Epidemiology 200C Homework #3
Due 4/29/10
Read Lopez-Garcia et al, “Coffee Consumption and Risk of Stroke in Women” and respond to the following questions.
- The authors divided exposure (coffee drinking) into five categories: < 1 cup per month, 1 cup per month to 4 cups per week, 5 to 7 cups per week, 2 to 3 cups per day, and 4+ cups per day. What could be some disadvantages of using categories such as these?
Some of the categories are very broad (1 cup/month – 4 cups/wk and 4+ cups per day) so the desired homogeneity of exposure levels in these categories is likely not achieved. The category of 1 cup/month – 4 cups/wk especially would have people with completely different exposure levels and thus the measure in this category could be sensitive to the distribution of coffee use in this category. Such a broad category could distort trends and obscure actual important differences in intake (e.g., <1 cup a wk vs. 1 cup a wk).
- The authors suggest a relationship between blood pressure, coffee consumption and risk of stroke. Suppose an unknown risk factor (U) affects both blood pressure and coffee drinking (like working at a high pressure job). Draw a DAG below to represent the suggested relationship between these variables. Would controlling for blood pressure lead to bias in the analysis?
C = coffee drinking
BP = blood pressure
S = risk of stroke
U = unknown risk factor
(U)
C S
BP
Although BP is a collider among C and (U), since (U) does not affect the risk of stroke (assuming the above DAG is correct), controlling for BP would not create any open biasing paths from coffee drinking to risk of stroke. On the other hand, controlling BP would remove the indirect effect of coffee on stroke from the estimate, and thus could give a distorted impression of the total effect.
3.The authors state “One prior report had suggested a detrimental effect of caffeinated coffee consumption on stroke among hypertensive men; by contrast, in our cohort we found an inverse association among nonhypertensive women and no association among hypertensive patients.” Comment on the use of the word contrast to compare the results of the two studies, given that you do not know the point estimate and 95% confidence limits of the effect measure from the previous study.
The term “detrimental effect” likely means only that the 95% confidence interval for the effect measure from the previous study was entirely above the null. The confidence intervals for the hazard ratio for the effect of coffee consumption on stroke in hypertensive women are compatible with effects above the null.
Table 5 lists the actual RR and confidence interval from the previous study (Hakim et al). However, according to table 5, the method for defining the exposed an unexposed categories and the outcome under study differ from those used to calculate the hazard ratios in Table 3, making it difficult to compare the two results.
- Suppose that your prior for the hazed ratio is lognormal with 95% prior limits for the effect of consuming four or more cups of caffeinated coffee a day on total stroke in hypertensive women of 1 and 4. Calculate a posterior median and 95% posterior interval using the information from Table 3.
If your 95% prior interval is 1 to 4, then the natural log of your prior median is the natural log of the geometric mean of your prior limits:
=
You could also have found this value by taking the arithmetic mean of the natural logs of the prior limits.
The prior variance of the log hazard ratio is calculated from the log prior limits:
=
The variance of the log of the hazard ratio point estimate is calculated the same way:
= 0.03
To combine prior with data, use inverse variance weighting:
=0.2
So the posterior median is or 1.2
The posterior variance of the log hazard ratio is the inverse of the sum of the inverse variances:
=
Now use the log posterior mean and variance to calculate the posterior limits:
= =
= = 0.9
So the 95% posterior interval is 0.9 to 1.6. Although the prior median was much larger than the hazard ratio point estimate, the prior was not very precise, so the posterior median and95% posterior interval limits were fairly close to the hazard ratio point estimate and 95% confidence limits