Stereology is the science that uses geometric probability to extract the internal quantitative properties of a three dimensional object based on lower dimensional information. It is a valuable research tool in biological science and relies heavily on statistical principles. In this dissertation, we focus on studies that examine the number of neurons in a brain region of interest using stereological techniques in order to compare subjects in different diagnostic groups, e.g., subjects with schizophrenia and control subjects. A large number of counting frames are usually used to obtain a prespecified precision for an individual in these kinds of studies. Typically, researchers determine the number of counting frames for each individual by controlling the coefficient of error for the individual. However, the researchers from the Conte Center for the Neuroscience of Mental Disorders (CCNMD) at University of Pittsburgh primarily focus on comparing biomarkers among different diagnosis groups rather than evaluating individuals. A design goal for such stereological studies is to keep study cost within budget and time constraints, while maintaining sufficient statistical power to address the research aims. Statistical power can be increased by either adding more subjects or more counting frames. And the cost of a study can be approximated by a linear combination of the number of subjects and number of counting frames. To address this need, we have developed new technologies that enable researchers to design a cost efficient study balancing the number of subjects with the number of counting frames for each subject.

We also develop adaptive designs to conduct stereological studies. Adaptive designs allow the opportunity to look at the data at an interim stage, and to modify the design based on the information obtained from the first stage data. In our adaptive design, we estimate the stereological variance without breaking the blind of the Stage I data, and re-design the second stage based on the stereological variance estimator obtained from the first stage. Based on our procedure, we show researchers can cost-effectively modify the design while maintaining the desired study power.