Editing Randomized controlled trial (section)

== Randomization ==
The advantages of proper [[randomized experiment|randomization]] in RCTs include:<ref name="SchulzGrimes2002">{{Cite journal |vauthors=Schulz KF, Grimes DA |date=February 2002 |title=Generation of allocation sequences in randomised trials: chance, not choice |journal=Lancet |volume=359 |issue=9305 |pages=515–519 |doi=10.1016/S0140-6736(02)07683-3 |pmid=11853818 |s2cid=291300}}{{dead link|date=December 2021|bot=medic}}{{cbignore|bot=medic}}</ref>
* "It eliminates bias in treatment assignment," specifically [[selection bias]] and [[confounding]].
* "It facilitates blinding (masking) of the identity of treatments from investigators, participants, and assessors."
* "It permits the use of probability theory to express the likelihood that any difference in outcome between treatment groups merely indicates chance."

There are two processes involved in randomizing patients to different interventions. First is choosing a ''randomization procedure'' to generate an unpredictable sequence of allocations; this may be a simple random assignment of patients to any of the groups at equal probabilities, may be "restricted", or may be "adaptive." A second and more practical issue is ''allocation concealment'', which refers to the stringent precautions taken to ensure that the group assignment of patients are not revealed prior to definitively allocating them to their respective groups. Non-random "systematic" methods of group assignment, such as alternating subjects between one group and the other, can cause "limitless contamination possibilities" and can cause a breach of allocation concealment.<ref name="Schulz-2002" />

However empirical evidence that adequate randomization changes outcomes relative to inadequate randomization has been difficult to detect.<ref name="Howick-2014">{{Cite journal |vauthors=Howick J, Mebius A |date=December 2014 |title=In search of justification for the unpredictability paradox |journal=Trials |volume=15 |page=480 |doi=10.1186/1745-6215-15-480 |pmc=4295227 |pmid=25490908 |doi-access=free}}</ref>

=== 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>

=== Allocation concealment ===
{{main|Allocation concealment}}
"Allocation concealment" (defined as "the procedure for protecting the randomization process so that the treatment to be allocated is not known before the patient is entered into the study") is important in RCTs.<ref name="Forder-2005">{{Cite journal |vauthors=Forder PM, Gebski VJ, Keech AC |date=January 2005 |title=Allocation concealment and blinding: when ignorance is bliss |journal=The Medical Journal of Australia |volume=182 |issue=2 |pages=87–89 |doi=10.5694/j.1326-5377.2005.tb06584.x |pmid=15651970 |s2cid=202149}}</ref> In practice, clinical investigators in RCTs often find it difficult to maintain impartiality. Stories abound of investigators holding up sealed envelopes to lights or ransacking offices to determine group assignments in order to dictate the assignment of their next patient.<ref name="Schulz-2002">{{Cite journal |vauthors=Schulz KF, Grimes DA |date=February 2002 |title=Allocation concealment in randomised trials: defending against deciphering |url=https://www.who.int/entity/rhl/LANCET_614-618.pdf |journal=Lancet |volume=359 |issue=9306 |pages=614–618 |doi=10.1016/S0140-6736(02)07750-4 |pmid=11867132 |s2cid=12902486 |archive-url=https://wayback.archive-it.org/all/20120911210240/http://www.who.int/entity/rhl/LANCET_614-618.pdf |archive-date=September 11, 2012}}</ref> Such practices introduce selection bias and [[Lurking variable|confounders]] (both of which should be minimized by randomization), possibly distorting the results of the study.<ref name="Schulz-2002" /> Adequate allocation concealment should defeat patients and investigators from discovering treatment allocation once a study is underway and after the study has concluded.  Treatment related side-effects or adverse events may be specific enough to reveal allocation to investigators or patients thereby introducing bias or influencing any subjective parameters collected by investigators or requested from subjects.{{cn|date=November 2023}}

Some standard methods of ensuring allocation concealment include sequentially numbered, opaque, sealed envelopes (SNOSE); sequentially numbered containers; pharmacy controlled randomization; and central randomization.<ref name="Schulz-2002" /> It is recommended that allocation concealment methods be included in an RCT's [[Clinical trial protocol|protocol]], and that the allocation concealment methods should be reported in detail in a publication of an RCT's results; however, a 2005 study determined that most RCTs have unclear allocation concealment in their protocols, in their publications, or both.<ref name="Pildal-2005">{{Cite journal |vauthors=Pildal J, Chan AW, Hróbjartsson A, Forfang E, Altman DG, Gøtzsche PC |date=May 2005 |title=Comparison of descriptions of allocation concealment in trial protocols and the published reports: cohort study |journal=BMJ |volume=330 |issue=7499 |page=1049 |doi=10.1136/bmj.38414.422650.8F |pmc=557221 |pmid=15817527}}</ref> On the other hand, a 2008 study of 146 [[meta-analysis|meta-analyses]] concluded that the results of RCTs with inadequate or unclear allocation concealment tended to be biased toward beneficial effects only if the RCTs' outcomes were [[Subjectivity|subjective]] as opposed to [[Objectivity (philosophy)|objective]].<ref name="Wood-2008">{{Cite journal |vauthors=Wood L, Egger M, Gluud LL, Schulz KF, Jüni P, Altman DG, Gluud C, Martin RM, Wood AJ, Sterne JA |date=March 2008 |title=Empirical evidence of bias in treatment effect estimates in controlled trials with different interventions and outcomes: meta-epidemiological study |journal=BMJ |volume=336 |issue=7644 |pages=601–605 |doi=10.1136/bmj.39465.451748.AD |pmc=2267990 |pmid=18316340}}</ref>

=== Sample size ===
{{Main|Sample size determination}}

The number of treatment units (subjects or groups of subjects) assigned to control and treatment groups, affects an RCT's reliability. If the effect of the treatment is small, the number of treatment units in either group may be insufficient for rejecting the null hypothesis in the respective [[statistical hypothesis testing|statistical test]]. The failure to reject the [[null hypothesis]] would imply that the treatment shows no statistically significant effect on the treated in a given test. But as the sample size increases, the same RCT may be able to demonstrate a significant effect of the treatment, even if this effect is small.<ref name="Glennerster-2013">{{Cite book |title=Running randomized evaluations: a practical guide |vauthors=Glennerster R, Kudzai T |date=2013 |publisher=Princeton University Press |isbn=978-0-691-15924-9 |location=Princeton |chapter="Chapter 6" |doi=10.2307/j.ctt4cgd52 |jstor=j.ctt4cgd52}}</ref>