Loss to follow-up and attrition
Why it is not simply lost power
If people left at random, attrition would cost precision and nothing else. They do not: people who are doing badly withdraw, people who feel better stop attending, people who move away differ systematically. So the analysed sample is selected on something post-randomization, which is exactly the structure of selection bias.
Design comes before analysis
- Plan retention actively: minimise burden, keep contact details current, allow flexible visit windows, use registry or record linkage as a backstop for the primary outcome.
- Collect the reason for every withdrawal, in a structured field, because the reason is the evidence about the mechanism.
- Distinguish withdrawal from the intervention (still followed for outcomes) from withdrawal of consent to be followed at all. Only the second creates missing outcome data, and conflating them loses outcomes unnecessarily.
- Record enough about non-completers to model the missingness.
- Report the flow of participants completely, with numbers and reasons at each stage.
Analysis
Name the assumed mechanism. Complete-case analysis is unbiased under a narrower condition than people suppose, and with covariate adjustment it can perform as well as multiple imputation when the same predictors of missingness are included. Multiple imputation is more flexible and is not a repair: it assumes missing at random unless deliberately extended. Where missingness may be informative, run a tipping-point or delta analysis showing how different the missing outcomes would have to be to overturn the conclusion.
The honest report
Give the numbers in each arm, the reasons, a comparison of baseline characteristics between completers and non-completers, and a sensitivity analysis. Attrition described only as a limitation, with a complete-case analysis presented as the result, leaves the reader unable to judge.
Weighting for dropout: inverse probability of censoring weights
When the reasons for dropout are measured, inverse probability of censoring weighting is an alternative to imputation. A model predicts each participant's probability of remaining under observation from the variables, at baseline and during follow-up, that predict both dropout and the outcome. Participants who remain are then weighted by one over that probability, so a completer who resembles the people who left stands in for them. It assumes dropout is explained by the variables in that model; it cannot correct dropout driven by the unobserved outcome itself. Very large weights mark participants with little chance of staying and should be inspected rather than silently truncated, and the standard error must account for the weights having been estimated.
What to watch out for
Rules of thumb about acceptable attrition, five percent is fine and twenty percent is trouble, are not defensible: what matters is whether the people missing differ, and a two percent loss that is entirely deaths in one arm is far worse than a symmetric twenty percent. Attrition also does not just add uncertainty, it breaks randomization, because the people who remain are a group selected after allocation. And analysing only completers is a decision to assume the missing are like the observed, made silently.
Clinical example
A trial of a rehabilitation programme loses 18 percent of the intervention arm and 9 percent of controls, mostly because the programme was burdensome for the frailest participants. The completers analysis compares a fitter intervention group with a less selected control group, and the direction of the resulting bias is predictable.
- Dealing with missing outcome data in randomized trials and observational studies (opens in a new tab) · Am J Epidemiol · doi 10.1093/aje/kwr302
- CONSORT 2010 statement: updated guidelines for reporting parallel group randomised trials (opens in a new tab) · BMJ · doi 10.1136/bmj.c332
- Correcting for noncompliance and dependent censoring in an AIDS Clinical Trial with inverse probability of censoring weighted (IPCW) log-rank tests (opens in a new tab) · Biometrics · doi 10.1111/j.0006-341x.2000.00779.x