Background

Your colleague is attempting to examine the effects of educational intervention and support strategies on the outcome measure “number of cigarettes smoked in one week by eighth graders” one month after the assigned “treatments.” The first treatment is an educational intervention: (1) no educational intervention; or (2) a two-hour intervention with a PowerPoint presentation and testimonials from ex-smokers. The other treatment is one of four support strategies: (a) no support; (b) a video shown to the students one week after the assigned intervention; (c) a one-hour question-and-answer session with an ex-smoker one week after the assigned intervention; or (d) the video followed by a one-hour question-and-answer session with an ex-smoker one week after the assigned intervention.

The investigator will approach a number of school districts and identify two schools in each. The two schools in each district will be randomly assigned to the two educational interventions, one school to each. Within each school, four homerooms of eighth graders—each of size 8–12 students—will be identified. Each group will be randomized to receive one of the four support strategies. One month after the educational and support strategies have been applied, all children in the study will be questioned to determine the number of cigarettes each student has smoked in the week prior to the day of the questionnaire.

Because smoking by a minor is considered socially unacceptable, the school boards have privacy concerns. Thus, the investigator will not have access to the individual responses to the number of cigarettes smoked, since this might get students in trouble with their parents. The investigator will have access only to the total number of cigarettes smoked in each group and the number of students in each group.

Your task is to design a study that will address the two null hypotheses:

● H1,0 :  The expected number of cigarettes smoked by each student is unaffected by the educa- tional intervention; and

● H2,0 :  The expected number of cigarettes smoked by each student is unaffected by the support strategy.

To help you design the study you will need to develop some planning parameters. To understand plausible target differences for the two interventions and the variance in the student level of number of cigarettes smoked, the investigator did two pilot studies.

Pilot Study #1

In the course of developing the educational intervention, two groups of 10 children each were either administered or not administered the educational intervention and the number of cigarettes smoked by each student was determined. The data are on Blackboard, in the “Final Project (Part 1)” item on the “Assignments” tab, in the Excel file Smoking  data.xlsx, on the sheet Pilot  1.

The data are coded as:

ID   —   Student ID

RES   —   Number of cigarettes smoked in the prior week

INV   —   Educational intervention given (1 = No presentation; 2 = Presentation)

Analyze these data to obtain estimates for the effect of the educational intervention on average number of cigarettes smoked. You can also use this to get an estimate of the student-level variation in number of cigarettes smoked.

Pilot Study #2

In this study, the investigator recruited two students per day on 24 days (not necessarily consecutive) and administered to each one a support strategy. Each student reported the number of cigarettes  smoked. The data are on Blackboard, in the “Final Project (Part 1)” item on the “Assignments” tab, in the Excel file Smoking  data.xlsx, on the sheet Pilot  2.

The data are coded as:

BLOCK   —   Day intervention was administered

RES   —   Number of cigarettes smoked in the prior week

TRT   —   Support strategy administered. (1 = No support; 2 = Video;

3 = Meeting with an ex-smoker; 4 = Video plus Meeting with an ex-smoker)

Analyze these data to obtain estimates for the effect of the support strategies on the average number of cigarettes smoked. Since the days were selected at random, treat the block effect as a random effect.

The design for the definitive trial will require an estimate of the District XEducational Intervention standard deviation and the Educational InterventionXSupport Strategy standard deviation. We will rely on the statement that these “interaction” standard deviations are usually no larger than the standard deviations for the main effects which contribute to them. You will also need an estimate of

the standard deviation associated with District. For this we will assume that the standard deviation associated with District is no larger than the largest standard deviation for the main effects.

Part 1 (I strongly suggest your first attempt be submitted by Friday, April 30, 5 PM)

1.  Select the largest Type I error that you wish associated with each hypothesis test. You do not need to control the experiment-wise error; choose the unadjusted level for each test. Justify why you selected that particular Type I error.

2.  Select the minimum power that you wish associated with each hypothesis test. Justify why you selected that particular power.

3. With the parameters you have estimated above, design a trial to assess H1,0  and H2,0 . Select a design by giving your recommendation for the number of districts that will be approached.

4. Post your calculations (code and output if you used R or SAS; a screenshot if you used PASS or the Lenth app) to the “Final Project (Part 1)” link on Blackboard.

5. Then, send an e-mail to [email protected] with the subject line PM  513  Design. In the text of the e-mail, specify how many districts will be recruited.

I strongly suggest you submit your first attempt at Part 1 by Friday, April 30. Keep in mind that I will make you re-do Part 1 until you get an acceptable design! (And that you can’t do Part 2 until you’ve completed Part 1 satisfactorily!)

Part 2 (due Friday, May 14, 5 PM)

Once I have verified that your Part 1 analysis is acceptable, I will e-mail you an Excel file with the results of the experiment. Each observation in the file will contain the following data:

Variable Name   Description                            Coding

DN

EDUC

SUPP

CS

STUDENTS

District number              Educational intervention

Support strategy

Total number of cigarettes smoked

Number of students in the EDUC/SUPP Group

1 = No educational intervention

2 = Two-hour presentation

1 = No support strategy

2 = Video

3 = Meeting with ex-smoker

4 = Video plus Meeting with ex-smoker

4. Test H1,0  and H2,0 . Is there any evidence to indicate that either the educational intervention or the support strategy are significantly related to the number of cigarettes smoked?

5. Provide point estimates and 95% CIs for the effects of educational intervention and each of the support strategies (in our usual parametrization), and also the pairwise comparisons among the support strategies.

6. Recommend a combination of educational intervention and support strategy to use in the future and provide a justification for these recommendations.

7.  (Bonus) The investigator posits that the effect of the support strategy, if it does exist, is due entirely to the interview with the ex-smoker; the video has no effect on the number of cigarettes smoked. Test this hypothesis without introducing a new variable to the data set.