A 2016¹ article in JAMA reports the results of a study of treatment outcomes for children with mild gastroenteritis who were given oral rehydration therapy.Enrolled children were randomized to received either rehydration with diluted apple juice (DAJ), or an electrolyte maintenance solution (EMS).As per the study authors:

"The primary outcome was a composite of treatment failure defined by any of the following occurring within 7 days of enrollment: intravenous rehydration, hospitalization, subsequent unscheduled physician encounter, protracted symptoms, crossover, and 3%or more weight loss or significant dehydration at in-person follow-up. Secondary outcomes included intravenous rehydration, hospitalization, and frequency of diarrhea and vomiting."

Of the 323 children randomized to DAJ, 54 experienced treatment failure. (17%).Of the 324 children randomized to EMS, 81 experienced treatment failure.(25%)

1.What is the proportion of children randomized to the DAJ group who experienced treatment failure?

2.Estimate the standard error for the proportion from question 1.

3.What does the quantity from question 2 estimate?

4.Estimate a 95% CI for the population proportion of children who would experience treatment failure if all children with mild gastroenteritis were treated with DAJ.

5.Estimate a 95% CI for the population proportion of children who would experience treatment failure if all children with mild gastroenteritis were treated with EMS.

6.Do the intervals in questions 4 and 5 overlap?

7.What is the risk difference in treatment failure for the DAJ group compared to the EMS group?

8.Estimate a 95% CI for the risk difference from question 7. (Note, (when rounded to 2 decimal places): you may verify this on your own if you wish.)

9.Does the interval from question 8 contain the null value for risk differences?

10.What is the relative risk of treatment failure for the DAJ group compared to the EMS group?

11.What is the natural log (ln) of the relative risk from question 10?

12.Estimate a 95% CI for the natural log (ln) of the relative risk from question 7. (Note: (when rounded to 2 decimal places): You may verify this on your own if you wish.)

13.Does the interval in question 12 include the null value for ln(relative risk)s?

14.Estimate a 95% confidence interval for the relative risk from question 10.

15.Does the interval from question 14 include the null value for relative risks?

16.Based on what you have done in the previous items, will the estimated odds ratio of treatment failure for the DAJ group compared to the EMS group be greater or less than 1 in value?

17.Based on what you have done in the previous items, will the 95% CI for the odds ratio of treatment failure for the DAJ group compared to the EMS group include 1?

18.After accounting for sampling variability, is there a statistically significant association between the treatment (DAJ vs. EMS) and treatment failure in the population of children from which the study sample was taken?

¹Freedman S, et al. Effect of Dilute Apple Juice and Preferred Fluids vs Electrolyte Maintenance Solution on Treatment Failure Among Children With Mild Gastroenteritis A Randomized Clinical Trial.JAMA. 2016;315(18):1966-1974. doi:10.1001/jama.2016.5352