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In this chapter we describe methods for creating a randomization schedule for interventional studies. The definition, rationale, and importance of randomization are discussed in Chapter 20. Randomization is closely linked to the use of blinding, which is described in Chapters 22 and 23.
21.1 Requirements for a Valid Randomized Study
There are three basic requirements for a valid randomized study, as we discussed in Chapter 20. An additional requirement applies when the study is blinded (Chapter 22). Blinding, in which knowledge of the specific treatment is kept secret after enrollment, ideally from the participant and everyone working with the participant, is an important method for avoiding bias in a study, and should be used whenever possible. In this chapter we assume it will be a component of most randomized studies.
Requirement 1: There is a random process allocating the intervention. This implies that there must not be any pattern or structure in the randomization schedule (also called the “randomization table,” the “randomization list,” or the “treatment assignment list”). This means that assignment cannot be based on such things as day of birth, day of the week that individual entered the study, and the like. As mentioned in Chapter 20, although a given participant may chose to enter the study on a random day, this is not randomization.
Requirement 2: The process is under the direction of the investigator. This means that the investigator is responsible for how the allocation of one intervention or another to a participant is made – that is, how the randomization schedule is created. This does not mean that the investigator has access to the randomization schedule before or during the study.
Requirement 3: No one knows what the intervention for the next participant will be until the participant has completed all the screening and is enrolled in the study. When an individual is screened for eligibility for a study, the individuals making the decision on the participant’s eligibility must not know what intervention the person would receive if enrolled. This is true even if the study itself will not involve any blinding. This is why there cannot be any pattern in the treatment assignment schedule, as it could lead to manipulation in various ways. Knowledge of a pattern could result in the subconscious introduction of selection bias (Section 17.1.2).
Requirement 4: As an additional requirement in a blinded study, the randomization schedule must be kept secret from all the individuals involved in the study who are to be blinded. This gives another reason for not having a systematic component to treatment assignment. Sometimes it is necessary to break the blind for a specific participant, and if the assignment was systematic, breaking the blind for this participant could reveal the treatment for other, possibly all, participants in the study.
21.2 Creating a Randomization Schedule
In a study with randomization, participants actually have two distinct ID numbers. The first, which all participants have in all studies, is the Study ID number (Section 29.1). This is a number that is used on all the participant’s case report forms. This number is assigned when a participant is enrolled into the study (generally when the consent form is signed). Even participants that fail the screening criteria will usually have a Study ID number, as it is important to be able to account for screening failures when preparing the study for publication.
The second number is the randomization number, which is linked to an intervention. There are actually two separate lists that are needed. We use the term “list” since in theory it could be done on a piece of paper, but normally there would be two different computer files. One file contains the case report form that links the Study ID number with the randomization number. The second file would be the computer file linking the randomization number with the treatment group. Without this second computer file, the randomization number by itself cannot tell you the intervention a participant has received.
The following sections are written as if you, the investigator, are creating the randomization schedule. In practice, very often a statistician, a computer specialist, a pharmacist, or someone else in your institution who will not be working with the participants will create the schedule according to your needs.
Generally, you would make a sequential list of numbers for the randomization numbers. You generally create a list with many more numbers than you are actually likely to need for the study, in case a large number of participants drop out of the study and you need to recruit more participants than expected. Often sample size is determined for the number of participants completing a study, and then enrollment is adjusted for the expected dropout rate. If more participants drop out than you initially planned when designing the study, more participants will need to be recruited to have enough participants completing the study.
In a study of treatment of patients with COPD with one of two alternative therapies or a placebo, there are three treatment groups. The study design specifies 40 participants completing in each group. The investigators estimate that no more than 20% of the participants will drop out of the study, so if a total of 150 participants are enrolled, and 20% (30 participants) drop out before completing the study, then there would be 120 participants left, approximately 40 in each group, the number determined to be needed when the study was designed. In case the actual dropout rate is higher than 20%, however, the statistician creates a randomization list using blocking (see Section 21.3.2) for 200 people, to ensure that the randomization list is long enough to ensure that enough participants can be enrolled to get the target of 120 completing the study.
If you use strata (see Section 21.3.1), there would be a separate list, one for each stratum, and often the first number on the list would show the stratum. As an example, for a study of 200 participants in total, the list for stratum 1 would be numbers 1001–1200, the list for stratum 2 would be numbers 2001–2200, and so forth. If there are only 200 participants in total, obviously some of the randomization numbers will not be used. Most of the participants might come from a single stratum as in the second continuation of Example 21C at the end of Section 21.3.1.
You then need to create a list of treatment assignments. The simplest way to do this is to use a computer program to generate a list of random numbers that determine the intervention group. The first randomization number is assigned the intervention determined by the first random number, the second randomization number is assigned the intervention determined by the second random number, and so on. If stratification is used (see Section 21.3.1), then this process is done once for each of the stratum, so the treatment order will vary between different strata.
Since there were three equal-sized treatment groups, the statistician used a computer program to generate random numbers, with a uniform distribution from 0 to 3. A uniform distribution means that any number in the range is equally likely, so the chance of the next number being 2.000000 or 0.343629 is equal. If the number was between 0 and less than 1, the treatment was the control group; if the number was between 1 and less than 2, the treatment was the first experimental treatment; and if the number was between 2 and less than 3, the treatment was the second experimental treatment. These treatment assignments were assigned to the sequential list of randomization numbers.
As participants are enrolled in the study, they are assigned the next randomization number on the sequential list; if strata are used, the number is assigned from the list for the participant’s stratum. Once a randomization number has been assigned, it should not be used for any other participant. In some studies, a set of treatment materials for the entire study are prepared in advance for each participant so that if a participant begins treatment but then drops out, there will not be a complete set of treatments for that randomization number if it is used again. This is another reason that the sequential list contains many more randomization numbers than are specified in the study design as the total number needed for the study.
In a placebo-controlled study comparing drug treatment of depression, the participant is given a series of escalated doses over time until the maximum dosage is reached. Individual sets of the active drug or placebo are prepared by the manufacturer labeled according to the dosage schedule, and given to the investigator, identified by randomization number but not contents, so the study is blinded (see Section 23.1.1). If a participant drops out of the study after one week, he will have used part of the set for his randomization number.
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