Electronic Thesis and Dissertation Repository


Master of Science


Epidemiology and Biostatistics


Dr. Guangyong Zou


Introduction: Measurement errors can seriously affect quality of clinical practice and medical research. It is therefore important to assess such errors by conduct- ing studies to estimate a coefficients reliability and assessing its precision. The intraclass correlation coefficient (ICC), defined on a model that an observation is a sum of information and random error, has been widely used to quantify reliability for continuous measurements. Sample formulas have been derived for explicitly incorporation of a prespecified probability of achieving the prespecified precision, i.e., the width or lower limit of a confidence interval for ICC. Although the concept of ICC is applicable to binary outcomes, existed sample size formulas for this case can only provide about 50% assurance probability to achieve the desired precision.

Methods: A common correlation model was adopted to characterize binary data arising from reliability studies. A large sample variance estimator for ICC was derived, which was then used to obtain an asymmetric confidence interval for ICC by the modified Wald method. Two sample size formulas were derived, one for achieving a prespecified confidence interval width and the other for requiring a prespecified lower confidence limit, both with given assurance probabilities. The accuracy of the formulas was evaluated using numerical studies. The utility of the formulas was assessed using example studies.

Results: Closed-form formulas were obtained. Numerical study results demon- strated that these formulas are fairly accurate in a wide range of scenarios. The examples showed that the formulas are simple to use in design reliability studies with binary outcomes.

Discussion: The formulas should be useful in the planning stage of a reliability study with binary outcomes in which the investigator wishes to obtain an estimate of ICC with prespecified precision in terms of width or lower limit of a confidence interval. It is no longer justified to conduct reliability studies on the basis of sub-optimal formulas that provide only 50% assurance probability.