The Principles of Experimental Design and the Determination of Sample Size When Using Animal Models of Traumatic Brain Injury

Abstract

There is a crisis in preclinical research involving laboratory animals. Too many experiments, in all disciplines, have been found to give results which turn out to be irreproducible. And, unfortunately, the results of clinical trials of potential treatments of traumatic brain injury (TBI), suggested by extensive animal research, have so far been disappointing. Faulty experimental design could be one of several possible causes. This chapter briefly covers the basic principles of experimental design, with emphasis on completely randomized, randomized block (cohort), and factorial designs. The determination of sample size is discussed together with some aspects of the statistical analysis and presentation of the results. The Standardized Effect Size (Cohen’s d) is introduced as a description of the magnitude of a response.

Appendix

An example of a possible protocol for testing a proposed treatment using a randomized block/cohort design. This could easily be modified to investigate different treatments or times.

The protocol might have two factors “Treatment” and “Time following treatment.”

Four treatments might be:

• 1. Sham

• 2. TBI + vehicle

• 3. TBI + Treatment-low dose

• 4. TBI + Treatment-high dose

The factor “Time” might have two levels, say 12 h and 48 h following the treatments.

Each block/cohort would therefore involve eight animals (4 treatments × 2 times post treatment).

Six of the rats in each block would have TBI and two would be shams. It is assumed that the treatments could be done conveniently in one day.

Various outcomes could be measured in the live animals including, say, a “neural sensitivity score,” and other types of behavior. It is assumed that all eight rats in a block could be measured in a relatively short period. Histological and anatomical outcomes would be made after the animals are euthanized at the two time points.

With, say, five blocks/cohorts the protocol would involve 40 animals. In this case the ANOVA table to be used for all the outcome variables such as behavior and brain water content would be as follows:

Source	DF
Blocks	4
Treatments	3
Times	1
Trt. × Time	3
Error	28
Total	39

In the absence of a Treatment × Time interaction sample sizes for comparing the four groups will be n = 10. If a power analysis justification is needed for that sample size, the SES for a sample size of 10 can be looked in Table 3. It is 1.53 SDs. This is the predicted detectable effect size in units of standard deviations. So multiplied by the SD of a character, it predicts the effect size in original units that the experiment will be able to detect for a 90% power and a 5% significance level. The sample size for comparing the times will be N = 20. This with 28 degrees of freedom in the error term will provide plenty of power. If a Treatment × Time interaction is detected it implies that the observed treatment differences are not equally valid at the two time points. An experiment like this one is really much more powerful than suggested by these sample sizes because there is a much better estimate of the error (28 DF) which is above the suggested maximum using the Resource Equation method.