The length K should be close to the actual number of true associations, but this is generally unknown. A range of lengths could be tested, with the most significant length used to select genes for follow-up analysis; but there is no formal basis for this strategy, and simulation studies show that it is capable of grossly over-or under-estimating the number of true associations [33]. A judicious choice of a fixed length, say K < 20 for a genome-wide association scan, is generally advisable provided that the tests are reasonably independent. When there is strong dependency between tests, such as in single-marker analysis of a dense genome-wide scan, then the variable-length approach can be used to establish statistical significance, but not to estimate the number of follow-up genes. Informally, genes would be followed up in rank order of significance; and if the prior power is high, this will tend to identify the true associations[32] In fact, formal adjustments based on the closure principle are available for individual tests, which allow strong control of FWER [34], but the primary use of truncated products is to show that the strongest associations indeed arise from true effects.
