Estimation of blood platelet survival—V. A method for the analysis of population data

Abstract

A maximum likelihood estimator of the parameters for a multiple-hit curve which fits best the empirical decay of a population label of circulating platelets is derived. The model is deterministic with errors of measurement which are normally and independently distributed and with constant variance. The justification for these assumptions has been discussed in an earlier paper. The method, which is iterative, is discussed in considerable detail and the properties of the estimator have been explored by Monte-Carlo simulation. The adequacy of the large-sample estimates of the variances and covariances is explored where the ‘data’ comprise ten equally-spaced points, a realistic simulation of natural experimental conditions. The following statements appear to be warranted. Individual estimates of n (the number of ‘hits to destruction’) and a (the ‘intensity of the risk’ of a hit) are very imprecise and positively biased. However, the ratio of them, which estimates the mean survival, is highly stable with very little bias. Thus even if the multiple-hit model is not treated as a literal description of the economy of the platelet it provides an excellent smoothing function when the data points are few and experimental error not trivial. In any case the estimate of the intercept on the vertical axis is excellent. From the residual sum of squares with the best fitting multiple-hit curve the variance of experimental error can be satisfactorily estimated by dividing by the number of data points less three. From this estimate the standard error of the estimate of the mean can be estimated in the individual set of data. Attempts to find a variance-stabilizing transformation for the estimate of the mean which will render it independent of n have failed. This method is now available for practical use.