Randomized controlled trial

Random treatment assignment makes treatment independent of baseline potential outcomes in expectation.

A recorded medically attended injury depends both on an injury occurring and on care being sought and recorded. An intervention that changes recognition of injuries or the threshold for seeking care can change recorded attendance even without changing underlying injury incidence. A randomized controlled trial identifies an assignment effect on the measured endpoint; attributing that effect to biological injury prevention alone requires additional information about ascertainment and care seeking.

Risk compensation is a possible behavioral response to a prevention intervention: feeling better protected can reduce vigilance or increase exposure to hazards, partially offsetting the intervention's direct protective effect. It is a hypothesis to investigate, not a conclusion established merely by an unfavorable treatment comparison. A randomized controlled trial of the overall package estimates its net assignment effect, which can include both physical protection and behavioral changes.

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 $1+(m-1)\rho$ for cluster size $m$. 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.

Reporting a favorable prespecified outcome while omitting a less favorable one can give an exaggerated impression of consistency of evidence. Multiple primary outcomes should be summarized transparently even when some lack statistical significance. A short abstract can prioritize results, but should not hide a materially different primary result; absence of information does not by itself establish deliberate misconduct.

For a beneficial intervention reducing an adverse-event risk from $p_C$ to $p_I$ over a stated follow-up period, the number needed to treat is the reciprocal of the absolute risk reduction. Its clinical interpretation requires the population, outcome, horizon and comparison to be specified. Invert confidence limits for the risk difference in reversed order if both are positive. If the interval includes zero, the transformed confidence set is unbounded and may include both benefit and harm, rather than being one ordinary finite interval.

An outcome assessor is kept unaware of randomized treatment assignment to limit differential questioning, interpretation and recording. This does not require the participant or intervention provider to be blinded. Participants can reveal their assignment, so standardized interviews and restricted records help preserve blinding. Blinding after assignment is different from allocation concealment before enrollment.

An intention-to-treat analysis compares participants according to their randomized assignment, retaining that assignment even when they do not use the assigned intervention. Its causal effect is the effect of assignment under the study's actual adherence pattern, rather than the effect of perfect adherence. Randomization protects this comparison from baseline confounding; missing data can still require assumptions or additional analysis.

Treatment contamination occurs when participants in one arm of a randomized controlled trial receive an intervention assigned to another arm. This is distinct from contamination in robust estimation. The intention-to-treat analysis still compares randomized assignments, but intervention receipt becomes less separated between the arms, often diluting the assignment effect. Receipt-based comparisons can introduce confounding because receipt need not be randomized.

Assume treatment receipt gives event risk $p_1$, nonreceipt gives risk $p_0$, and a fraction $c$ in each equally sized randomized arm crosses to the opposite treatment. The two assignment risks are $(1-c)p_1+c{p}_0$ and $c{p}_1+(1-c)p_0$. Subtracting yields the displayed attenuation, with ${\Delta }_{\mathrm{receipt}}=p_0-p_1$. It depends on the stated equal crossover fractions and unchanged receipt-specific risks; it is not a universal formula for every form of treatment contamination.

A treatment consequence is not interchangeable with a baseline covariate in an intention-to-treat analysis. Let randomized $Z$ be independent of $U,\epsilon$, and let actual intervention use be $D=Z+U$, with $Y=D+\epsilon$ and independent centered errors. The assignment changes the mean outcome by one. But the conditional expectation $\mathbb{E}[Y\mid Z,D]=D$ has coefficient zero on $Z$. Thus adjustment for the post-randomization variable $D$ changes the estimand even in a simple identified linear regression.

Randomization assigns experimental units to treatments using a random mechanism, allowing treatment-group differences to be calibrated against the known assignment distribution.

For each new eligible participant, compare the imbalance that would result from each treatment assignment across prespecified baseline covariate margins. Assign with a probability favoring the less imbalanced choice, while retaining a random component and allocation concealment. This targets marginal balance when a large number of joint strata makes stratified randomization with blocks inefficient. It is a sequential allocation rule, and inference should respect its design.

Divide participants into strata defined by prespecified baseline prognostic variables and randomize independently within each stratum. Permuted blocks can keep treatment counts close throughout recruitment. This balances the stratification variable between arms by design, while allocation concealment keeps upcoming assignments hidden. Analyses should account for important design strata where appropriate.

Within each prespecified stratum, choose a block containing fixed equal counts of the two treatment assignments, then randomly permute their order. Every completed block gives exact treatment balance. Variable block sizes and allocation concealment protect against predicting the next assignment. Incomplete final blocks permit a small unavoidable imbalance; odd stratum sizes cannot have exact equal allocation.

Allocation concealment prevents those deciding whether to enroll an eligible participant from knowing the upcoming randomized assignment. It protects the randomized controlled trial against selection based on that assignment. It concerns access to the assignment before enrollment; keeping participants or assessors unaware after assignment is a separate design feature.

Restricted randomization samples assignments from a specified subset preserving features such as block balance, fixed group sizes or allowable treatment sequences. Inference must respect the chosen allocation scheme rather than treating all label permutations as admissible.

Complete randomization chooses uniformly among all treatment assignments having prespecified treatment-arm sizes.