THE STANDARD CHI-2 TEST USED IN LIMITING DILUTION ASSAYS IS INSUFFICIENT FOR ESTIMATING THE GOODNESS-OF-FIT TO THE SINGLE-HIT POISSON MODEL

Limiting dilution analysis is a common technique that is used in immun ology to estimate accurately the frequency of cells possessing a wide variety of functional activities, such as growth, cytotoxicity and pro duction of lymphokines. In the literature, most experiments are fit we ll by the single-hit Poisson model (SHPM), which assumes that only one cell of one defined cell subset is necessary for a positive response. This is somewhat surprising since other models such as multi-hit or m ulti-target models that involve the interaction of one or more cells f rom one or more cell subpopulations for generating or inhibiting a pos itive response are conceivable. Since the validity of the SHPM is usua lly investigated by performing a standard chi(2) test, based on the nu mber of observed and expected positive and negative responses, we ques tioned here the efficiency of this test in comparison with other valid ity tests for the SHPM, the log likelihood test derived by Cox, and th e modified Weibull plot tests, the principles of which are entirely di fferent from that of the standard chi(2) test. We used the following t heoretical approach. First, we generated artificial data corresponding to multi-hit and multi-target models. Second, considering that these data were derived from real experiments, we calculated the frequency o f the desired cell subset according to the SHPM using the maximum like lihood method. Then, the goodness-of-fit of these data with the SHPM w as evaluated. The log likelihood test and the modified Weibull plot te sts rejected the SHPM hypothesis, while the standard chi(2) test did n ot. Thus, the standard chi(2) test is unable to discriminate sensitive ly between the SHPM and more complicated (non-single-hit) Poisson mode ls. We concluded that the results of limiting dilution studies publish ed thus far must be evaluated with caution. The statistical tests pres ented here should be routinely applied for each limiting dilution expe riment.