title: Evidence for overdispersion in the distribution of malaria parasites and leukocytes in thick blood smears.
abstract: BACKGROUND
  Microscopic examination of stained thick blood smears (TBS) is the gold standard for routine malaria diagnosis. Parasites and leukocytes are counted in a predetermined number of high power fields (HPFs). Data on parasite and leukocyte counts per HPF are of broad scientific value. However, in published studies, most of the information on parasite density (PD) is presented as summary statistics (e.g. PD per microlitre, prevalence, absolute/assumed white blood cell counts), but original data sets are not readily available. Besides, the number of parasites and the number of leukocytes per HPF are assumed to be Poisson-distributed. However, count data rarely fit the restrictive assumptions of the Poisson distribution. The violation of these assumptions commonly results in overdispersion. The objectives of this paper are to investigate and handle overdispersion in field-collected data.
  
  
  METHODS
  The data comprise the records of three TBSs of 12-month-old children from a field study of Plasmodium falciparum malaria in Tori Bossito, Benin. All HPFs were examined systemically by visually scanning the film horizontally from edge to edge. The numbers of parasites and leukocytes per HPF were recorded and formed the first dataset on parasite and leukocyte counts per HPF. The full dataset is published in this study. Two sources of overdispersion in data are investigated: latent heterogeneity and spatial dependence. Unobserved heterogeneity in data is accounted for by considering more flexible models that allow for overdispersion. Of particular interest were the negative binomial model (NB) and mixture models. The dependent structure in data was modelled with hidden Markov models (HMMs).
  
  
  RESULTS
  The Poisson assumptions are inconsistent with parasite and leukocyte distributions per HPF. Among simple parametric models, the NB model is the closest to the unknown distribution that generates the data. On the basis of model selection criteria AIC and BIC, HMMs provided a better fit to data than mixtures. Ordinary pseudo-residuals confirmed the validity of HMMs.
  
  
  CONCLUSIONS
  Failure to take overdispersion into account in parasite and leukocyte counts may entail important misleading inferences when these data are related to other explanatory variables (malariometric or environmental). Its detection is therefore essential. In addition, an alternative PD estimation method that accounts for heterogeneity and spatial dependence should be seriously considered in epidemiological studies with field-collected parasite and leukocyte data.
authors.affiliation: , Laboratoire de Mathématiques Appliquées (MAP5) UMR CNRS 8145Université Paris Descartes, Paris, France. imen.hammami@parisdescartes.fr.
authors.forename: Imen
authors.initials: I
authors.lastname: Hammami
authors.forename: André
authors.initials: A
authors.lastname: Garcia
authors.forename: Grégory
authors.initials: G
authors.lastname: Nuel
mesh_terms: D001541:Benin; D001769:Blood / Q000469:parasitology*; D003951:Diagnostic Errors; D005260:Female; D006801:Humans; D007223:Infant; D007231:Infant, Newborn; D007958:Leukocyte Count / Q000379:methods*; D016778:Malaria, Falciparum / Q000175:diagnosis*; D008297:Male; D008853:Microscopy / Q000379:methods*; D015233:Models, Statistical; D059208:Parasite Load / Q000379:methods*; D018512:Parasitemia / Q000175:diagnosis*