Elsevier

Controlled Clinical Trials

Volume 9, Issue 4, December 1988, Pages 312-326
Controlled Clinical Trials

Properties of simple randomization in clinical trials

https://doi.org/10.1016/0197-2456(88)90046-3Get rights and content

Abstract

This article presents the properties of complete randomization (e.g., coin toss) and of the random allocation rule (random permutation of n/2 of n elements). The latter is principally used in cases where the total sample size n is known exactly a priori. The likelihood of treatment imbalances is readily computed and is shown to be negligible for large trials (n > 200), regardless of whether a stratified randomization is used. It is shown that substantial treatment imbalances are extremely unlikely in large trials, and therefore there is likely to be no substantial effect on power.

The large-sample permutational distribution of the family of linear rank tests is presented for complete randomization unconditionally and conditionally, and for the random allocation rule. Asymptotically the three are equivalent to the distribution of these tests under a sampling-based population model. Permutation tests are also presented for a stratified analysis within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for analysis when some patients' responses are assumed to be missing-at-random.

Using the Blackwell-Hodges model, it is shown that complete randomization eliminates the potential for selection bias, but that the random allocation rule yields a substantial potential for selection bias in an unmasked trial. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimate of treatment effect due to covariate imbalance. Asymptotically, this probability approaches zero for complete randomization and for the random allocation rule. However, for finite n, complete randomization minimizes the probability of accidental bias, whereas this probability is slightly higher with a random allocation rule.

It is concluded that complete randomization has merit in large clinical trials.

References (11)

There are more references available in the full text version of this article.

Cited by (129)

  • Designing and testing treatments for alcohol use disorder

    2024, International Review of Neurobiology
  • Improving evaluations of advanced robots by depicting them in harmful situations

    2023, Computers in Human Behavior
    Citation Excerpt :

    Moreover, in both experiments, there were at least 93 participants assigned to each condition. This is a lot more than the required number to make sure that randomization is successful so that individual differences do not differ systematically between conditions—not only in a liberal (Mittring, 2004) but also in a more conservative reading (Elliott et al., 2007; Lachin, 1988). Of course, diverse samples from different cultures, age ranges, and educational backgrounds will be all but needed to establish generalizability for the findings at hand.

  • Incomparability of treatment groups is often blindly ignored in randomised controlled trials – a post hoc analysis of baseline characteristic tables

    2021, Journal of Clinical Epidemiology
    Citation Excerpt :

    In other words, the chance of comparability increases with the trial sample size, or conversely, the risk of imbalance turns greater in smaller trials [10]. Strong imbalance (incomparability) of important prognostic variables, even though caused by mere chance, can be responsible for substantial discrepancy between the estimate and the true value of treatment effect – this divergence being sometimes termed “accidental bias”, [9], or “estimation error”. [4]. It is clear that strong imbalance of prognostic variables should not be ignored [11,12] (methods for correction have been described elsewhere, e.g. analysis of covariance. [13])

View all citing articles on Scopus
View full text