Andreeva et al. (2017) report the results of an analysis that questioned whether there was any interaction in the relationship between 5-year change in body weight and sleep time. As part of their study, they examined potential effect modification by sex and by overweight/obesity status.

The sex-stratified results of a simulated cohort study based on their results are below. A total of 2,137 individuals were recruited to a 5-year cohort study and asked about their average nighttime sleeping hours. Individuals with six hours of sleep or less were categorized as short sleep time while those with greater than six were categorized as normal sleep time. At five years, those with greater than twenty pounds of weight gain were categorized as having gained weight, while those who maintained weight, lost weight, or gained less than 20 pounds were categorized as no weight gain. Use the tables to answer the questions that follow about the role of sex in the relationship between sleep deficiency (defined as a short average sleep time) and weight gain.

1. What was the risk of weight gain among females with normal sleep habits? Please show your work. (2 points)
2. What was the risk of weight gain among males with normal sleep habits? Please show your work. (2 points)
3. What was the risk of weight gain among females with short sleep habits? Please show your work. (2 points)
4. What was the risk of weight gain among males with short sleep habits? Please show your work. (2 points)

5. What was the risk ratio comparing weight gain among males with normal sleep habits to females with normal sleep habits? Please show your work. (2 points)

6. What was the risk ratio comparing weight gain among females with short sleep habits to females with normal sleep habits? Please show your work. (2 points)

7. What is the observed joint effect of being male and sleeping six or fewer hours a night on weight gain over 5 years? Put another way, what is the observed risk ratio comparing the risk among men with short sleep patterns to women with normal sleep patterns? Please show your work. (3 points)

8. Use the stratified tables as well as your answers to Questions 1 through 7 to fill in the following table. Note that the risk ratio of 1 indicates the referent category, which means that the RRs for all remaining groups should be compared to female participants with normal sleep schedules. (4 points)
9. What is the expected joint effect of being male and sleeping six or fewer hours a night on weight gain over 5 years? Put another way, what is the expected risk ratio comparing the risk among men with short sleep patterns to women with normal sleep patterns? Please show your work. (3 points)

10. Briefly describe how the expected joint effect of being male and sleeping less per night compares to what was observed in the study. (2 points)

11. Based on this comparison, do you think that sex is an effect modifier in the relationship between sleep and weight gain? Why or why not? (Do not use the Breslow-Day test in your answer.) (1 point)

MALES Short sleep Normal sleep FEMALES Short sleep Normal sleep Weight gain 115 149 Weight gain 117 130 No weight gain 269 540 No weight gain 523 294 Sleep Sex Weight gain No weight gain Risk RR Normal Female 1.00 Normal Male Short Female Short Male MALES Short sleep Normal sleep FEMALES Short sleep Normal sleep Weight gain 115 149 Weight gain 117 130 No weight gain 269 540 No weight gain 523 294 Sleep Sex Weight gain No weight gain Risk RR Normal Female 1.00 Normal Male Short Female Short Male