14. Intention to Treat, Subgroups, Missing Data, and Estimands
After this lesson you can
- Compute a risk ratio, risk difference and number needed to treat by intention to treat
- Explain why a per-protocol contrast exaggerates the effect
- Choose pre-specified baseline covariates and avoid post-randomization ones
- Read subgroups with an interaction test
- Split alpha across secondaries and bound a result under the worst case for missing data
Video coming soon
Lessons publish daily from November 17, 2026.
This lesson analyzes the completed fictional Oakhaven trial by intention to treat and compares it with per-protocol and as-treated analyses. It covers baseline adjustment, subgroups with an interaction test, multiplicity across secondaries, missing-data mechanisms and a worst-case bound, all driven by the estimand.
Questions and answers
Questions a learner would ask about this lesson. Think through your own answer before you open each one.
- What is intention to treat, and why is it the primary analysis?
Show answer
Intention to treat counts every randomized participant in the arm they were assigned, regardless of adherence, switching or loss. It compares the groups the coin made, so the balance of known and unknown factors is kept. It estimates the effect of offering the program, and it is the primary analysis in a superiority trial.
- What is the Oakhaven primary result?
Show answer
With the 10 lost per arm counted as poor control by the pre-specified rule, the program has 25 of 125 (20 percent) and usual care 50 of 125 (40 percent). The risk ratio is 0.20 over 0.40, which is 0.5. The risk difference is 20 points, and the number needed to treat is 1 over 0.20, which is 5.
- Why not just drop the 25 who skipped the sessions?
Show answer
The coin made the arms, but choices made the 25, so dropping them undoes the randomization. The per-protocol contrast, adherent 9 of 90 (10 percent) against usual care 40 of 115 (35 percent), gives a risk ratio of about 0.3. That extra strength reflects the adherers' head start, because adherers are not a random sample of their arm.
- How should subgroup results be read?
Show answer
Ask whether the effect differs by a baseline characteristic, using an interaction test rather than two separate p values. In Oakhaven, the under-50 stratum gives 12 of 75 versus 30 of 75, a risk ratio of 0.4, and the 50-and-over stratum 13 of 50 versus 20 of 50, a risk ratio of 0.65, but the interaction p is about point three. With twenty subgroups each at point zero five, one false positive is expected.
- How did Oakhaven handle multiplicity and missing data?
Show answer
The three secondary endpoints share alpha by a simple split, 0.05 over 3, about point zero one seven each. For missing data, the worst-case bound counts all lost program participants as poor control and all lost usual-care participants as controlled: 25 of 125 versus 40 of 125, 20 versus 32 percent, a risk ratio of about 0.63. The result survives even that assumption.
Practice quiz
- Question 1The Oakhaven intention-to-treat result is:
- Question 2With 20 percent poor control in the program arm and 40 percent in usual care, what is the number needed to treat?
- Question 3Which analysis population groups participants by what they actually received and breaks randomization completely?
- Question 4Comparing adherent program participants (10 percent poor control) with usual care (35 percent) is:
- Question 5Which variable may be adjusted for in the primary analysis?
- Question 6Why should a baseline table not carry p values for differences between arms?
- Question 7In the under-50 stratum, the program had 12 of 75 with poor control and usual care 30 of 75. What is the risk ratio?
- Question 8With twenty subgroups each tested at point zero five and no true difference anywhere, how many false positives are expected?
- Question 9Complete-case analysis (dropping the lost) is valid only if the data are missing:
- Question 10The worst-case missing-data bound gives:
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Design of Clinical Studies is education only. Every lesson follows the fictional Oakhaven Adherence Trial with invented numbers; the course uses no real data and cites no real studies.