, you take half the pot. If it lands on nun, nothing happens. If it lands on \(\operatorname{shin}\), you put a coin in. Then the next player takes a turn. Each of the four outcomes is believed to be equally likely. One of the author's families got the following outcomes while playing with a wooden dreidel during Hanukah. Determine whether the outcomes allow us to conclude that the dreidel is biased (the four outcomes are not equally likely). Use a significance level of \(0.05\). $$ \begin{array}{cccc} \text { gimmel } & \text { hey } & \text { nun } & \text { shin } \\ 5 & 1 & 7 & 27 \end{array} $$

Here are the conviction rates with the "stand your ground" data mentioned in the previous exercise. "White shooter on nonwhite" means that a white assailant shot a minority victim. $$ \begin{array}{lr} & \text { Conviction Rate } \\ \hline \text { White shooter on white } & 35 / 97=36.1 \% \\ \text { White shooter on nonwhite } & 3 / 21=14.3 \% \\ \text { Nonwhite shooter on white } & 8 / 22=36.4 \% \\ \text { Nonwhite shooter on nonwhite } & 11 / 45=24.4 \% \end{array} $$ a. Which has the higher conviction rate: white shooter on nonwhite or nonwhite shooter on white? b. Create a two-way table using White Shooter on Nonwhite and NonWhite Shooter on White across the top and Convicted and Not Con- victed on the side. c. Test the hypothesis that race and conviction rate (for these two groups) are independent at the \(0.05\) level. d. Because some of the expected counts are pretty low, try a Fisher's Exact Test with the data, reporting the p-value (two-tailed) and the conclusion.

The following table shows the average number of vehicles sold in the United States monthly (in millions) for the years 2001 through 2018 . Data on all monthly vehicle sales for these years were obtained and the average number per month was calculated. Would it be appropriate to do a chi-square analysis of this data set to see if vehicle sales are distributed equally among the months of the year? If so, do the analysis. If not, explain why it would be inappropriate to do so. (Source: www.fred.stlouisfed.org) $$ \begin{array}{|l|l|} \hline \text { Month } & \text { Avg Sales per Month (in millions) } \\ \hline \text { Jan } & 15.7 \\ \hline \text { Feb } & 15.7 \\ \hline \text { Mar } & 15.8 \\ \hline \text { Apr } & 15.8 \\ \hline \text { May } & 15.8 \\ \hline \text { June } & 15.7 \\ \hline \text { July } & 16.1 \\ \hline \text { Aug } & 16.1 \\ \hline \text { Sept } & 15.8 \\ \hline \text { Oct } & 15.9 \\ \hline \text { Nov } & 15.9 \\ \hline \text { Dec } & 15.9 \\ \hline \end{array} $$

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