Statistical evaluation of cell kinetic data from DNA flow cytometry (FCM) by the EM algorithm

Abstract

Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A DNA histogram normally consists of a mixture of one or more constellations of G₀/G₁-, S-, G₂/M-phase cells, together with internal standards, debris, background noise, and one or more populations of clumped cells. We have modelled typical DNA histograms as a mixed distribution with Gaussian densities for the G₀/G₁ and G₂/M phases, an S-phase density, assumed to be uniform between the G₀/G₁ and G₂/M peaks, observed with a Gaussian error, and with Gaussian densities for standards of chicken and trout red blood cells. The debris is modelled as a truncated exponential distribution, and we also have included a uniform background noise distribution over the whole observation interval. We have explored a new approach for maximum-likelihood analyses of complex DNA histograms by the application of the EM algorithm. This algorithm was used for four observed DNA histograms of varying complexity. Our results show that the algorithm works very well, and it converges to reasonable values for all parameters. In simulations from the estimated models, we have investigated bias, variance, and correlations of the estimates.