DSC6008 Chap.7 Paired Designs and Clinical Trials
Paired Designs and Clinical Trials
Use dependence instead of pretending it is absent
A paired design links two observations because they come from the same subject or from deliberately matched units. The analysis first forms one difference per pair and then treats those differences as independent across pairs.
This removes stable pair-level variation from the treatment comparison when the matching is effective.
Choose and preserve the subtraction direction
Define every pair difference in the same order, such as treatment A minus treatment B or after minus before. Reversing the order changes the sign of the estimated effect even though its absolute test statistic may remain unchanged.
Pair identifiers and both raw measurements should survive cleaning so missing values do not silently turn the study into an unpaired comparison.
Recognize when pairing helps
Matching on a strong pre-treatment predictor can reduce the variation of pair differences and improve precision. Weak matching may add complexity without much gain.
Matching on an outcome consequence or another post-treatment variable can bias the comparison. The matching rule should therefore be set before assignment and justified by information available at that time.
Analyse differences rather than two unrelated groups
A paired t procedure is a one-sample analysis of the within-pair differences.
Its independent sample size is the number of usable pairs, not twice that number. A paired randomization test flips treatment order within pairs rather than shuffling all observations.
Both approaches reflect the dependence intentionally built into the design and use between-pair variation for uncertainty.
Follow allocation through a trial
Clinical trial reasoning distinguishes the unit randomized, the treatment received, the outcomes measured and the population targeted by the conclusion. Control groups, masking and prespecified outcomes protect different parts of that chain.
Several visits from one participant remain repeated observations on one randomized unit unless the design says otherwise.
Separate concealment from masking
Allocation concealment prevents recruiters from knowing the next assignment before a participant enters. Masking prevents named people from knowing the received treatment after assignment.
A masked assessor can reduce measurement bias even when participants know their treatment, but that protection does not repair predictable allocation. State who is concealed or masked and at which stage.
Account for time, carryover and attrition
In crossover or repeated-condition studies, the second observation can reflect period change or lingering effects from the first treatment.
Randomized order and a justified washout can help separate these influences. Missing pairs also alter the represented population when completion relates to treatment or response. Record reasons for missingness and report which paired units remain in the analysis.
Conclude on the population of pairs
Report the mean signed difference, its uncertainty and the design feature that formed the pairs.
Then state whether treatment order was randomized and whether carryover, missing outcomes or imperfect matching limit the claim. Random assignment protects the comparison inside the trial sample, while wider generalization depends on recruitment and eligibility.
What this chapter covers
- 01
Matched pairs
- 02
Within-pair differences
- 03
Paired t tests
- 04
Trial allocation
- 05
Control groups
- 06
Masking
Worked example · free
Analyse changes rather than separate visit means
- 1Sum the five subject-level changes to obtain 10.
- 2Divide by five to obtain mean change 2.
- 2State that the independent sample size is five subjects, not ten measurements.
Key terms
- Matched Pair
- Two related observations joined by subject identity or a deliberate matching rule.
- Within-pair Difference
- One signed contrast computed inside each matched pair.
- Masking
- Keeping specified trial participants or personnel unaware of assigned treatment to limit bias.
Paired Designs and Clinical Trials FAQ
Why can pairing increase precision?
Pairing removes stable differences between matched units from the treatment contrast. When outcomes within a pair are positively related, the variation of their difference can be much smaller than the variation obtained by treating the groups as unrelated. Poor matching may offer little benefit.
What is the sample size in a before-and-after study?
For a basic paired analysis, it is the number of independently sampled subjects with usable paired differences. The two measurements per subject create the difference but do not double the independent sample size. Missing one member of a pair also affects the analysis differently from one missing unrelated observation.
Does random treatment allocation guarantee generalizability?
It supports internal comparison by making treatment groups comparable in expectation within the recruited sample. Generalization to a wider population also depends on recruitment, eligibility, adherence, outcome measurement and whether the sample represents the people and settings named in the claim.
Assessment move
Draw one row per pair and compute the signed difference explicitly. Check that every sign follows the same treatment order. For trial questions, make a four-column ledger for randomized unit, assigned treatment, observed outcome and target population; then locate each proposed conclusion in that ledger.
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