The Gold Standard of Experimental Design | Survivor Average Causal Effects, Truncation by Death and Sensitivity Bounds

1. Distinguish truncation from missingness

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A missing outcome exists but was not recorded; an outcome truncated by death is undefined at the assessment time. Imputing a quality-of-life score for a person who died changes the outcome rather than recovering a missing value. Define survival time, the outcome time and any composite alternative before analysis. Death can still be analysed directly, but it cannot be ignored while conditioning the survivor outcome on observed availability.

2. Define potential survival and the always-survivor stratum

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Let S(1) and S(0) indicate whether a person would survive under treatment and control. The always-survivor stratum contains people with S(1)=S(0)=1. The survivor average causal effect compares their potential survivor outcomes under both assignments. This is a principal-stratum estimand: membership is defined by two potential survival states, only one of which is observed. It is not simply the difference among people who happened to survive in each arm.

3. See why observed-survivor comparisons are selected

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If treatment improves survival, treated survivors include some people who would have died under control. Control survivors do not contain an equivalent group. Their outcome distributions can differ even when treatment has no direct effect on the survivor outcome. Baseline adjustment may reduce imbalance but does not generally reveal latent stratum membership. Draw the principal-strata table so the mixture problem is visible before fitting a regression.

4. Decide whether the estimand answers a useful question

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The always-survivor effect is causally coherent, but the target group may not be identifiable before treatment. Decision-makers may also care about joint survival and quality, mortality itself or a ranked composite. Explain why the SACE is scientifically relevant and present survival risks alongside it. Avoid language suggesting a benefit “for survivors” generally; the effect concerns people who would survive under either treatment condition.

5. State identification assumptions in ordinary language

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Randomisation identifies marginal survival and observed outcome distributions, not the joint potential survival states or their stratum-specific outcomes. Point estimation often invokes monotonicity, which rules out treatment-caused deaths, plus assumptions about outcome distributions, covariates or latent associations. These assumptions are not guaranteed by the trial. Give a subject-matter reason for each and specify sensitivity analyses before examining the preferred result.

6. Worked example: rehabilitation after critical illness

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In an invented trial, 800 patients receive an early rehabilitation programme or usual care. Ninety-day survival is 82 percent versus 75 percent, and mean mobility among observed survivors is 64 versus 61. The three-point survivor difference is not automatically causal because treatment survivors include people who might not have survived under control. Investigators estimate a SACE under monotonicity and vary an unobserved rank-correlation parameter linking survival type to mobility. Estimates range from a one-point disadvantage to a four-point benefit, so the report foregrounds survival and the sensitivity range rather than one adjusted survivor mean.

7. Use bounds before claiming point identification

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Nonparametric or assumption-assisted bounds can show what the randomised data permit without selecting one latent mixture. Monotonicity, stochastic dominance or baseline covariates may narrow bounds, but each restriction changes their meaning. Report the unrestricted or minimally restricted range where feasible, then show how additional assumptions sharpen it. A wide bound is useful evidence that the design cannot answer a precise SACE question on its own.

8. Changed-context transfer check: cognitive outcome after surgery

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Move from critical-care mobility to cognition one year after two surgical strategies. Treatment may improve survival while survivors differ in frailty and neurological risk. The SACE framework transfers, but monotonicity may be doubtful if surgery can both prevent and cause deaths for different people. Preoperative predictors can support stratified bounds without identifying individuals’ counterfactual survival. A composite such as alive with intact cognition answers a different, sometimes more actionable, question.

9. Know the limits and common misconceptions

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Randomisation does not make observed survivors comparable. Monotonicity is not “no average harm”; it rules out an entire individual potential-survival type. A SACE does not describe people who survive only because of treatment, and it may not generalise to all randomised participants. Sensitivity parameters need substantive scales and ranges. Assigning death the worst numeric score creates a composite estimand rather than solving truncation invisibly.

10. Audit the estimand and every assumption

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Publish survival and outcome time points, causes and timing of death, outcome definition, treatment assignment, missing outcomes among survivors and baseline covariates. Show the principal-strata mapping, observed mixtures, identification restrictions, bound formulas, code and sensitivity grid. Report convergence and finite-sample behaviour where modelling is complex. Keep ordinary missingness among survivors separate from truncation and address both in the analysis plan.

11. Frequently asked questions

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Why not analyse survivors only? Treatment can change who survives. Is death just missing data? No; the survivor outcome is undefined after death. Who are always survivors? People who would survive under either treatment. Can we identify them individually? Usually not. Does monotonicity follow from better average survival? No. What if bounds are wide? That honestly shows limited identification and can motivate a different endpoint or design.

12. The gold standard keeps survival inside the causal question

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A credible survivor-effect analysis begins by admitting that death changes the existence of the outcome. It defines the always-survivor estimand, displays the selected mixtures in observed survivor groups and separates randomisation from untestable identification assumptions. Bounds and sensitivity analyses then reveal what the data support. The gold standard is not a single adjusted mean; it is a causal claim whose dependence on survival has been made impossible to miss.