A study examines the association between benzodiazepine use and hip fracture in elderly patients 70 years of age. A total of 180 patients admitted to 20 hospitals with hip fracture were included in the analysis; 10 patients used benzodiazepines in the week before admission. For comparison, the investigators selected 200 patients who were admitted for a different reason; 7 of them used benzodiazepines in the week before admission. Which of the following is the best measure of association to be reported for this study?
A)(10 / 180) / (7 / 200)
B)(10 *193) / (7 * 170)
C)(10 / 170) − (7 / 193)
D)(10 * 200) / (7 * 180)
E)(10 + 7) / (180 + 200)

Question

A study examines the association between benzodiazepine use and hip fracture in elderly patients >70 years of age.  A total of 180 patients admitted to 20 hospitals with hip fracture were included in the analysis; 10 patients used benzodiazepines in the week before admission.  For comparison, the investigators selected 200 patients who were admitted for a different reason; 7 of them used benzodiazepines in the week before admission.  Which of the following is the best measure of association to be reported for this study?
A)(10 / 180) / (7 / 200)
B)(10 *193) / (7 * 170)
C)(10 / 170) − (7 / 193)
D)(10 * 200) / (7 * 180)
E)(10 + 7) / (180 + 200)

Quizplus · Accepted Answer

Explanation: This is a case-control study; the case group includes individuals with the outcome of interest (eg, hip fracture) and the control group includes individuals without it. The distribution of the exposure (eg, benzodiazepine use) is retrospectively measured within each group. The odds ratio (OR) is a measure of association commonly used in case-control studies, where it represents the odds that a case was exposed divided by the odds that a control was exposed. Controls represent an unknown fraction of the population, so it is impossible to calculate a true risk, relative risk, or risk ratio in a case-control study. Contingency (2x2) tables are useful for solving such problems and are usually presented in the format below: 11ec2b69_c0f5_3ad1_8f63_f5bb4c1d844f_MD0005_00 For this particular study, the following contingency table can be constructed: 11ec2b69_c0f5_3ad2_8f63_2d6b2455bb03_MD0005_00 Odds is defined as probability divided by (1 minus probability); mathematically, odds = P / (1 − P), where P is probability. For patients with hip fractures: there was a (10 / 180) probability that they used benzodiazepines and a (170 / 180) probability that they did not; note that (170 / 180) = [1 − (10 / 180)]. Therefore, these patients had an odds of (10 / 180) / (170 / 180) = 10/170 of having used benzodiazepines. In general, odds of an event (eg, hip fracture) among patients with an exposure (eg, benzodiazepine use) is given by (a / c). Similarly, patients without hip fractures had odds of (7 / 200) / (193 / 200) = 7/193 of having used benzodiazepines. In general, odds of an event (eg, hip fracture) among patients without an exposure (eg, benzodiazepine use) is given by (b / d). The OR refers to the ratio of these 2 measures: OR = (a / c) / (b / d) = (10 / 170) / (7 / 193). This result can be further manipulated to give (a * d) / (b * c) = (10 * 193) / (7 * 170), which is a mathematical shortcut to calculate OR. (Choice A) (10 / 180) / (7 / 200) represents [a / (a + c)] / [b / (b + d)]. This is the formula for the positive likelihood ratio in a contingency table of test results and disease. The formula for relative risk, which should not be calculated for case-control studies as such studies do not follow patients over time, is given by [a / (a + b)] / [c / (c + d)]. (Choice C) (10 / 170) − (7 / 193) is the difference of the odds and does not give a useful measure of association. (Choice D) (10 * 200) / (7 * 180) is mathematically equivalent to the formula given in choice A, (10 / 180) / (7 / 200). (Choice E) (10 + 7) / (180 + 200) refers to the proportion of patients who used benzodiazepines in cases and controls combined. It does not give a measure of association. Educational objective: Odds ratios (but not relative risks or risk ratios) can be obtained in case-control studies and are a useful measure of association. References: Explaining odds ratios. (http://www.ncbi.nlm.nih.gov/pubmed/20842279) Statistics notes. The odds ratio. (http://www.ncbi.nlm.nih.gov/pubmed/10827061)

A Study Examines the Association Between Benzodiazepine Use and Hip