Statistical Considerations in Food Safety Determination

The process of establishing the safety of food products, especially infant formulas, is complex and requires empirical evidence from many disciplines. Each step in the process requires the application of the highest standards, whether using methods of bioassay, nutritional analysis, or basic chemistry. Eventually studies involving human subjects (particularly in the case of infants) must be conducted in order to demonstrate the product s safety for the human consumer. Studies involving humans are almost always conducted as randomized clinical trials and standard methods of design and analysis are followed. 

The most typical analytical approach to interpreting the data from scientific studies, including clinical trials, is the statistical significance test, also known as the null hypothesis significance test (NHST). This approach, which has recently come under much scrutiny and debate, formally 

a set of two mutually exclusive alternative conditions is specified. For example, the addition of substance X to an infant formula either (a) hinders the ability of the infant to maintain proper physical growth, or (b) it does not hinder proper physical growth. Second, a set of risk probabilities are specified (the alpha level of the test and the power of the test), which allows the researcher to control the probabilities of drawing an incorrect inference. Third, a set of assumptions is specified that, taken together with the null and alternative hypotheses, allow the complete specification of the behavior of some statistical index. 

From this model one can specify a set of decision rules to draw some conclusions based on the empirical results of the experiment. The result of such a statistical test procedure does not establish with certainty the true state of nature, but rather it expresses a degree of confidence that one of the two states is not likely to occur. The randomized clinical trial and associated NHST are the mainstays of certain safety and efficacy approaches, such as the FDA drug trials described later, but they have certain potential limitations in their application to the safety of ingredients new to infant formulas. 

The first limitation is that NHST lacks a certain degree of direct applicability. The basic concept underlying the safety of an ingredient added to infant formulas is the reasonable certainty of no harm concept without a requirement for the demonstration of benefit. NHST, however, is generally formulated to demonstrate the superiority of one condition versus another. The fundamental idea in the formulation of reasonable certainty of no harm is one of equivalence, not of difference. While one can manipulate the null and alternative hypothesis in this circumstance (e.g., to make the no difference condition the alternative hypothesis), the resulting formulation is awkward and shifts the probabilistic control of the important error rate to that of power rather than to the more direct alpha level of the resulting test. Due to its highly unusual nature, it is likely that this test s results will not be properly understood and interpreted. 

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