Editing Randomized controlled trial (section)

=== Procedures ===
The treatment allocation is the desired proportion of patients in each treatment arm.

An ideal randomization procedure would achieve the following goals:<ref name="Lachin-1988a">{{Cite journal |vauthors=Lachin JM |date=December 1988 |title=Statistical properties of randomization in clinical trials |journal=Controlled Clinical Trials |volume=9 |issue=4 |pages=289–311 |doi=10.1016/0197-2456(88)90045-1 |pmid=3060315}}</ref>
* Maximize [[statistical power]], especially in [[Subgroup analysis|subgroup analyses]].  Generally, equal group sizes maximize statistical power, however, unequal groups sizes may be more powerful for some analyses (e.g., multiple comparisons of placebo versus several doses using Dunnett's procedure<ref>{{Cite web |title=STAT 503 - Design of Experiments |url=https://onlinecourses.science.psu.edu/stat503/node/16 |access-date=24 September 2012 |publisher=Pennsylvania State University |vauthors=Rosenberger J}}</ref> ), and are sometimes desired for non-analytic reasons (e.g., patients may be more motivated to enroll if there is a higher chance of getting the test treatment, or regulatory agencies may require a minimum number of patients exposed to treatment).<ref name="Avins-1998">{{Cite journal |vauthors=Avins AL |date=December 1998 |title=Can unequal be more fair? Ethics, subject allocation, and randomised clinical trials |journal=Journal of Medical Ethics |volume=24 |issue=6 |pages=401–408 |doi=10.1136/jme.24.6.401 |pmc=479141 |pmid=9873981}}</ref>
* Minimize selection bias.  This may occur if investigators can consciously or unconsciously preferentially enroll patients between treatment arms.  A good randomization procedure will be unpredictable so that investigators cannot guess the next subject's group assignment based on prior treatment assignments. The risk of selection bias is highest when previous treatment assignments are known (as in unblinded studies) or can be guessed (perhaps if a drug has distinctive side effects).
* Minimize allocation bias (or confounding).  This may occur when [[covariate]]s that affect the outcome are not equally distributed between treatment groups, and the treatment effect is confounded with the effect of the covariates (i.e., an "accidental bias"<ref name="SchulzGrimes2002" /><ref name="Buyse-1989">{{Cite journal |vauthors=Buyse ME |date=December 1989 |title=Analysis of clinical trial outcomes: some comments on subgroup analyses |journal=Controlled Clinical Trials |volume=10 |issue=4 Suppl |pages=187S–194S |doi=10.1016/0197-2456(89)90057-3 |pmid=2605967}}</ref>).  If the randomization procedure causes an imbalance in covariates related to the outcome across groups, estimates of effect may be [[bias of an estimator|biased]] if not adjusted for the covariates (which may be unmeasured and therefore impossible to adjust for).

However, no single randomization procedure meets those goals in every circumstance, so researchers must select a procedure for a given study based on its advantages and disadvantages.{{cn|date=March 2025}}

==== Simple ====
This is a commonly used and intuitive procedure, similar to "repeated fair coin-tossing."<ref name="SchulzGrimes2002" /> Also known as "complete" or "unrestricted" randomization, it is [[Robust statistics|robust]] against both selection and accidental biases. However, its main drawback is the possibility of imbalanced group sizes in small RCTs.  It is therefore recommended only for RCTs with over 200 subjects.<ref name="Lachin-1988b">{{Cite journal |vauthors=Lachin JM, Matts JP, Wei LJ |date=December 1988 |title=Randomization in clinical trials: conclusions and recommendations |journal=Controlled Clinical Trials |volume=9 |issue=4 |pages=365–374 |doi=10.1016/0197-2456(88)90049-9 |pmid=3203526 |hdl-access=free |hdl=2027.42/27041}}</ref>

==== Restricted ====
To balance group sizes in smaller RCTs, some form of [[restricted randomization|"restricted" randomization]] is recommended.<ref name="Lachin-1988b" />  The major types of restricted randomization used in RCTs are:
* [[Randomized block design|Permuted-block randomization]] or blocked randomization: a "block size" and "allocation ratio" (number of subjects in one group versus the other group) are specified, and subjects are allocated randomly within each block.<ref name="Schulz-2002" /> For example, a block size of 6 and an allocation ratio of 2:1 would lead to random assignment of 4 subjects to one group and 2 to the other. This type of randomization can be combined with "[[stratified randomization]]", for example by center in a [[multicenter trial]], to "ensure good balance of participant characteristics in each group."<ref name="Moher-2010" /> A special case of permuted-block randomization is ''random allocation'', in which the entire sample is treated as one block.<ref name="Schulz-2002" /> The major disadvantage of permuted-block randomization is that even if the block sizes are large and randomly varied, the procedure can lead to selection bias.<ref name="Lachin-1988a" /> Another disadvantage is that "proper" analysis of data from permuted-block-randomized RCTs requires stratification by blocks.<ref name="Lachin-1988b" />
* Adaptive biased-coin randomization methods (of which urn randomization is the most widely known type): In these relatively uncommon methods, the probability of being assigned to a group decreases if the group is overrepresented and increases if the group is underrepresented.<ref name="Schulz-2002" /> The methods are thought to be less affected by selection bias than permuted-block randomization.<ref name="Lachin-1988b" />

==== Adaptive ====
At least two types of "adaptive" randomization procedures have been used in RCTs, but much less frequently than simple or restricted randomization:
* Covariate-adaptive randomization, of which one type is [[Minimisation (clinical trials)|minimization]]: The probability of being assigned to a group varies in order to minimize "covariate imbalance."<ref name="Lachin-1988b" /> Minimization is reported to have "supporters and detractors"<ref name="Schulz-2002" /> because only the first subject's group assignment is truly chosen at random, the method does not necessarily eliminate bias on unknown factors.<ref name="Moher-2010" />
* Response-adaptive randomization, also known as outcome-adaptive randomization: The probability of being assigned to a group increases if the responses of the prior patients in the group were favorable.<ref name="Lachin-1988b" /> Although arguments have been made that this approach is more ethical than other types of randomization when the probability that a treatment is effective or ineffective increases during the course of an RCT, ethicists have not yet studied the approach in detail.<ref name="Rosenberger-1993">{{Cite journal |vauthors=Rosenberger WF, Lachin JM |date=December 1993 |title=The use of response-adaptive designs in clinical trials |journal=Controlled Clinical Trials |volume=14 |issue=6 |pages=471–484 |doi=10.1016/0197-2456(93)90028-C |pmid=8119063}}</ref>