The distribution of the paternity index as a basis for evaluation of sequential testing in paternity analysis

Several procedures for evaluation of paternity testing data have been suggested in the literature, the majority of them being based on the paternity index statistic (L) or some transform of it. A major problem has been that the true distribution of the paternity index has not been known, making it difficult to perform quantitative evaluations of different procedures. We present an algorithm for computation of the distribution of the paternity index within the limits of a completely controlled amount of approximation. Using this algorithm we evaluate the power and the rate of erroneous classifications of a standard routine test based on a fixed number of genetic marker systems. The efficiency of this standard test procedure is compared to a stepwise (sequential) procedure where in each step one or several marker systems are scored for the mother-child-putative father trio. We suggest that a sequential strategy for testing may be more efficient than one that is based on a fixed number of systems. A sequential procedure can provide information about the accused man's state of paternity in a considerably larger fraction of cases without a substantial increase of the frequency of incorrect classifications. In addition, the cost measured as the average number of marker systems that has to be tested for each trio may be lower in the case of sequential testing than with a fixed number of systems.