Keywords: Mixture models, grouped data
In a study of the effect of ticks on cattle in North Queensland, the disease status of animals exposed to the tick-borne parasite Anaplasma marginale is of some concern. A symptom of infection from this parasite, the number of red blood cells can be redu ced by up to 80% at the point of peak anaemia. The problem to be considered here concerns a way of quantifying the change in red blood cell populations during the recovery stages of the disease.
In a laboratory trial, cows were inoculated with the parasite and their red blood cells monitored before and after inoculation. The data collected were in the form of red cell volume distributions obtained from a Coulter counter, truncated and sorted into groups. In work as yet unpublished, McLaren et al. have addressed the problem of fitting distributions to similar data from humans suffering myelodysplastic anaemia, and McLaren (private communication) has suggested the need to develop hypothesis testing procedures for this type of data.
The observed counts of red cell volume from one of the cows on days 21 (Freq1) and 23 (Freq2) after inoculation are listed. The counts are grouped into 18 intervals of equal width of 7.2 fl. The first column (Group) lists the group number, the second (Vol) lists the truncated lower endpoint of the cell volume interval. The lower and upper truncation values for these red cell volume counts were 21.6 fl and 151.2 fl respectively. A cursory inspection of the two sets of observed frequency counts in histogram form on the logarithmic scale suggest that the red blood cell volume distribution is bimodal, at least at 21 days after inoculation.
Data file (tab-delimited text)
|McLachlan, G.J., and Jones, P.N. (1988). Fitting Mixture Models to Grouped and Truncated Data via the EM Algorithm, Biometrics, 44, 571-578|