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Data Analysis Project: Treating Depression: A Randomized Clinical Trial Continuing the Research This Applications Project will continue to analyze the outcomes from the study introduced in the first Exam Application

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Data Analysis Project: Treating Depression: A Randomized Clinical Trial

Continuing the Research

This Applications Project will continue to analyze the outcomes from the study introduced in the first Exam Application.

The Study

The attached data are the results of a 1980s study done on subjects who had experienced clinical depression. Patients were randomly assigned either Imipramine (Imip), Lithium (Li), or a Placebo (Pl) where Imip and Li are active drugs. Like most other medical studies where new, unexplored treatments are evaluated, patients chose themselves to participate in the study by signing a consent form. Patients were followed for 2-4 years to see whether or not they had a recurrence of depression.

Variables

• AcuteT            The number of days the patient had been depressed before the study started
• Treat                L=Lithium; I=Imipramine; P=Placebo
• Outcome        S=Success F=Failure (depression returns)

Link to the Data

Use the following link to open the dataset: Dataset for Depression Drug Outcomes and AcuteT

Directions

To analyze this data, you will create a contingency table (2-way table) by following the steps below. Once the contingency table is designed you will answer a few questions, and then form an informal conclusion about which drug worked best.

1. Use the website: https://istats.shinyapps.io/EDA_categorical/ 
2. Click on "Two Categorical Variables" on the top menu bar.
3. Change the option “Enter Data as:” to “Individual Observations”
4. Change the Name of the variables to reflect the context of the project.
5. Copy and paste both columns of data into the web app.
6. Copy the contingency table counts and totals into the table below or make your own in a document.

Part 1 Summarizing Distributions

Use technology to fill in the contingency table below (6 points)

	Failure	Success	Totals
Imipramine
Lithium
Placebo
Totals

Part 2 Calculating Probabilities

Use your contingency table to answer the following questions assuming we randomly select one individual that participated in the study. Show your work, write your answer rounded to the nearest percent, and answer with a sentence.

1. Find the probability that the individual was in the Lithium treatment group (4 pts).

 

2. Find the probability that the individual had a successful outcome (4 pts).


 

3. Find the probability the individual was in the placebo or Imipramine treatment group (4 pts).


 

4. Find the probability the individual had a successful outcome and was in the placebo group (4 pts).

 

 

 

Part 3 Calculating Meaningful Numerical Summaries

Show your work for problems 5-7, write your answer rounded to the nearest percent (Note: the calculations for the proportion is not any different than if you were asked to find the probability).

5. What proportion of the individuals in the Imipramine treatment group had a successful outcome? (4 pts).


 

6. What proportion of the individuals in the Lithium treatment group had a successful outcome? (4 pts).


 

7. What proportion of the individuals in the placebo group had a successful outcome? (4 pts).


 

8. Write a paragraph summarizing 5-7 above AND what the proportions (in questions 5-7) indicate about which of the drugs in this study are most likely to result in success (effective in preventing the recurrence of depression) (6 pts)? 




 

 

 

Part 4 Reflecting on Statistical Practices 

9. Who could find this information useful in making decisions? Explain. (2 pts)









 

10-A. A larger study had shown Imipramine been shown to be effective in treating depression in 87% of individuals. Assume the 38 individuals we selected to receive Imipramine represent random trials of individuals with depression, use the binomial distribution calculator to calculate the probability of 27 or less successful outcomes?  (3 pts)



10-B. Is the result of our study unusual? (1 pt)


 

11. Assume on average an individual will wait for 120 days with a standard deviation of 60 days to begin treatment for depression. What is the probability a sample of 109 individuals has a mean AcuteT of 136 days or more? Include a picture of your distribution that is shaded to represent the probability (either drawn or a screenshot). (4 pts)