Why is it important to randomly assign the order of the treatments for the subjects?

Confounding

Many factors can influence whether or not a subject will develop an outcome of interest. As a simple example, consider a study with the goal of determining whether physical activity reduces the risk of heart disease. An overly simplistic approach would be to enroll a cohort of subjects without pre-existing heart disease and divide them into exposure groups based on their activity level at the time of enrollment. They could then be followed longitudinally in order to measure and compare the incidence of heart disease in each group. Both groups would likely have subjects with a range of ages, but the 'active' group would probably have a somewhat younger age distribution than the inactive group, because younger people tend to be more active than older people. The problem, of course, is that age is also an independent risk factor for developing heart disease, so we wouldn't be evaluating just the effect of activity. The "risk" in each group is measured as their cumulative incidence of heart disease, but the risk ratio or risk difference that we measure is really going to reflect the sum total of all differences between the groups that influence their probability of developing heart disease. This would include not only differences in age, but also differences in a host of known (and yet to be discovered) risk factors such as smoking, gender, body mass index, blood pressure, family history, medications used, etc. All of these are factors that influence the risk of heart disease, and they confound our estimation of the association between activity and heart disease.

Confounding distorts the measure of association that is our main concern; in the example above, it is the association between activity and heart disease. However, all of these 'other risk factors' can distort the measure of association we are interested in if they are unevenly distributed among the groups we are comparing. The primary advantage to randomized clinical trials is that random assignment of a sufficiently large number of subjects tends to result in similar distributions of all other factors, including factors unknown to us, among the groups. If the groups have the same distributions of all of these other risk factors at baseline (i.e., the beginning of the trial) then they will not distort our estimate of effect (measure of association).

Methods of Assignment

The distinguishing feature of an intervention study is that the investigators assign subjects to a treatment (or "exposure") in order to establish actively treated groups of subjects and a comparison group. There are several means of assigning exposure for the purposes of comparison, many of which do not, in fact, randomly assign subjects to different groups or have too few subjects to rely on the randomization process to balance factors between groups.

• Historical comparison group: One can simply compare results with an intervention to an historical control group. For example, vascular surgeons at Boston Medical Center wanted to test the efficacy of a "critical pathway," a protocol for patient management after surgery for atherosclerotic occlusions in the arteries in the leg. They compared 67 consecutively treated patients before institution of the pathway with care of 69 consecutively treated patients with the critical pathway in place. This is a convenient method when there is a sudden shift in treatment or management that is applied to all patients, but the limitation of this approach is an inability to control for confounding factors.
• Non-random assignment: Non-random assignment methods such as alternate patients or alternate days of the week are not optimal because they are predictable and can be exploited by caretakers either consciously or unconsciously. This may lead to biased assignment.
• Randomization: Randomized assignment means that all subjects have an equal chance of being allocated to any of the available treatment options. To be effective, It must be done by a method that is unpredictable. One can use published tables of random numbers and simply assign subjects based on the next number listed on the table, or one can use a random number generated by a computer, such as the random number function in Excel. The Epi_Tools application has a worksheet that allows you to specify the number of study groups and then enter a "seed" number that triggers the generation of a random number that specifies which treatment group a subject should be assigned to. The unpredictability means that, if a sufficiently large number of subjects are randomly assigned to treatment groups, the groups will have similar distributions of all characteristics. As a result both known and unknown confounders will tend to be equally distributed among the study groups. By avoiding an imbalance in other risk factors, the estimate of association is less likely to be influenced by confounding. However, in order to ensure baseline comparability of the groups, the sample size must be sufficiently large. The other advantage to assigning subjects to treatment groups by a random method is that it avoids the potential for bias in assignment. Thus, two major advantages to random allocation to treatment groups (randomization) are:

1. Control of confounding by producing baseline comparability of the groups with respect to all other factors that might influence the outcome
2. Unbiased assignment to treatment groups.

Importantly, it is the number of units randomized, not the number of people, that determine whether randomization is likely to work. If the study is an individual trial, then the number of subjects equal the number of units. However, in a group-randomized trial, the number of units is smaller than the number of individuals in the trial. For example, in the trial of peer counseling for smokers in public housing, entire public housing developments were assigned to either the intervention or control arm, so that every participant at a particular development received the same treatment. Twenty developments were randomized. The likelihood that the 10 developments in each arm were balanced on potential confounding factors was the same as if the study consisted of 20 individuals (or the same as the likelihood that flipping a coin 20 times would produce a balanced number of heads and tails), even though there were 500 individuals in the study. In the fluoride trial described previously, even though tens of thousands of people were involved, there were only two cities, and randomization can never balance confounders between two units, whether they are individuals or groups. However, in both these cases, random assignment did avoid the possibility that the investigators would consciously or unconsciously assign the groups based on their feeling about what would be most likely to produce a result consistent with their hypothesis.

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