Open AccessLarge and finite sample properties of a maximum-likelihood estimator for multiplicity of infection
Author(s) -
Kristan A. Schneider
Publication year - 2018
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0194148
Subject(s) - sample size determination , estimator , statistics , sample variance , mathematics , sample (material) , minimum variance unbiased estimator , bias of an estimator , restricted maximum likelihood , upper and lower bounds , multiplicity of infection , consistency (knowledge bases) , estimation theory , variance (accounting) , algorithm , computer science , biology , physics , discrete mathematics , mathematical analysis , genetics , accounting , business , cell culture , thermodynamics
Reliable measures of transmission intensities can be incorporated into metrics for monitoring disease-control interventions. Genetic (molecular) measures like multiplicity of infection (MOI) have several advantages compared with traditional measures, e.g., R 0 . Here, we investigate the properties of a maximum-likelihood approach to estimate MOI and pathogen-lineage frequencies. By verifying regulatory conditions, we prove asymptotical unbiasedness, consistency and efficiency of the estimator. Finite sample properties concerning bias and variance are evaluated over a comprehensive parameter range by a systematic simulation study. Moreover, the estimator’s sensitivity to model violations is studied. The estimator performs well for realistic sample sizes and parameter ranges. In particular, the lineage-frequency estimates are almost unbiased independently of sample size. The MOI estimate’s bias vanishes with increasing sample size, but might be substantial if sample size is too small. The estimator’s variance matrix agrees well with the Cramér-Rao lower bound, even for small sample size. The numerical and analytical results of this study can be used for study design. This is exemplified by a malaria data set from Venezuela. It is shown how the results can be used to determine the necessary sample size to achieve certain performance goals. An implementation of the likelihood method and a simulation algorithm for study design, implemented as an R script, is available as S1 File alongside a documentation (S2 File) and example data (S3 File).