Analysis of the volume of red blood cells: application of the expectation-maximization algorithm to grouped data from the doubly-truncated lognormal distribution.

In accordance with general principles recommended by the International Committee for Standardization in Haematology (1982, Journal of Clinical Pathology 35, 1320-1322), we have developed statistical methods for the analysis of red cell volume distributions. To select an appropriate reference distribution for goodness-of-fit testing, we derived a mathematical model of erythropoiesis that predicted a lognormal form for the distribution of erythrocyte volumes. Model predictions were then tested using samples obtained from 50 healthy individuals. Each grouped red cell volume distribution was doubly-truncated to eliminate artifactual frequency counts. Distribution parameter estimates were computed using the expectation-maximization algorithm, a missing information technique. Results of the one-sample chi-square goodness-of-fit test showed a fairly even distribution of P-values over the interval. Examples of the application of these statistical procedures to distributions from patients with anemia are given. Our results suggest that, for the analysis of red blood cell volumes, (i) parameter estimation should be made with the expectation-maximization method, and (ii) the truncated lognormal distribution should be used as a reference distribution for goodness-of-fit testing. This method could be applied to any set of grouped doubly-truncated data which, after transformation, follows the normal model.