Statistical analysis of experimental designs applied to biological assays

Bioassays are methods employed to estimate the effect of a given substance in living matter, and therefore they are frequently used in the pharmaceutical industry. The experimental design of bioassays has to take into account the intrinsic variability in the biological test units and other factors as operators, day variation, batch variation, etc. Thus, statistical models employed to analyse bioassays include both fixed and random effects. The sample size estimation in mixed models is a complicated issue and no general formulas can be applied. An alternative approach to estimate the sample size to obtain a certain estimate with a confidence interval of a specific width is to perform computer simulations. In this thesis, simulations are performed to calculate the confidence interval of the logarithm of the effect of the test relative to the standard as a function of the number of replicates. The simulated data is compared with experimental data. The results obtained with the simulations agree well with the experimental ones. Furthermore, the method discussed here can also be used to analyse other experimental designs in which the size of the main sources of data variability are known.