1. A randomized trial, as in the typical clinical trial, and a (nonrandomized) crossover trial are both methods for attempting a causal comparison by ensuring a valid substitute population to represent the counterfactual condition for the index (exposed) group. This question, which is not directly focused on the study article, asks about the respective advantages of these two techniques (randomized trial, crossover trial) for making a valid comparison for inferring causality. (60 words overall maximum).

  1a. What is an advantage that is afforded by the typical randomized trial and that is not provided by a (nonrandomized) crossover trial?

  1b. What is an advantage that is afforded by a (nonrandomized) crossover trial and that is not provided by the typical randomized trial?

  2. Why is blinding so important in the Colford et al. study? Give two (2) specific sources of error or improper influence that could result if the blinding were compromised? (100 words maximum)

  3. The investigators employed a number of procedures to achieve and maintain the triple-blinding (of installers, participants, and investigators). State three (3) procedures the investigators employed for this purpose. (100 words maximum)

  4. In selecting the community for this study, the authors had to balance diverse and somewhat conflicting objectives. Some of the selection criteria pertain to the cooperativeness of the water utility and availability of monitoring data. Others were presumably intended to to increase the power of the study to detect an effect of water filters, whereas others were presumably intended to make the results more generalizable.

  4a. What is an example of a selection criterion, other than population size, intended to increase the statistical power of this study?

  4b. What is an example of a selection criterion intended to increase the generalizability of the results of this study?

  5. Use the data in Table 1 (and not Figure 1) to estimate the average household size (number of study participants per household) separately for the active device group and the sham-device group. Show the calculation.

  6. Participants in the trial were asked to guess whether they thought they were using the active device or the sham device. Suppose we regard guessing as a “screening test” for detecting an active filter device in the participant’s home (on analogy to mammography as a screening test for breast cancer). (For all parts of this question, treat the responses “Sham device” and “Don’t know” as equivalent, and ignore the fact that participants share households.)

  6a. What was the “sensitivity” of guessing as a test for detecting the active device during the first month of Cycle 1? Show the calculation (as a percentage with one decimal place) and state the meaning of your result, without using the word “sensitivity”.

  6b. What was the “specificity” of guessing as a test for detecting use of the active device during the first month of Cycle 1? Show the calculation (as a percentage with one decimal place) and state the meaning of your result, without using the word “specificity”.

  6c. What was the positive predictive value of “guessing” for detecting use of the active device during the first month of Cycle 1? Show the calculation (as a percentage with one decimal place) and state the meaning of your result, without using the words “predictive value” or PPV.

  6d. How did “sensitivity” and “specificity” change between the first month of Cycle 1 and the first month of Cycle 2?

  7. The precise meaning of the term "rate" is, according to Regina Elandt-Johnson (see "Definition of rates: some remarks on their use and misuse", Am J Epidemiol 1975;102:267-271; http://aje.oxfordjournals.org/cgi/reprint/102/4/267), "a measure of change in one quantity (y) per unit of another quantity x on which y depends". x is usually time. Because population sizes differ, rates in epidemiology are usually expressed not as an 'absolute' change but relative to a population size. (See Understanding the fundamentals of epidemiology - an evolving text, www.epidemiolog.net, chapter on "Measuring disease and exposure".) So the incidence rate is the number of new cases per person per unit time. Have Colford et al. presented any incidence rates derived from their data (look only in the Results section, tables, and figures)? (Select A or B and support your answer.)

A. The paper contains at least one such rate (give an example, including page and column).

B. The paper contains no such rate(s).

  8. Suppose that the authors wanted to estimate HCGI incidence in this trial with a cumulative incidence (CI)-type measure.

  8a. How could they define and calculate a CI-type measure for HCGI in the context of this trial?

  8b. What data that are not provided in the paper are needed to estimate a CI-type measure for HCGI incidence for the active device participants during Cycle A (Cycle 1)?

  9. Use the data in table 4 to estimate the following (crude) incidence rates of highly credible gastrointestinal illness (HCGI). Show calculations and units.

  9a. rate of HCGI during Cycle A among active device participants

  9b. rate of HCGI during Cycle A among sham device participants

  9c. rate of HCGI in both cycles combined among active device participants

  9d. rate of HCGI in both cycles combined among sham device participants

10. Use your results from the preceding question to show the calculation for the following crude statistics, giving units where appropriate. Use the active device participants as the reference group.

  10a. For both cycles combined, what was the crude rate ratio for HCGI comparing sham device participants to active device participants? How does your result compare with the comparable estimate (“device only”) from the authors’ mathematical model?

  10b. What was the crude rate difference for HCGI in both cycles combined comparing sham device participants to active device participants?

11. It turns out that the article has some incorrect numbers. In one case the correct value can be calculated using numbers in the article and information that this course has touched upon. In two cases there are inconsistent numbers, and in another the number seems quite improbable. The authors told me about others that cannot be detected by the reader (the lead author is sending the journal a letter with the corrections). Without spending too much time, try to identify one of the incorrect values and make a case for why the number you have identified is suspect. (60 words maximum)