Ageing, health & public statistics
Statistics Lab · step 04
Calculate absolute risk, risk difference, risk ratio and odds ratio—and know which study designs support each one.
Outcome: a correctly oriented 2 × 2 table and measures whose names, directions and denominators are explicit.
Seven-step investigationNow: 04 · Measure association
Analysis checkpoint
Work through these six prompts in order. Each one supplies what the next one needs.
Have the checked medication-review by disability table from Step 03, including the outcome count and denominator within each exposure group.
A p-value does not say how large an association is. Because this is a cohort with a defined follow-up period, risks, absolute differences and risk ratios can be estimated directly before regression.
Run Section 04 in Stata or SPSS. Check the printed row and category order: software may display a reciprocal ratio if the reference group is reversed.
For a difference, compare with 0; for a ratio, compare with 1. Read both the point estimate and confidence interval, then translate the absolute measure into cases per 100 people when useful.
You can explain risk, odds and their ratios in plain language, name the reference group and identify whether the interval includes the null value.
Begin here
We are asking whether disability during six months was more or less common among participants who received a medication review. Before using any ratio, start with people and denominators.
What happened? Here it is new disability by six months: yes or no.
Which groups? Medication review is compared with no review.
How common? People with disability divided by all people followed in that group.
In ordinary language, risk is a probability: the chance that a person in a defined group experiences the outcome during a stated period.
Work from people
| Medication review | Disability | No disability | Total | Risk |
|---|---|---|---|---|
| Yes | 45 | 155 | 200 | 45 ÷ 200 = 22.5% |
| No · reference group | 112 | 400 | 512 | 112 ÷ 512 = 21.9% |
22.5% − 21.9% = +0.6 percentage points
About 6 more cases per 1,000 reviewed people. Zero means no absolute difference. The 95% confidence interval, −6.2 to +7.4 percentage points, includes both fewer and more cases.
22.5% ÷ 21.9% = 1.03
The observed risk was 1.03 times the risk in the no-review group: roughly 3% higher on the relative scale. One means equal risk; below one means lower risk; above one means higher risk. The 95% confidence interval is 0.76 to 1.40.
(45 ÷ 155) ÷ (112 ÷ 400) = 1.04
Odds compare people with the outcome with people without it. They are not probabilities: 45 cases among 200 people is a 22.5% risk, but its odds are 45 to 155. The odds ratio is essential in case-control studies and is produced by logistic regression. Its 95% confidence interval is 0.70 to 1.54.
Reviewed risk 45 / 200 = 0.225
No-review risk 112 / 512 = 0.219
Risk difference +0.006 (95% CI -0.062 to 0.074)
Risk ratio 1.03 (95% CI 0.76 to 1.40)
Odds ratio 1.04 (95% CI 0.70 to 1.54)Over six months, observed disability risk was 22.5% in the reviewed group and 21.9% in the no-review reference group. The point estimates are close to no association, while every confidence interval is also compatible with clinically meaningful benefit and harm. Because this is a cohort, risks and a risk ratio are directly estimable; the odds ratio is shown mainly to connect the table with later logistic regression.
Six-month disability occurred in 45/200 reviewed participants (22.5%) and 112/512 participants without review (21.9%), giving a crude risk difference of +0.6 percentage points (95% CI −6.2 to +7.4) and a risk ratio of 1.03 (95% CI 0.76 to 1.40).
These are crude, unadjusted comparisons. None shows that medication review caused disability. The reviewed participants may have been frailer before the study began.
Which measure?
| Measure | What it compares | When it belongs | Read this value |
|---|---|---|---|
| Risk difference | Two probabilities, by subtraction. | Cohort or trial with a defined follow-up period. | +5 percentage points means 5 more outcomes per 100 people. |
| Risk ratio | Two probabilities, by division. | Cohort or trial where both group risks are observed. | 0.70 means the observed risk is 30% lower; 1.00 means equal risk. |
| Odds ratio | Two sets of outcome odds. | Case-control studies and logistic regression. | 2.00 means twice the odds, not twice the probability. |
| Rate ratio | Events per unit of person-time. | Different follow-up times or outcomes that can recur, such as falls. | 1.40 means 40% more events per person-year. |
| Hazard ratio | Modelled event rates at each moment. | Time-to-event data with censoring, such as time to admission. | 0.80 is a relative hazard, not “20% fewer people admitted”. |
For a cohort with equal follow-up, cs reports risks, the risk difference and risk ratio; or adds the odds ratio.
cs disability_6m med_review, or
* For case-control data, estimate an odds ratio instead:
* cc disability_6m med_reviewRISK adds cohort risk estimates and the odds ratio to a 2×2 Crosstabs table; check the printed direction carefully.
CROSSTABS
/TABLES=med_review BY disability_6m
/STATISTICS=CHISQ RISK
/CELLS=COUNT ROW COLUMN.Name the four cells, then calculate risks and odds explicitly so the numerator, denominator and reference group remain auditable.
tab <- with(cohort, table(med_review, disability_6m))
a <- tab["1", "1"] # reviewed cases
b <- tab["1", "0"] # reviewed non-cases
c <- tab["0", "1"] # no-review cases
d <- tab["0", "0"] # no-review non-cases
risk_review <- a / (a + b)
risk_no_review <- c / (c + d)
risk_difference <- risk_review - risk_no_review
risk_ratio <- risk_review / risk_no_review
odds_ratio <- (a * d) / (b * c)Every result needs four labels: the measure, the reference group, the follow-up period and the confidence interval. “Relative risk” is too vague if you actually mean a risk ratio, rate ratio, prevalence ratio or hazard ratio.
Procedure reference
Official guidance for cohort risks, case-control odds and stratified tables.
Open the manualIBM’s definitions for chi-square, risk estimates and Mantel–Haenszel statistics.
Open IBM documentation