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

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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) PAGE 56
CHAPTER 4 ST 520, A. TSIATIS and D. Zhang Disadvantages • The major disadvantage is that the number of patients assigned to the different treatments are random. Therefore, the possibility exists of severe treatment imbalance. – leads to less efficiency – appears awkward and may lead to loss of credibility in the results of the trial For example, with n = 20, an imbalance of 12:8 or worse can occur by chance with 50% probability even though π = .5. The problem is not as severe with larger samples. For instance if n = 100, then a 60:40 split or worse will occur by chance with 5% probability. 4.2.2 Permuted block randomization One way to address the problem of imbalance is to use blocked randomization or, more precisely, permuted block randomization. Before continuing, we must keep in mind that patients enter sequentially over time as they become available and eligible for a study. This is referred to as staggered entry. Also, we must realize that even with the best intentions to recruit a certain fixed number of patients, the actual number that end up in a clinical trial may deviate from the intended sample size. With these constraints in mind, the permuted block design is often used to achieve balance in treatment assignment. In such a design, as patients enter the study, we define a block consisting of a certain number and proportion of treatment assignments. Within each block, the order of treatments is randomly permuted. For illustration, suppose we have two treatments, A and ⎛B, and we choose a block size of 4, ⎜ with two A’s and two B’s. For each block of 4 there are ⎝ 4 ⎞ ⎟ ⎠ or 6 possible combinations of 2 treatment assignments. PAGE 57
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ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

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