1. The Atherosclerosis Risk in Communities Study (ARIC) is a major, multi-site project funded by the National Heart Lung and Blood Institute (NHLBI) of the National Institutes of Health (NIH) to study cardiovascular disease in the general U.S. population. The study enrolled people in four communities, each studied by a different team of investigators, who worked under the direction of a steering committee for the overall study. People who enrolled in the study had thorough medical examinations and completed extensive questionnaires. Participants were re-examined after several years and again several years later. One of the examinations that participants underwent was measurement of the thickness of the walls of their carotid arteries, with B-mode ultrasound, a technique that was fairly new when ARIC began. Atherosclerosis in the carotid arteries serves as an indicator of atherosclerosis elsewhere in the arterial bed, so this measurement provided a non-invasive measure of subclinical (prior to symptoms) atherosclerosis that could lead to coronary events and strokes. The studies by Williams et al. were carried out using data from the ARIC study. What are advantages and disadvantages of conducting a study of anger temperament and anger reaction as part of a large, multi-center investigation designed for multiple purposes?

  2. 14,348 persons were examined at the second clinic visit. A previous article by Williams et al. explains that these participants represented about 93% of those examined at baseline. Williams et al. apparently excluded 1,140 participants with a history of myocardial infarction (MI), coronary bypass surgery, or electrocardiographic evidence of MI, as well as an additional 222 participants most of whom were missing data on hypertension or the anger scale, leaving 12,990 participants for analysis (the arithmetic does not quite work out, so perhaps several people listed as excluded in the earlier article, which says 12,896, were retained after all).

1. What is the reason for excluding the 1,140 participants with evidence of clinical coronary heart disease?
   
   
2. How might losing 7% of the original cohort by the second visit affect the study results?

  *3. Table 1 presents various participant characteristics for each category of hypertension and anger.

1. Are there marked differences between those with low and high anger trait? What are the implications of these differences?


2. Use data in the table to derive the number of normotensive males with low anger-temperament.


3. Use data in the table to derive the percentage of hypertensives who are female.

  4. Participants were followed up from the date of their second clinic examination visit through December 31, 1995. How many person-months would be contributed to the follow-up by each of 3 participants whose second clinic exam visit took place on December 31, 1990, June 30, 1991, and January 31, 1992, assuming that none of them experienced a CHD event?

  5. Table 3 shows the total number of participants in each category of hypertension and Spielberger trait anger-temperament score range at the time of the second examination visit and the number in each category experiencing an incident event. What was the cumulative incidence (incidence proportion) for the four subgroups: normotensive, low trait anger ("CInL" in the table); normotensive, high trait anger (CInH); hypertensive, low trait anger (CIhL); hypertensive, high trait anger (CIhH)? State the meaning of these incidences. Do these incidences require units? Why not?

Cumulative incidence of CHD events by anger-temperament and hypertension
	Spielberger trait anger-temperament scores
	Normotensive		Hypertensive
	Low (≤8)	High (>8)	Low (≤8)	High (>8)
Population	8,021	456	4,231	282
No. with events	167	23	213	13
Cumulative incidence	CInL	CInH	CIhL	CIhH

  6. If participants who did not have a CHD event were followed for an average of 54 months and those who did have an event contributed an average of 27 months before the event, what would the total number of person-years have been for participants in each of the four groups (labelled nL, nH, hL, and hH in the table below)? What was the incidence rate (a.k.a. [also known as], incidence density) in each of the four groups? (See table below.)

Incidence density of CHD events by anger-temperament and hypertension
	Spielberger trait anger-temperament scores
	Normotensive		Hypertensive
	Low (≤8)	High (>8)	Low (≤8)	High (>8)
Population	8,021	456	4,231	282
No. with events	167	23	213	13
Person-years	PYnL	PYnH	PYhL	PYhH
Incidence density	IDnL	IDnH	IDhL	IDhH

  7. What is the approximate relationship between the incidence proportions in the first table and the incidence rates in the second table? (You can find an interactive example of the relation between incidence rates and incidence proportions at www.epidemiolog.net/studymat/).

  8. What are the incidence density ratios (IDR, a.k.a. incidence rate ratios) for high trait anger in (a) normotensive persons and (b) hypertensive persons? (A rate ratio is usually the ratio of the rate in the "exposed" to the rate in the "unexposed".) Write down the formula and the calculation as well as the result. Then translate the result into English or a language of your choice. What do these ratios appear to show?

  9. Compare the incidence rate ratios that you computed for the preceding question to the incidence rate ratios (referred to in the paper as "hazard ratios") for CHD events combined, Age-adjusted in Table 3. What does their similarity imply in regard to the age distributions of participants with low and high trait anger? Explain.

10. In the text, under Results (page 232, col 1), Williams et al. write: "There was a monotonic increase in CHD risk as a result of trait anger-temperament in the multivariate-adjusted models. Normotensive persons experienced a 68 percent greater risk of CHD (age-adjusted, hard events) for each four-unit increase in trait anger-temperament (95 percent confidence interval: 1.53, 1.84). "

1. Since the authors used Cox proportional hazards regression, which estimates rate ratios, by "68 percent greater risk" they are referring to a 68 percent greater incidence rate of CHD. To what incidence rate ratio (or "hazard ratio") does a 68 percent increase correspond? In other words, what is the rate ratio for a 4-point increase in trait anger-temperament in these data?
2. Based on this statement, what was the estimated rate ratio for an 8-point increase in trait anger-temperament?

11. What are appropriate interpretations of the 95% confidence interval referred to in the preceding question and of "statistically significant" in the authors’ following sentence ("In contrast, the association between trait anger-temperament and CHD risk among hypertensives was not statistically signficant.")?

12. Examine Figures 1-3. Besides providing an easy way to see the difference in CHD incidence in the groups being compared, what additional information do the figures provide that is not available from the tables?

13. The appendix to this paper contains the Spielberger subscales used as the exposure measures for this article. How would you establish the reliability and validity of a scale?

14. Cohort studies are considered observational studies, whereas clinical trials are considered experimental. Could a randomized intervention trial be conducted to test the hypothesis that anger-temperament increases CHD risk? Would it provide stronger evidence for a causal relation?