## Archive for February, 2011

## It’s A Math, Math World (Randomization)

Some of the information in this article (i.e. some definitions and examples) is attributed to a lecture at Rutgers University by Adele Gilpin during the spring 2004 semester.

In a clinical trial, we want to help control for bias and variance. To accomplish this, we want to make our treatment and control groups as *comparable* or similar as possible on certain characteristics which are pre-defined. The way we will do this is to **randomize **which patient is assigned to which treatment group. This helps accomplish 3 things:

1. Provides study groups with known statistical properties at baseline

2. Provides a statistical basis for tests of significance

3. Eliminates Selection bias

**Randomization is the process of assigning patients to treatment groups in which there is a known unbiased probability for each outcome of assignment**. The randomization method must be both *reproducible* and *well documented* for the regulatory authorities. This means you can’t flip a coin to perform the randomization since a sequence of coin flips is not reproducible and the coin could be biased. This randomization is done using a computer generated sequence of random numbers as we shall see later.

Other properties of a good randomization scheme include:

1. Release of patient assignments prevented until necessary conditions are satisfied

2. Assignments masked to all involved parties until no longer needed

3. Future assignments not predictable from past assignments (not true for blocked designs)

4. Clear audit trail for assignments

Randomization helps protect against selection bias in the assignment process, however it *does not* *ensure* comparable study groups. They can still differ by chance. Another popular misconception is that “random” numbers are random. If you generate random numbers by computer, you start with a “seed” number. If you use the same seed in the same process, you will get the same string of numbers every time. This is why it is reproducible.

An example of a simple computer randomization scheme:

**Generate random uniform U (0,1) numbers X _{i}**

**If: X _{i} > 0.5 then subject gets treatment A**

** X _{i }<0.5 then subject gets treatment B**

The treatment assignment ratio (or allocation ratio) is the ratio of the number of persons to be in one treatment group relative to another.

**Ex**. a ratio of 1:1 indicates a treatment group and control group of equal numbers of participants

**Ex**. a ratio of 1:1:1:1:2.5 indicates 4 treatment groups of equal size and a control group that has 2.5 as many people assigned to it than any of the treatment groups.

Randomization can cause an imbalance in the group sizes if left to its own devices. There are ways to compensate for this. One way is to use *blocking*. Blocking is used to maintain balance in treatment assignments over time as recruitment progresses. This will be discussed in the next blog post.

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