University of North Carolina at Chapel Hill
School of Public Health, Department of Epidemiology

Fundamentals of Epidemiology (EPID 168)

Final Examination, Fall 1998 - Answer Guide

1. Briefly list two reasons why a case control study is (or is not) appropriate to examine individual risk factors for hip osteoarthritis. (2 pts) 

Condition rare, faster to complete than cohort study, wide range of exposures of interest.

  2. The authors state that their cases come from a defined population. List four features of the population or the study design that support this statement or helped the authors to achieve it? (4 pts) 

1. The two health districts had a centralized orthopedic facility for assessment and treatment of hip osteoarthritis;

2. Local orthopedic surgeons were willing to enter all patients into the study;

3. All men and women 45 years and older who were placed on the waiting list for primary total hip arthoplasty were considered for the study;

4. The authors included patients who consulted orthopedic surgeons privately.

5. The study excluded patients who lived outside the two districts.

The diverse socioeconomic profile was an advantage for generalizability but does not make this a defined population.

  3. Considering the study population, study design, and other information in the article, which of the following statements is TRUE and which are FALSE . (2 pts each) 

a. In these two health districts, the incidence density of symptomatic hip osteoarthritis of sufficient severity to warrant hip arthroplasty exceeds 40 per 100,000 person-years.

[TRUE - 726 eligible cases / 1 million population over 18 months = 48.4 per 100,000] 

b. If about 12% of the population was age 65 years or older, then about 12,000 people age 65 years or older in the two districts have radiographic evidence of hip osteoarthritis.

[TRUE - 10% population prevalence in age 65 years and older * 12% of one million] 

c. The data in Table 1 demonstrate that women are 1.9 times as likely to develop severe symptomatic hip osteoarthritis as are men.

[FALSE - the data in Table 1 cannot demonstrate this female excess, since there is no information about the sex ratio in the older population; this ratio may well reflect a greater incidence of severe symptomatic hip osteoarthritis in women, but some of the excess presumably derives from greater mortality among men.] 

d. The data in Table 2 indicate that female gender is not a risk factor for hip osteoarthritis.

[FALSE - controls were matched to cases on gender (and age), so the sex ratio in the controls must match that in the cases] 

e. In this study, matching the control group to the cases on age, as opposed to a random sample of the general adult population, probably resulted in greater statistical power and precision.

[TRUE - the mean age of the cases is 70 years old, with the majority older than 60; thus, the use of general population controls without regard to age would result in relatively little overlap between the age distributions of cases and controls on this very important variable.]

4. The case identification process was based on a register in each district made up of persons on a waiting list for a total hip arthoplasty (surgical reformation of the hip joint). Waiting lists for procedures are common in societies with a national or social medicine system. In the United States, a region wide waiting list for a hip arthoplasty is unlikely, as the availability of receiving this procedure would be more related to insurance status or ability to afford such a procedure. Explain how using the register system in the Untied Kingdom to select cases either increases or decreases the possibility of selection bias as compared to a study conducted in the United States. (4 pts) 

Using the registry may reduce selection bias if affluence or ability to pay for a hip replacement is associated with exposures like BMI, physical activity, Heberdenís nodes. Cases selected from surgery lists in the United States system may have a differential association with a risk factor as compared cases not receiving this procedure, so measures of association may be more biased in a U.S. study. 

5. How was the diagnosis of hip osteoarthritis made in this study? Was this based on manifestional or causal criteria? Explain your answer. (3 pts) 

(page 517, left column, 2nd paragraph): Diagnosis of hip osteoarthritis in this study was based on pelvic radiographs. This is based on manifestional criteria.

6. According to the authors: "For each case, a control of the same sex and age was selected from the list of the same general practice held by the county Family Health Service Association". State in one sentence the rationale for using a list from general practioners? (3pts) 

(page 517, left column, 3rd paragraph): In England and Wales, almost everyone is registered with a general practitioner so that these lists essentially provide an enumeration of the general population.

7. Eighty-four percent of the patients listed for total hip arthroplasty fulfilled the criteria for entry into the study as cases. Which of the following best describes the criteria: (3 pts)

a. age > 45 years, being on the waiting list for hip arthroplasty, and the presence of Heberdenís nodes.

b. age > 45 years, pain duration at least for 36 months, and presence of Heberdenís nodes.

c. history of hip fracture within the past year, being on the waiting list for hip arthroplasty and reside in the study area.

d. presence of Heberdenís nodes, history of hip fracture within the past year, and reside in the study area.

e. being on the waiting list for hip arthroplasty, reside in the study area, and age > 45 years (answer)

8. The authors report that 89% of the eligible cases agreed to participate and 60% of the 1060 controls approached agreed to participate. Which of the following best states a condition regarding the non-responders that could lead to an odds ratio reported for the risk of osteoarthritis associated with previous hip injury that is biased away from the null (>1). Choose one best answer. (3 pts) 

a. control non-responders are more likely to have a history of hip injury compared to case non-responders. (answer)

b. control non-responders are less likely to have a history of hip injury compared to case non-responders.

c. being a non-respondent is not related to previous hip injury.

d. none of the above 

9. What was accomplished by replacing controls who refused to participate? (Choose one best answer) (3 pts) If controls who refused had not been replaced:

a. selection bias would have been greater;

b. the control group would have been less representative of the study base;

c. probability of a Type I error would have been greater;

d. probabillty of a Type II error would have been greater; (answer)

e. nondifferential misclassification bias would have been greater.

f. it would have been necessary to control for age and sex in the analysis.

 Answer: d. Failure to replace controls who refused would have reduced both the number of controls and of cases (due to the matching), with a loss of statistical power and increase in the probability of a type II error.

10. The authors selected controls who were individually matched to cases by age, gender, and family practitioner. Matching in the design stage is usually considered only for those variables that are known to be confounders. Under which of the following circumstances could gender be a confounder of the association between a risk factor (obesity) and the outcome (hip osteoarthritis)? Circle all that apply. (4 pts) 

a. the prevalence of obesity and the prevalence of hip osteoarthritis are both higher in men that in women (true)

b. the prevalence of obesity is lower in men than women, but the prevalence of hip osteoarthritis is higher in men than women. (true)

c. the prevalence of obesity is higher in men than women, but the prevalence of hip osteoarthritis is the same in men and women.

d. the prevalence of obesity is the same in men and women, but the prevalence of hip osteoarthritis is higher in men than women.

11. The odds ratios in Table 2 are "mutually adjusted for the other two variables" by logistic regression. The following questions concern the models used to estimate the odds ratios in the table (ignore the fact that it was "conditional" logistic regresion and ignore the middle categories for body mass index and presence of Heberdenís nodes) (2 pts each): 

a. How many logistic models were necessary to estimate the odds ratios for body mass index >28.0, definite Heberdenís nodes, and previous hip injury among women.

"Mutually adjusted" means that each odds ratio comes from a model that includes the other two factors, which therefore means that all three factors are included in the same model. So one model yields an adjusted odds ratio for each variable. So one model was used.

b. The odds ratio estimate for hip injury in women was 2.8. What must the logistic coefficient have been?

The OR for a dichotomous or indicator variable is exp(beta), where beta is the logistic coefficient. Therefore the coefficient was 1n(2.8) = 1.0296.

c. From this table, estimate the odds ratio for women who had both definite Heberdenís nodes and previous hip injury compared to women who had neither.

The logistic model is based on additivity of the logit or multiplicativity of the odds. Therefore the odds ratio for the double exposure is the product of the adds ratio for each of the risk factors: 1.5*2.8=4.2. 

12. In this study, information on medical history, life style, and leisure time physical activities was obtained through a "structured interviewer-administered questionnaire". (page 517). It is possible that persons on a waiting list for a hip arthoplasty would be more keenly aware of hip injuries they may have had in the past than controls. If true, this is an example of which of the following? Choose one best answer. (3 pts) 

a. differential case ascertainment bias

b differential misclassification bias (answer)

c. differential selection bias

d. differential precision bias

e. none of the above 

13. Among women, the odds of previous hip injury is higher among cases than controls (Table 2; OR=2.8). As indicated in the footnotes for Table 2, the odds ratio for pervious hip injury is adjusted or controlled for the other two variables in the Table (body mass index and Heberdenís nodes). Using the counts shown in Table 2, calculate an unadjusted (crude) odds ratio for previous hip injury in women. (3 pts)

Unadjusted (crude) odds ratio = __________ 2.9

14. Which of the following conclusions can be made from the above results? (chose one best answer) (3 pts) 

a. the unadjusted (crude) association between hip injury and hip osteoarthritis in women is completely confounded by body mass index and Heberdenís nodes.

b. since the unadjusted and adjusted odds ratios are similar, the risk factor (hip injury) must not be associated with the adjustment variables (body mass index and Heberdenís nodes)

c. since the unadjusted and adjusted odds ratios are similar, there is no effect-measure modification of the association between hip injury and hip osteoarthritis.

d. none of the above (answer)

15. The odds ratios presented in Table 5 are adjusted for previous hip injury. Why might they still be confounded by hip injury? (3 pts) 

There may be residual confounding by type of hip injury or by how long ago the hip injury occurred, or imperfect recall of hip injury (non-differential misclassification).

16. In Table 6, is the crude association between previous hip injury and risk of unilateral hip osteoarthritis biased towards the null or away from the null? (2 pts)

Towards the null (crude OR = 7.6 vs. adjusted OR = 10.6)

17. Based on the data in Table 3, what is the odds ratio for Heberden's nodes (definite versus none) for persons in the Upper tertile of body mass index? (3 pts) 

OR for Definite Heberden's nodes / none = 3.2 / 1.6 = 2.0

18. Rothman has proposed that "public health synergism" is present when an observed joint effect exceeds that expected under the additive model. Do the odds ratios in Table 3 indicate the presence of "public health synergism" for effect of Heberden's nodes and elevated body mass index on hip osteoarthiritis? If not, do the odds ratios conform to a multiplicative model? Include in your answer a 1-2 sentence assessment of whether these data indicate "public health synergism". (For this question, ignore the row for "Possible" Heberden's nodes and the column for the middle tertile of body mass index, and assume that both Heberdenís nodes and elevated BMI reflect casual risk factors for hip osteoarthritis. Note: do not necessarily rely on the authors' description of this table.) (6 pts)

Odds ratios for hip osteoarthiritis


Body mass index


Heberden's nodes

Lowest third

Middle third

Highest third



1.1 (0.7-1.8)*

1.6 (1.0-2.7)


1.5 (0.8-2.7)

1.5 (0.8-2.6)

2.0 (1.1-3.6)


1.4 (0.9-2.3)

2.2 (1.4-3.7)

3.2 (1.9-5.4)

* Numbers in parentheses, 95% confidence interval.

Ignoring the intermediate categories for Heberden's nodes and body mass index gives the following expression for the additive model:

Expected joint excess risk = excess risk for factor 1 + excess risk for factor 2

= excess risk for Heberden's nodes + excess risk for Body mass index

Since hip osteoarthritis of this severity is rare, the following approximate expressions are appropriate:

Expected excess risk = (OR for Heberden's nodes - 1) + (OR for Body mass index - 1)

Expected joint excess risk = (1.4 - 1) + (1.6 - 1) = 1.0

Observed joint excess risk = (3.2 - 1) = 2.2

The substantial difference between 2.2 and 1.0 indicates that the odds ratios in this table do not conform to an additive model for expected joint effect.

The odds ratios do not conform to a multiplicative model, either:

Expected joint OR = (OR for Heberden's nodes) * (OR for Body mass index )

= 1.4 * 1.6 = 2.24, vs. 3.2 observed

Thus, the relationship is "supramultiplicative", though not greatly so.

Since these odds ratios indicate a joint effect greater than that expected under an additive model, "public health synergism" is present, to a moderate degree (we expect a 100% increase in risk but observe a 220% increase in risk)

19. The authors investigated the association of specific sporting activities with risk of hip osteoarthritis. Their data are presented in Table 5. Using their data, compute separately the unadjusted (crude) risk of osteoarthritis associated with playing golf and for swimming in men and women combined. Consider those who do not participate in any sport as the reference group and assume no missing data. Show two appropriate 2x2 table and your calculations. (4 pts)










OR = 1.7










OR = 1.6

19a. Compare these unadjusted (crude) odds ratios with the ones presented in Table 3. Briefly describe and explain the comparison. (3 pts) 

Table shows 1.4 and 1.5, respectively. This suggests that BMI, nodes, and hip injury explain very little of the association of these two sports with hip osteoarthritis. 

19b. Consider the possibility that golfers who have hip osteoarthritis are reluctant to seek medical attention for their condition for fear it will mean the end of their ability to play golf. Therefore, cases who golf are less likely to be selected for this study than cases who do not golf. If the true OR associated with golf is 2.0, then which of the following best describes the selection bias and its impact on the odds ratio you computed. (3 pts) 

a. non-differential selection bias resulting in an odds ratio biased toward the null.

b. non-differential selection bias resulting in an odds ratio biased away from the null.

c. differential selection bias resulting in an odds ratio biased away from the null.

d. differential selection bias resulting in an odds ratio biased toward the null. (answer)

e. none of the above

19c. The authors state that "...the association with swimming may have arisen because patients with hip osteoarthritis were advised to swim..." (page 521). Suppose that 25% of the cases had been incorrectly classified as swimmers and assume that the misclassified cases had not participated in any other sporting activity, either. Re-compute the odds ratio for the association of hip osteoarthritis and swimming, after re-classifying these individuals, using the number from the 2x2 table in question 19 above. Briefly discuss how your conclusion about the role of swimming does (or does not) change. In what direction did misclassification bias the study OR? (3 pts)





156-25% = 117



140 + 39 = 179


OR = 0.96: The misclassification was differential and biased the odds ratio upward.

20. The odds ratio (95% confidence interval) estimating the risk of osteoarthritis associated with a previous hip injury was 24.8 (3.1-199.3) in men and 2.8 (1.4-5.8) in women (see Table 2).  

a. Which estimate indicates a stronger association? (2 pts) 24.3

b. Which estimate is more precise? (2 pts) 2.8 (1.4-5.8)

c. Which estimate is more compatible with a population odds ratio of 4.0? (2 pts) 2.8 (1.4-5.8)

21. Which one of the statements best interprets the following passage? (3 pts) 

"In a previous case-control study (17) of men aged 60-76 years, we observed a doubling of risk for hip osteoarthritis among those in the highest third of body mass index distribution, as compared with those in the lowest third, although the increased risk was not statistically significant." (p519 bottom of right column) 

a. Hip osteoarthritis is not as significant when it occurs in obese older patients, because it is expected that overweight that lasts for many years will lead to damage to the joints.

b. A doubling of risk is not significant from a statistical perspective, because it represents only a moderate association.

c. The doubling of risk was not statistically significant because a p-value was not computed, so it is not possible for the authors to know whether the increased risk was due to chance.

d. If 1,000 independent random samples the same size as that study population were drawn from a population with no increased risk of hip osteoarthritis, fewer than 950 would have an OR between 0.5 and 2.0. (answer)

e. If 1,000 independent random samples the same size as that study population were drawn from a population with a doubling of risk of hip osteoarthritis for the highest third of the body mass distribution, as compared with the lowest third, more than 5% of the samples would display no elevation in risk.

f. If 1,000 independent random samples the same size as that study population were drawn from a population with a doubling of risk of hip osteoarthritis for the highest third of the body mass distribution, as compared with the lowest third, fewer than 80% would display an association of that magnitude.

Answer: d. "Statistically significant", as conventionally used, means that in the absence of any true association a model based on chance would yield an association as strong or stronger than the observed value less than 5% of the time. 

22. A medical journalist, confused by the thrust of this article, comes to you and says: "I've read this article several times, but I can't figure out what it shows about the relationship of body mass index, Heberden's nodes, and hip osteoarthritis. The authors explain that 'two broad mechanisms are believed to underlie the pathogenesis of osteoarthritis at any joint site: mechanical stress and a generalized predisposition to the disorder' as indexed by Heberdenís nodes [p519 right column]. That seems straightforward enough, and they later conclude that the analysis 'supports the notion that this condition arises through an interaction between a generalized predisposition to the disorder and specific mechanical insults to the hip' [p521]. Yet on page 518 [right column], the authors state that there was 'no statistically significant interaction' between body mass index and Heberden's nodes, and on page 519 [left column] they refer to obesity and a tendency to polyarticular involvement as 'independent risk factors for hip osteoarthritis'. Would you please assess for me what this article shows about the relationship among body mass index, Heberden's nodes, and hip osteoarthritis? I have room for 40-60 words. Thanks!" (6 pts) 

Points to include:

1. Both body mass index and presence of Heberden's nodes were associated with greater risk of hip osteoarthritis, even when the other is absent.

2. People with both elevated BMI and Heberden's nodes have a greater risk for hip osteoarthritis than people with only one of these risk factors and even greater than would be expected from adding or multiplying their individual effects (i.e., greater than expected by both additive or multiplicative models).

3. The authors seem to believe and the study does not show otherwise that most cases of hip osteoarthritis in their study result from a combination of mechanical stress (which could be something other than obesity) and biologic predisposition (which might not yet have manifested in other joints).

4. The paper presents no biological theory or other information suggesting a mechanistic interaction between obesity and osteoarthritis at other sites in regard to hip osteoarthritis, but rather discusses a possible etiologic role for each individually;

Grading: 6 points for 3 of these, 5 points for two of them, 3 points for one. If none was mentioned then 1-2 points awarded depending upon the relevance and accuracy of what was written. 

23. Write a brief statement for or against a causal relationship between hip injury and risk of osteoarthritis. Comment specifically on at least two of Bradford Hillís criteria for causal inference. Support your conclusion with data or statements from the article. (4 pts)

(You're on your own here!)


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4/10/1999, 8/4/2000, changes to 19c 12/14/2000vs