The Approaches of Successful Sample Size Calculation

In an extract from our CROS Academy course: “Understanding Study Designs & Successful Sample Size Calculation”, we discuss the different approaches to sample size calculation and why it is an important statistical component in successful clinical trial methodology and strategy.

The target of drug development is to license a drug for a particular disease which is beneficial to all patients and bears a minimal risk on a patient’s health. That being said, the drug development cycle consists of a pre-clinical phase followed by Phases I through IV, and each phase has its own population characteristics and defined endpoints. The target populations are as follows:

  • Pre-clinical Phase: vitro- and animal testing to test for kinetics, toxicity and carcinogenicity
  • Phase I: Phase Ia looks for healthy volunteers, while Phase Ib looks for diseased patients with a sample size of approximately less than 10 per dose level to determine the highest possible dose with an “acceptable” rate of dose-limiting toxicity.
  • Phase II: Restricted diseased patient population with a sample size of approximately 30-100 per dose level to examine the preliminary evidence of efficacy
  • Phase III: Unrestricted diseased patient population with a sample size of over 100 in order to confirm efficacy
  • Phase IV/Post-market: Unrestricted diseased patient population with a wide variety of medical conditions; with a sample size of usually between 300-10,000 to monitor the safety of a drug once it is released on the market.

There are two approaches to sample size calculation: the precision-based approach and the power-based approach.

The precision-based approach estimates an unkown parameter with a certain precision. This approach limits the confidence interval of the parameter to a certain width.

In the power-based approach, the target is to reject a Null-hypothesis with certain error probabilities. This approach is related to hypothesis testing. The necessary assumptions provided include the level of significance and power, standard deviation, clinically relevant significance and effect size.

The power-based approach is also used for time-to-event data such as “survival” time (time) or “failure” and “censored” (event). In the case of time-to-event data, the Kaplain-Meier method estimates survival time and log-rank-test can be used where the sample size is calculated in two steps: determining the number of events needed, and then determining the number of patients needed.

It should be noted that that the following practical considerations have an effect on sample size:

  • Type I and Type II error
  • Variability of data
  • Effect size

The determination of sample size is critical in the planning and success of clinical trials, however sample size formulas exist for many situations. In complex situations, sample size can also be determined by simulation. Sample size calculation is always based on assumptions about real effect sizes and variation of the data, therefore it is important to get as realistic assumptions as possible. CROS NT biostatisticians recommend calculating sample size under different assumptions as well as in a conservative manner.

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