13 Research methods, statistics, critical review and evidence-based practice13.3 Experimental studies
13.3.1.6 Intention to treat and missing data
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Written by Resident Doctor Committee · Published
Analysis populations
Population | Who is included | What it estimates |
|---|---|---|
Intention to treat | Every randomised participant, in the allocated arm | Real-world effectiveness, the effect of being assigned treatment |
Per-protocol | Only participants who adhered to the protocol | Efficacy, whether the drug works when taken |
As treated | Participants grouped by treatment received | Association with treatment received, without randomisation's protection |
Intention-to-treat analysis keeps each participant in their allocated arm whatever happens afterwards, including dropout, non-adherence, crossover or never receiving treatment, so the denominators equal the numbers randomised.
It preserves the balance of prognostic factors that randomisation produced, and moving or excluding people after allocation biases the comparison.
In an antipsychotic trial, excluding people who stop for persistent symptoms or adverse effects leaves a group selected for tolerance and improvement, which favours the drug.
Modified intention to treat has no standard definition, so check which participants were excluded.
Non-adherence dilutes differences, so intention to treat tends to be conservative in superiority trials but makes non-inferiority or equivalence easier to claim.
Missing outcomes
Intention to treat defines the groups but cannot recover an unmeasured outcome. Analysing only those seen at the final visit is a complete case analysis, even if it is labelled intention to treat.
Mechanism | Assumption | Consequence |
|---|---|---|
Missing completely at random | Missingness is unrelated to any data, observed or not | Complete case analysis can be unbiased but loses precision |
Missing at random | Given observed data, missingness does not depend on the missing values | Suitable modelling or imputation can be valid |
Missing not at random | Missingness depends on unobserved values, such as unrecorded relapse | Needs extra assumptions that cannot be tested |
Single imputation
Method | Value inserted for each missing score | Note |
|---|---|---|
Last observation carried forward | The participant's own most recent recorded score | Can favour either arm |
Baseline observation carried forward | The participant's pre-treatment score | Assumes the dropout gained nothing, a conservative assumption |
Mean imputation | The arm's average among completers | Ignores the person's own earlier ratings and reduces variability |
Worst-case scenario | Failure for losses on active treatment, success for losses on placebo | A finding that survives it is robust |
Under last observation carried forward, a participant who leaves at week 4 with a Hamilton Depression Rating Scale score of 19 scores 19 at every later visit.
It may understate improvement in depression and overstate later function in progressive Alzheimer's disease.
Single imputation ignores uncertainty about the missing values, so the usual standard errors are unreliable.
Multiple imputation
Multiple imputation predicts missing values from observed variables many times with chance variation, analyses each completed dataset and pools the results using Rubin's rules.
The pooled confidence interval therefore reflects uncertainty about the missing data.
Standard methods assume data are missing at random and the model is appropriate.
Sensitivity analysis
Sensitivity analysis checks whether conclusions survive plausible alternative assumptions about the missing data.
Worst-case and best-case imputation give bounds on the sample result, not a confidence interval for the population effect.
Tipping point analysis shifts imputed outcomes until the conclusion changes.