Graphical representation of a generalized linear model-based statistical test estimating the fit of the single-hit Poisson model to limiting dilution assays.

Standardized statistical and graphical methods for analysis of limiting dilution assays are highly desirable to enable investigators to compare and interpret results and conclusions with greater accuracy and precision. According to these requirements, we present in this work a powerful statistical slope test that estimates the fit of the single-hit Poisson model to limiting dilution experiments. This method is readily amenable to a graphical representation. This slope test is obtained by modeling limiting dilution data according to a linear log-log regression model, which is a generalized linear model specially designed for modeling binary data. The result of the statistical slope test can then be graphed to visualize whether the data are compatible or not with the single-hit Poisson model. We demonstrate this statistical test and its graphical representation by using two examples: a real limiting dilution experiment evaluating the growth frequency of IL-2-responsive tumor-infiltrating T cells in a malignant lymph node involved by a B cell non-Hodgkin's lymphoma, and a simulation of a limiting dilution assay corresponding to a theoretical non-single-hit Poisson model, suppressor two-target Poisson model.

Fitting limiting dilution experiments with generalized linear models results in a test of the single-hit Poisson assumption.

Limiting dilution analysis is a common technique that is used in immunology to estimate accurately the frequency of cells possessing a wide variety of functional activities such as growth, cytotoxicity and production of lymphokines. The reliability of the estimated frequency is usually checked by a standard chi-square (x2) test validating the goodness-of-fit to the single-hit Poisson model (SHPM). We present evidence that modelling limiting dilution data according to a generalized linear model offers an alternative to the standard x2 test for detecting departures from the SHPM, with a considerable increase in power compared to the x2 test.