Limiting dilution assays for the determination of immunocompetent cell frequencies. I. Data analysis.

TLDR

The authors developed a statistical method for analyzing data from limiting dilution assays. The method derives formulas for estimating immunocompetent cell frequency using weighted averaging, likelihood maximization, and X² minimization, with the latter two solved by Newton’s iterative approximation. X² minimization proved superior to least‑squares fitting, producing more accurate and precise estimates, and reanalysis of published data revealed significant differences, demonstrating the method’s validity and providing a quick, reliable procedure for determining immunocompetent cell frequencies.

Abstract

A statistical method was developed for the analysis of experimental data from limiting dilution assays. Formulas for the estimation of the frequency of immunocompetent cells within a test population were derived by the statistical methods of weighted averaging, likelihood maximization, and X2 minimization. Equations for the latter 2 were solved by Newton's method of iterative approximation. Estimates obtained by these methods were found to be more valid than those obtained by least squares (LS) fitting as judged by the X2 test and as established by Monte Carlo experiments. X2 minimization was chosen as the preferable estimation method with maximum accuracy and precision (minimum bias and variance) for the standard determination of frequencies; likelihood maximization was used only for the confirmation of results. When data from previously published experiments were reanalyzed, both results and conclusions were found to differ significantly from those originally obtained by LS fitting, thus demonstrating the importance of using proper data analysis methods. In conjunction with the use of available calculators or microcomputers, the method presented here provides a simple and rapid procedure for the valid determination of immunocompetent cell frequencies.