title: Towards eliminating bias in cluster analysis of TB genotyped data.
abstract: The relative contributions of transmission and reactivation of latent infection to TB cases observed clinically has been reported in many situations, but always with some uncertainty. Genotyped data from TB organisms obtained from patients have been used as the basis for heuristic distinctions between circulating (clustered strains) and reactivated infections (unclustered strains). Naïve methods previously applied to the analysis of such data are known to provide biased estimates of the proportion of unclustered cases. The hypergeometric distribution, which generates probabilities of observing clusters of a given size as realized clusters of all possible sizes, is analyzed in this paper to yield a formal estimator for genotype cluster sizes. Subtle aspects of numerical stability, bias, and variance are explored. This formal estimator is seen to be stable with respect to the epidemiologically interesting properties of the cluster size distribution (the number of clusters and the number of singletons) though it does not yield satisfactory estimates of the number of clusters of larger sizes. The problem that even complete coverage of genotyping, in a practical sampling frame, will only provide a partial view of the actual transmission network remains to be explored.
authors.affiliation: The South African Department of Science and Technology/National Research Foundation (DST/NRF) Centre of Excellence in Epidemiological Modelling and Analysis, Faculty of Science, University of Stellenbosch, Stellenbosch, South Africa. carivs@sun.ac.za
authors.forename: Cari
authors.initials: C
authors.lastname: van Schalkwyk
authors.forename: Madeleine
authors.initials: M
authors.lastname: Cule
authors.forename: Alex
authors.initials: A
authors.lastname: Welte
authors.forename: Paul
authors.initials: P
authors.lastname: van Helden
authors.forename: Gian
authors.initials: G
authors.lastname: van der Spuy
authors.forename: Pieter
authors.initials: P
authors.lastname: Uys
mesh_terms: D000465:Algorithms; D015982:Bias; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D016208:Databases, Factual; D024881:Drug Resistance, Bacterial / Q000235:genetics; D004813:Epidemiology; D005838:Genotype; D006801:Humans; D015233:Models, Statistical; D017720:Molecular Epidemiology; D009169:Mycobacterium tuberculosis / Q000235:genetics; D011336:Probability; D015203:Reproducibility of Results; D014376:Tuberculosis / Q000453:epidemiology* / Q000235:genetics / Q000382:microbiology* / Q000635:transmission