91828 Chap.9 Trial Aims, Outcomes and Sample Size
Trial Aims, Outcomes and Sample Size
A sample-size calculation is only as defensible as the clinical question and numerical assumptions that enter it. This chapter aligns the primary aim, endpoint, target effect, variability or control event rate, alpha, power, allocation and attrition allowance.
It explains why unrealistic effect assumptions create underinformative trials, why recruitment inflation does not solve biased missingness, and how clusters or repeated measures change information.
What this chapter covers
- 01
Primary aim and estimand
- 02
Primary outcome
- 03
Target effect
- 04
Alpha and power
- 05
Variability assumptions
- 06
Attrition inflation
Worked example · free
Inflate an evaluable sample for attrition
- +1Retained proportion = 1 - 0.15 = 0.85.
- +1Recruitment target = 270/0.85 = 317.65.
- +1Round up to at least 318, adjusting if balanced groups require another whole participant.
- +1Extra recruitment preserves expected numbers but not validity when missingness is informative or differs by arm.
Key terms
- Primary Outcome
- A primary outcome is the prespecified endpoint that anchors the main trial conclusion and sample size.
- Target Difference
- A target difference is the effect magnitude a trial is designed to detect with stated operating characteristics.
- Statistical Power
- Statistical power is the probability of rejecting the null under a specified alternative and assumptions.
- Attrition Allowance
- An attrition allowance inflates recruitment to preserve the expected number with evaluable outcomes.
Trial Aims, Outcomes and Sample Size FAQ
Can I choose a large effect to make the trial feasible?
The target must be clinically important and empirically plausible. Choosing an unrealistically large effect reduces the sample but can leave the trial unable to detect a realistic meaningful benefit. Address feasibility through recruitment strategy, sites or design, not assumption inflation.
What inputs should a sample-size paragraph state?
Name the primary outcome, target difference, expected variability or control event rate, significance level, power, allocation ratio, analysis model and attrition allowance. Cite or justify values for a comparable population and explain any cluster or repeated-measure adjustment.
Should I calculate observed power after the trial?
Usually no. Observed power derived from the result adds little beyond the p-value and confidence interval. Interpret the completed study through its estimate, precision, design and plausible bias; reserve power for prospective planning under specified alternatives.
Why does a smaller target effect need more participants?
Smaller effects are harder to distinguish from random variation when variability and error rates stay fixed. The required information increases sharply as the target shrinks. A target should therefore be the smallest clinically important plausible difference, not a convenient number chosen after considering recruitment capacity.
How do cluster trials change sample size?
Participants within a cluster share context and provide less independent information than the same number individually randomised. Planning uses cluster size, intracluster correlation and the number of clusters, while analysis respects clustering. A large participant total cannot compensate automatically for very few independent clusters.
What should I do when inputs are uncertain?
Show a sensitivity range using credible alternatives for control risk, variability, attrition or target effect. Identify which assumption drives the recruitment total and plan a feasibility or internal-pilot response if appropriate. Transparency about uncertainty is stronger than reporting a single software output without provenance.
Assessment move
Start trial planning with one precise primary aim, then write the estimand in ordinary language: population, strategies compared, endpoint, handling of intercurrent events and summary measure. Define the primary outcome with instrument, scoring direction, assessor and time point. Check that it matters to patients and can be measured consistently.
Create a sample-size assumption table with a row for target difference, expected standard deviation or control event rate, significance level, power, allocation ratio, design effect and attrition. Add a source and plausibility range for every numerical input. A clinically important target should be supported by prior evidence, patient input or a justified decision threshold, not selected to fit available recruitment.
Recalculate directionally by making the target smaller, variability larger, power higher and allocation more unequal; explain why each change affects information. For binary outcomes, distinguish relative and absolute targets and keep baseline risk explicit. For cluster trials, add the intracluster correlation, average cluster size and number of clusters rather than treating all participants as independent.
For repeated outcomes, ensure the calculation matches the planned model and correlation assumptions. Inflate the evaluable requirement by dividing by the retained proportion, then round to a workable allocation and verify each arm count. Treat this inflation as precision protection, not a cure for informative missingness. Pair the total with retention procedures and sensitivity analysis.
Create a feasibility table containing eligible patients per site, expected consent rate, recruitment period and site capacity; a mathematically adequate target that cannot be recruited is not a valid plan. Avoid post-hoc observed power after results exist and interpret the completed study through its interval.
For AT2, turn the assumption table into concise textual-abstract reasoning and show the primary endpoint and timing visually. Finish with sensitivity calculations using optimistic and conservative inputs. The most defensible proposal shows which assumption drives the total and what operational response would be needed if that assumption is wrong.
