## Archive for May, 2011

## It’s A Math, Math World (Power/Smpl Size I)

In this post, we will examine type I and type II errors and their relation to sample size and power calculations.

We start with a few definitions:

In a clinical trial, there are 2 types of error that we want to control for:

- Type I error (False Positive or Consumer’s Risk):
**This is a decision that finds that the new treatment works better when in fact it really does not.**

This error rare is controlled by FDA or other regulatory agencies. Depending on setting, α = 0.05, 0.01 or 0.001 might be required.

- Type II error (False Negative or Producer’s Risk):
**This is a decision that fails to find that the treatment works better when in fact it does.**

This error rate is controlled more by the company. They have more say in setting this rate, but an irresponsible type II error rate will adversely influence drug approval. For research, a type II error β = 0.20 is usually adequate.

Power = 1 – Type II Error: **The chance to detect a difference when one exists**.

If there is no bias, then the quality of the study is directly proportional to the sample size.

- If you have more subjects, then the smaller the error of the estimates and the better the type I and type II errors.
- IF sample size is too small, then, given type I error is maintained, effective therapy may not be discovered.
- If sample size is too large, then the study is too expensive and difficult to be done.

**MAIN IDEA:**

It is important to either:

- Find the minimum sample size to obtain a specified power.
- Determine the specific power for a given sample size.

**However there are many formulas for power and sample size for different:**

**Outcome types:**

- Continuous
- Proportions
- Survival data

**Trial purpose:**

- Superiority vs. Non-equivalency

**Design of Trial:**

- Matched vs. unmatched study
- Cluster vs. independent sampling
- Adjusted for covariates vs. unadjusted analysis

Next time, we will look at specific examples of power calculations.

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