Bayesian statistics in medical research: an intuitive alternative to conventional data analysis

Statistical analysis of both experimental and observational data is central to medical research. Unfortunately, the process of conventional statistica l analysis is poorly understood by many medical scientists. This is due, in part, to the counter-intuitive nature of the basic tools of traditional (f requency based) statistical inference. For example, the proper definition o f a conventional 95% confidence interval is quite confusing, It is based up on the imaginary results of a series of hypothetical repetitions of the dat a generation process and subsequent analysis. Not surprisingly, this formal definition is often ignored and a 95% confidence interval is widely taken to represent a range of values that is associated with a 95% probability of containing the true value of the parameter being estimated. Working within the traditional framework of frequency-based statistics, this interpretati on is fundamentally incorrect. It is perfectly valid, however, if one works within the framework of Bayesian statistics and assumes a 'prior distribut ion' that is uniform on the scale of the main outcome variable. This reflec ts a limited equivalence between conventional and Bayesian statistics that can be used to facilitate a simple Bayesian interpretation based on the res ults of a standard analysis. Such inferences provide direct and understanda ble answers to many important types of question in medical research. For ex ample, they can be used to assist decision making based upon studies with u navoidably low statistical power, where non-significant results are all too often, and wrongly, interpreted as implying ino effect'. They can also be used to overcome the confusion that can result when statistically significa nt effects are too small to be clinically relevant. This paper describes th e theoretical basis of the Bayesian-based approach and illustrates its appl ication with a practical example that investigates the prevalence of major cardiac defects in a cohort of children born using the assisted reproductio n technique known as ICSI (intracytoplasmic sperm injection).