9.1. Introduction
Randomization, an allocation of subjects to treatment regimens using a random element, is an essential component of clinical trials. Randomization promotes comparability of the treatment groups with respect to known as well as unknown covariates and thus reduces the chance for bias in the evaluation of the treatment effect. It can also serve as a basis for a randomization approach to inference (Rosenberger and Lachin, 2002).
Several types of bias are considered in the context of randomization. Selection bias occurs in an unmasked (unblinded) trial when the investigator, either consciously or otherwise, uses knowledge of the upcoming treatment assignment to help decide whom to enroll (Blackwell and Hodges, 1957). Observer bias is the bias in the evaluation of responses to a treatment that can occur if some of the assignments are known to the investigator. Imbalance in a covariate strongly associated with the study outcome can also bias the results. Although it is possible to adjust for known covariates, imbalance in unobserved covariates can lead to accidental bias (Efron, 1971). Various allocation procedures differ in how susceptible they are to these types of bias and that influences the choice of an allocation procedure for a clinical trial. Another consideration that needs to be taken into account when selecting an allocation procedure is its ability to achieve a targeted allocation ratio.
Complete randomization, in which each subject is allocated at random with the probability determined by the targeted allocation ratio, is totally unpredictable and does not lead to selection bias in a trial unmasked to the investigator. Its significant drawback, though, is the risk of undesirable imbalance in the number of subjects allocated to each arm. Such imbalance can negatively affect the power of treatment comparisons, especially when the total number of subjects in the trial is small. Also, if the subjects' prognostic factors exhibit a time trend during the course of the trial, a considerable imbalance in treatment assignments throughout the trial can lead to accidental bias. Restricted randomization implemented through a permuted block design (Rosenberger and Lachin, 2002) provides a good balance in the treatment assignments throughout the enrollment and is more commonly used. Other designs that maintain a good balance in treatment assignments at any time and have low potential for selection bias have recently been suggested (Berger et al, 2003).
After an appropriate randomization procedure is selected, the sequence of random assignments for the study subjects is generated and documented in the randomization (allocation) schedule.
It might be desirable to maintain balance in important prognostic baseline covariates. Balance is typically achieved through stratified randomization, in which a separate restricted allocation schedule is prepared for each combination of levels of the stratification factors. Alternatively, balance in baseline covariates can be maintained with a dynamic allocation, in which a new subject is assigned to the treatment group that results in the best balance (in some sense) across his or her set of covariates. A fixed allocation schedule cannot be prepared for dynamic procedures, as the sequence of treatment assignments depends on the covariates of the subjects entering the trial.
The randomization schedule or a sequence of treatment assignments for a dynamic allocation procedure can be easily generated with SAS software, e.g., using PLAN procedure or random number generators. The flexibility of PLAN often allows the same schedule to be generated in many different ways; we will cover a variety of options in the examples throughout this chapter.
To save space, some SAS code has been shortened and some output is not shown. The complete SAS code and data sets used in this book are available on the book's companion Web site at http://support.sas.com/publishing/bbu/companion_site/60622.html.