| Abstract: | This study used the technique of waiting time modeling to analyze the combined effects of temperature, pH, carbohydrate, protein, and lipid on the time-to-toxicity of Clostridium botulinum 56A. Waiting time models can be used whenever the time to the occurrence of some event is the variable of interest. In the case of the time-to-toxicity data, the variable is the time from the beginning of an experiment until a tube is identified as positive. The statistical analysis used the SAS procedure LIFEREG and included determination of the form of the response surface, identification of the error distribution, and simplification of the response surface. We found that increasing the macromolecule concentration decreased the probability of toxin formation. The probability of toxin formation also decreased at lower temperatures and at pHs further from the optimum. The waiting time modeling approach to developing models for botulinal toxin formation compared favorably with other approaches but had one specific advantage. Waiting time models have the inherent advantage that safety concerns regarding predictions are automatically quantified in the analysis by formally identifying a distribution of times-to-toxicity. The use of this time-to-toxicity distribution permits a customizable margin of safety (e.g., one in a million) not possible with other approaches. |
