Randomized Block Design vs Completely Randomized Design

A randomized block design differs from a completely randomized design by ensuring that an important predictor of the outcome is evenly distributed between study groups in order to force them to be balanced, something that a completely randomized design cannot guarantee.

A Completely randomized design uses simple randomization to assign participants to different treatment options (in general, a treatment group and a control group).

Simple randomization however, is subject to error due to chance, and therefore does not guarantee equality of study groups regarding each and every participant characteristic (for a detailed discussion, see my other article: Purpose and Limitations of Random Assignment).

A randomized block design groups participants who share a certain characteristic together to form blocks, and then the treatment options get randomly assigned within each block.

The objective is to make the study groups comparable by eliminating an alternative explanation of the outcome (i.e. the effect of unequally distributing the blocking variable), therefore reducing bias.

When is randomized block design better?

When working with a small sample size

With small sample sizes, using simple randomization alone can produce, just by chance, unbalanced groups regarding the patients’ initial characteristics. In these cases, manually reducing variability between groups by using a randomized block design will offer a gain in statistical power and precision compared to a completely randomized design.

When is completely randomized design better?

When pre-randomization measurements are impractical:

Randomized block design requires that the blocking variable be known and measured before randomization, something that can be impractical or impossible especially when the blocking variable is hard to measure or control.

When group equality requires blocking on a large number of variables:

In order to force equality between the study groups regarding multiple variables, we need to block on all of them. The number of subgroups created will be the product of the number of categories in each of these variables.

For example:

If we want to block on gender (2 categories: males and females) and smoking (3 categories: smoker, ex-smoker, and non-smoker), we will have to create 2 × 3 = 6 subgroups.

So, as the number of blocking variables increases, the number of subgroups created increases, approaching the sample size — i.e. the number of participants in each subgroup would be very low — creating a problem for the randomized block design.

When working with a large sample size

The larger the sample of participants, the more likely it would be for simple randomization to produce equal groups. Therefore, when working with larges sample sizes (generally > 1000), a block randomization is not needed.

When the role of the blocking variable is not completely understood:

Blocking on some variable cannot be undone. This can cause a problem if, for example, it happens that after running the experiment, it turns out that the blocking variable is less important than we actually thought.

References

• Friedman LM, Furberg CD, DeMets DL, Reboussin DM, Granger CB. Fundamentals of Clinical Trials. 5th edition. Springer; 2015.
• Hulley SB, Cummings SR, Browner WS, Grady DG, Newman TB. Designing Clinical Research. 4th edition. LWW; 2013.