Lesson 7: Categorical Outcomes, Odds Ratio and Risk Assessment

Proportion

A proportion is a mathematical comparison between two numbers (e.g., how many women are in the room versus the total number of people in the room). The numerator (e.g. how many women are in the room) is included in the denominator (e.g. total number of people in the room). It can be written in two ways:

1. With a colon (e.g., 5:10)
2. As equivalent fractions (e.g., 5/10 = 1/2)

Odds

Odds reflect the number of ways an event can occur relative to the number of ways an event cannot occur. For example, if 4 out of 10 people developed a disease:

• Proportion: includes the numerator in the denominator, so the proportion is 4/10 or 40% of people developed the disease
• Odds: does not include the numerator in the denominator, so odds are 4/6
• both present the same information but in different ways

Odds ratio

The odds ratio (OR) is one of several statistics that have become increasingly important in clinical research and decision-making. The odds ratio:

• Measures the ratio of odds that an exposure occurred to the odds that an exposure did not occur
• Evaluates whether the odds of a certain outcome is the same for two groups
• Is a measure of effect size (i.e., it determines the strength of the relationship between two variables)
• Can be hand calculated in a clinic if necessary to determine the odds of a particular event for a patient at risk for that event

Odds ratio data is most commonly presented in a contingency table, which displays the frequency distribution of multiple variables in a single table. The most common construction is a 2 × 2 table although larger tables exist:

Based on this contingency table:

• odds of exposure in diseased = a/c
• odds of exposure in non-diseased = b/d
• exposure OR = (a/c)/(b/d) or (ad)/(bc)

Relative risk

Relative risk (RR) is the likelihood of developing the disease/outcome given that one is exposed divided by the individual likelihood of developing the disease/outcome given that one is non-exposed. Based on the contingency table above, RR = [a/(a+b)]/[c/(c+d)].

• RR = 1, there is no association between risk in exposed and risk in non-exposed
• RR > 1, increased risk for those exposed
• RR < 1, decreased risk for those exposed

In the case of a disease as the outcome of interest:

• RR is the likelihood of developing the disease given that one is exposed divided by the likelihood of developing the disease given that one is non-exposed.
• OR is the odds of exposure among diseased (cases) versus non-diseased (controls).

Odds ratio

Methods: Subjects were 49,985 women who completed Prenatal Substance Abuse Screening Questionnaires at obstetric clinics. Four groups were compared: women screened/assessed positive and treated by Early Start (‘SAT’, n=2,073); women screened/assessed positive without treatment (‘SA’, n=1,203); women screened positive only (‘S’, n=156); controls who screened negative (n=46,553).

^aEstimated from logistic regressions, controlled for maternal age, ethnicity, and prenatal care
^bWithin 30 days of discharge from birth hospitalization
^cWithin 180 days of discharge from birth hospitalization

Results: All but two ORs (low birth weight and NICU admission) comparing the controls to the SAT group were not significantly less than 1.0. All the ORs with the exception of two (cesarean section and infant emergency department visits) comparing the S group to the SAT group were elevated, particularly for placental abruption (OR=6.8) and intrauterine fetal demise (OR=16.2).

Relative risk

Methods: Data on the relative risk (RR) of cardiovascular events with individual NSAIDs were derived from meta-analyses of randomised trials and controlled observational studies.

Results: Three drugs (i.e., rofecoxib, diclofenac, and etoricoxib) ranked consistently highest in terms of cardiovascular risk compared with nonuse. Naproxen was associated with a low risk. NOTE: Table represents some but not all studies included in the meta-analysis.