A trial report may present an intention-to-treat result, a per-protocol result and an as-treated result. Those labels are not three interchangeable ways to calculate the same causal effect. They describe different ways of grouping or selecting people, with different assumptions behind the interpretation.
In this lesson, every participant's outcome is known. That keeps attention on treatment allocation and receipt, rather than missing data. Your task is to calculate each comparison, name what it actually compares and decide which causal claim the design supports.
Start with assignment and receipt separately
An intention-to-treat analysis retains participants in their randomized groups regardless of subsequent treatment receipt. Under appropriate trial conditions, it estimates the effect of assignment to the compared strategies. A per-protocol causal question concerns following specified treatment strategies; simply excluding people who did not adhere does not automatically answer it. An as-treated comparison instead groups people by treatment received. Cochrane Handbook, section 8.2.2
The question matters before the label. A service might want to know what happens when it offers Programme A instead of B under the delivery conditions studied. A different question asks what would happen if people followed A rather than B as specified. Neither question is inherently illegitimate, but randomization directly protects the assignment comparison, not every later grouping.
Worked example: all outcomes are complete
Original fictional teaching trial. One hundred people are individually randomized, 50 to A and 50 to B. Before the first session, ten in each group choose the other programme. Everyone then completes exactly one programme. There are no mixed courses, further changes or other protocol departures.
A favourable outcome means meeting a prespecified simulated-task threshold at eight weeks. Outcome assessment is identical for everyone, and all 100 outcomes are observed. Assume proper randomization, a well-defined programme in each arm and no effects of one participant's assignment on another's outcome.
| Randomized assignment | Programme received | Participants | Favourable outcomes |
|---|---|---|---|
| A | A | 40 | 28 |
| A | B | 10 | 2 |
| B | B | 40 | 16 |
| B | A | 10 | 8 |
The table contains the same people throughout. Only the analysis grouping will change. A higher favourable-outcome proportion is better.
Comparison 1: preserve randomized assignment
The A-assigned group includes the 40 who received A and the ten who received B:
A assignment: (28 + 2) ÷ 50 = 60%.
The B-assigned group includes the 40 who received B and the ten who received A:
B assignment: (16 + 8) ÷ 50 = 48%.
The intention-to-treat difference is 60% − 48% = +12 percentage points.
This is the trial's estimated effect of assignment to A rather than B under its delivery and switching conditions. It is not an estimate of universal adherence. Nor should it automatically be called the effect of offering A in every routine service: other settings can have different participants, supports and treatment-receipt patterns.
Randomization balances baseline prognostic factors in expectation, not exactly in every finite trial. We have calculated a point estimate, not its confidence interval or statistical significance.
Comparison 2: keep only those who followed assignment
A simple per-protocol analysis might exclude both switching groups:
A adherers: 28 ÷ 40 = 70%.
B adherers: 16 ÷ 40 = 40%.
The difference becomes 70% − 40% = +30 percentage points.
This accurately describes the selected adherers in the two arms. It does not automatically estimate what would happen if everyone followed A rather than B. The exclusion discards 20 known outcomes and may break the comparability created by randomization.
Suppose factors related to prognosis also affect which programme a person can attend. Selecting adherence can then select different types of people in the two groups. The fact that 40 remain in each group does not establish comparable prognosis. Equal denominators are not a substitute for an exchangeable comparison.
The distinction is between a per-protocol causal effect and a naive per-protocol analysis. More credible estimation can require explicit adherence definitions, measured prognostic information and suitable causal methods under additional assumptions. A restricted table alone does not provide those protections. Hernán and Hernández-Díaz
Comparison 3: regroup by programme received
An as-treated analysis places everyone who received A together, whatever their allocation:
Received A: (28 + 8) ÷ 50 = 72%.
Received B: (2 + 16) ÷ 50 = 36%.
The difference is 72% − 36% = +36 percentage points.
All outcomes remain included, but their inclusion does not preserve randomized grouping. People receiving A include eight successes among ten B-assigned switchers; people receiving B include two successes among ten A-assigned switchers.
Those contrasting outcomes could reflect prognostic selection, treatment effects, chance or a combination. The table does not identify which explanation dominates. It cannot establish that the largest observed contrast is the closest to the causal effect of receiving a programme.
Why three results do not identify a preferred answer automatically
The estimates are +12, +30 and +36 percentage points, but ranking them by size is not an analysis strategy. Start with the effect of interest, then examine whether the design and assumptions identify it.
Complete follow-up removes the missing-outcome problem from this exercise. It does not remove bias from conditioning on adherence or regrouping by receipt. “We analysed everyone” is therefore insufficient unless the report also says how participants were grouped.
A useful boundary case is perfect adherence: if everyone receives exactly their allocated programme and the outcome definitions are identical, these three simple groupings coincide. Agreement then follows from the data structure. When adherence is imperfect, agreement among estimates would still not prove that every causal interpretation is valid.
Similarly, intention-to-treat is not guaranteed to be conservative for every causal question. The direction and magnitude of differences depend on treatment receipt, prognosis, comparator behaviour and the effect being estimated. Hernán and Hernández-Díaz
Transfer exercise: the direction can change
Original fictional exercise. A second trial uses the same complete-outcome setup and definitions, but has these results:
| Assignment | Programme received | Participants | Favourable outcomes |
|---|---|---|---|
| A | A | 30 | 18 |
| A | B | 20 | 18 |
| B | B | 30 | 21 |
| B | A | 20 | 4 |
Which point estimate answers the randomized assignment comparison, A minus B?
A. +22 percentage points.
B. −10 percentage points.
C. −34 percentage points.
Feedback: A is correct. Assigned A has (18 + 18)/50 = 72% favourable outcomes; assigned B has (21 + 4)/50 = 50%. Their difference is +22 points.
B is the naive per-protocol comparison: 18/30 − 21/30 = 60% − 70% = −10 points. C is the as-treated comparison: (18 + 4)/50 − (18 + 21)/50 = 44% − 78% = −34 points.
The sign reversals show how consequential grouping can be. They do not prove that A is beneficial under every adherence strategy, or that receipt of A is harmful. Only the allocation contrast retains the randomized comparison in this stipulated example.
A practical reading note
For each trial result, record four things: the question, the grouping rule, who was excluded and why the remaining comparison might be causally interpretable. If “per-protocol” appears, inspect the actual method rather than assuming it means a valid adherence effect. If “as-treated” appears, ask what made receipt comparable after randomization.
Sources and further reading
- Cochrane Handbook, Chapter 8: Assessing risk of bias in a randomized trial. Relevant full-text sections on assignment, adherence and analysis populations consulted.
- Hernán and Hernández-Díaz: Beyond the intention to treat in comparative effectiveness research. Relevant full-text sections on assignment, as-treated and per-protocol comparisons consulted.