Log-linear, logistic model fitting and local score statistics for cluster detection with covariate adjustments.

The standard method for p-value computation of spatial scan statistics, with adjustments for covariate effects, is to conduct Monte Carlo simulations with these effects estimated under the null hypothesis of no clustering. However when the covariates are geographically unbalanced, the proposed Monte Carlo p-value estimates are too conservative, with corresponding loss of power, due to excessive adjustments for confounding between covariates and location. We show that the use of an alternative procedure that involves local score statistics, with parameters fitted on a log-linear or logistic model, addresses this problem. We also discuss extensions of the procedure when there are multiple or continuous covariates.

Importance sampling of word patterns in DNA and protein sequences.

Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern is too short for the application of asymptotic formulae. Naive direct Monte Carlo is undesirable for the estimation of small probabilities because the associated rare events of interest are seldom generated. We propose instead efficient importance sampling algorithms that use controlled insertion of the desired word patterns on randomly generated sequences. The implementation is illustrated on word patterns of biological interest: palindromes and inverted repeats, patterns arising from position-specific weight matrices (PSWMs), and co-occurrences of pairs of motifs.