Clinical equipoise 2026-10-14
Clinical equipoise is genuine professional uncertainty about the relative overall benefit and harm of the treatments being compared in a randomized controlled trial. A favorable intermediate endpoint does not by itself resolve uncertainty about mortality. Ethical design requires informed consent, meaningful benefit-risk assessment and monitoring of serious harms; an underpowered safety comparison is not evidence that harm is absent.
Cluster-randomized trial 2026-10-14
A cluster-randomized trial assigns whole groups, such as institutions, to an intervention rather than assigning individuals separately. Positive intraclass correlation reduces independent information: the equal-size exchangeable approximation has design effect for cluster size . The number of independent randomized clusters also matters for inference. Cluster assignment does not itself remove requirements for informed consent or justify dropping outcome ascertainment in the control arm.
Past exam of the mathematics course of the University of Cambridge 2004 iii Paper 38 4 e Solution Created 2026-10-03 Updated 2026-10-14
A trial can be well powered for a common reconviction outcome and poorly powered for a small difference in rare deaths. Failure to obtain a significant mortality comparison would not show that the treatments have equal safety. Participants' overall welfare cannot be reduced to reconviction alone: a decrease in that outcome must be weighed against possible loss of life.
Ethical randomization depends on clinical equipoise about the overall benefit-risk balance. Participants need voluntary informed consent that explains the uncertainty and possible mortality tradeoff; a criminal-justice setting demands particular care about coercion. The design should ascertain serious outcomes completely, use independent trial safety monitoring with prespecified stopping rules, and seek pooled safety evidence when an adequately powered mortality comparison needs collaboration. These principles are consistent with the research protections described in the Declaration of Helsinki.
A smaller efficacy trial is not automatically unethical, but deliberately avoiding adequate safety information is not a justification for it. A limited initial study needs a defensible scientific purpose, proportionate safeguards and an explicit plan for resolving serious-harm uncertainty; if evidence establishes an unfavorable net balance, continuing randomization merely to improve precision would not be justified.
Past exam of the mathematics course of the University of Cambridge 2008 iii Paper 46 2 b iii Solution Created 2026-10-03 Updated 2026-10-14
An ethical objection concerns the proposed saving of control-prison staff costs: the trial is explicitly based on individual informed consent, and institutional allocation does not justify omitting control participants' information, consent or appropriate outcome follow-up. These responsibilities remain in both arms. A cluster-randomized trial can sometimes be ethically defensible, but changing the randomized unit alone does not make those participant protections unnecessary.
The statistical objection is loss of independent information and potential prison-level imbalance. Outcomes within a prison may share baseline risks, management practices and release conditions, yielding positive intraclass correlation. For equal cluster size , the usual exchangeable approximation gives design effect , so the individual-randomization calculation understates the sample required when . There are also fewer independent randomized units, and prison-specific adoption of management practices can be unbalanced across arms. Thus randomizing prisons generally loses precision for this individually deliverable intervention, unless compensating design features and additional clusters are supplied.
Past exam of the mathematics course of the University of Cambridge 2012 iii Paper 41 1 a ii Solution Created 2026-10-03 Updated 2026-10-07
Obtain informed consent so that participation in the clinical trial is voluntary and based on an understanding of its procedures, potential benefits and risks, alternatives and withdrawal arrangements. Consent before allocation prevents willingness to participate from being selected according to the known treatment assignment.