ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

CHAPTER 4 ST 520, A. TSIATIS and D. Zhang
4.2.1 Simple Randomization
For simplicity, let us start by assuming that patients will be assigned to one of two treatments
A or B. The methods we will describe will generalize easily to more than two treatments. In
a simple randomized trial, each participant that enters the trial is assigned treatment A or B
with probability π or 1 − π respectively, independent of everyone else. Thus, if n patients are
randomized with this scheme, the number of patients assigned treatment A is a random quantity
following a binomial distribution ∼ b(n, π).
This scheme is equivalent to flipping a coin (where the probability of a head is π) to determine
treatment assignment. Of course, the randomization is implemented with the aid of a computer
which generates random numbers uniformly from 0 to 1. Specifically, using the computer, a
sequence of random numbers are generated which are uniformly distributed between 0 and 1 and
independent of each other. Let us denote these by U1, . . .,Un where Ui are iid U[0, 1]. For the
i-th individual entering the study we would assign treatment as follows:
⎧
⎪⎨ Ui ≤ π then assign treatment A
If
⎪⎩ Ui > π then assign treatment B.
It is easy to see that P(Ui ≤ π) = π, which is the desired randomization probability for treatment
A. As we argued earlier, most often π is chosen as .5.
Advantages of simple randomization
• easy to implement
• virtually impossible for the investigators to guess what the next treatment assignment
will be. If the investigator could break the code, then he/she may be tempted to put
certain patients on preferred treatments thus invalidating the unbiasedness induced by the
randomization
• the properties of many statistical inferential procedures (tests and estimators) are established
under the simple randomization assumption (iid)
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