91828 Chap.5 Risk, Odds and Treatment Effects
Risk, Odds and Treatment Effects
Risk and odds use different denominators, and the difference matters as events become common. This chapter starts with a two-by-two table, calculates event rates, risk ratio, relative risk reduction, absolute risk reduction and number needed to treat, and then interprets them together.
It shows how baseline risk changes absolute benefit even when a relative effect is stable, and why odds ratios should not be casually renamed risk ratios.
What this chapter covers
- 01
Risk and odds denominators
- 02
Experimental and control rates
- 03
Risk ratio
- 04
Relative risk reduction
- 05
Absolute risk reduction
- 06
Number needed to treat
Worked example · free
Calculate a complete treatment-effect chain
- +1EER = 12/80 = 0.15 and CER = 20/80 = 0.25.
- +1RR = 0.15/0.25 = 0.60.
- +1RRR = 1 - 0.60 = 0.40 or 40%.
- +1ARR = 0.25 - 0.15 = 0.10 or 10 percentage points.
- +1NNT = 1/0.10 = 10 people over the trial follow-up.
- +1Interpret with uncertainty, validity, harms and applicability rather than arithmetic alone.
Key terms
- Event Risk
- Event risk is the number with an event divided by everyone initially at risk in that group.
- Event Odds
- Event odds divide the number with an event by the number without the event.
- Risk Ratio
- A risk ratio divides intervention event risk by control event risk.
- Number Needed
- Number needed to treat is the reciprocal of absolute risk reduction expressed as a proportion.
Risk, Odds and Treatment Effects FAQ
Why can an odds ratio look more extreme?
Odds and risk have different denominators. When events are common, odds move farther from one than risk for the same event proportions, so calling an odds ratio a risk ratio can exaggerate the apparent effect. Keep the published measure name.
Can I calculate NNT from relative risk alone?
No. NNT requires absolute risk reduction, which depends on control risk as well as relative effect. Apply the plausible relative effect to a justified baseline risk, calculate the absolute difference and state the time horizon and uncertainty.
How should I round NNT?
For benefit, a non-integer NNT is commonly rounded up conservatively to the next whole person. Report the outcome and follow-up, and include an interval when available. If treatment increases harm, use absolute risk increase and number needed to harm.
What if the event is beneficial rather than harmful?
Name the event before interpreting direction. A ratio below one means less of the defined event, which is favourable for death but unfavourable for recovery. Reframe absolute differences consistently and avoid using risk reduction language when the outcome definition makes an increase desirable.
Why must every effect include a time horizon?
Event probability accumulates over follow-up, so a ninety-day NNT is not interchangeable with a one-year NNT. State the time window and check whether groups were observed equally. When censoring or unequal follow-up matters, a simple proportion may not be the appropriate measure.
How does uncertainty enter an NNT?
NNT is derived from absolute risk reduction, so uncertainty in the risk difference produces uncertainty in NNT and can become asymmetric. Use a confidence interval when available and interpret cases where the interval crosses no absolute difference rather than presenting the point NNT as fixed.
Assessment move
Make the two-by-two table your first move for every binary outcome. Label intervention and control rows, then record events, non-events and totals before calculating anything. Verify row sums so a denominator error cannot flow through the entire answer. Calculate experimental and control event risks as fractions and decimals, preserve full precision, and identify whether the event is desirable or harmful.
Only then compute risk ratio, relative risk reduction where appropriate, absolute risk reduction and number needed to treat. Write units explicitly: percent for risk, percentage points for absolute differences and people over a stated follow-up for NNT. Add an odds-ratio calculation from the same table and compare it with RR, especially when events are common. This makes the denominator difference visible rather than verbal.
Create three scenarios with the same RR but different control risks; calculate treated risk, ARR and NNT for each and explain why absolute decision value changes. Reverse the outcome from harm to recovery to test whether your direction language changes correctly. Include a scenario where treatment increases harm and use absolute risk increase and number needed to harm.
When a published study provides intervals, propagate the interpretation rather than presenting point estimates as certain. Every final sentence should name population, outcome and time horizon. Add one validity question about allocation, missing outcomes or measurement, because correct arithmetic cannot establish causality. Add one transfer question about whether local baseline risk and care differ from the trial.
For AT1, display event counts beside relative and absolute effects so readers can audit the calculation. For AT2, use the anticipated control event rate and clinically important absolute difference as linked sample-size assumptions, documenting their sources. Finish study sessions by explaining the difference among risk, odds, RR and OR without formulas.
If the explanation remains clear, the calculations are connected to clinical meaning rather than memorised as isolated operations.
