Bonnefoix T, Sotto J J
Laboratoire de Recherche en Immunopathologie Tumorale, CHU A. Michallon, Grenoble, France.
J Immunol Methods. 1994 Jan 3;167(1-2):21-33. doi: 10.1016/0022-1759(94)90071-x.
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. In the literature, most experiments are fit well 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 multi-target models that involve the interaction of one or more cells from one or more cell subpopulations for generating or inhibiting a positive response are conceivable. Since the validity of the SHPM is usually investigated by performing a standard chi 2 test, based on the number of observed and expected positive and negative responses, we questioned here the efficiency of this test in comparison with other validity tests for the SHPM, the log likelihood test derived by Cox, and the modified Weibull plot tests, the principles of which are entirely different from that of the standard chi 2 test. We used the following theoretical 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 of the desired cell subset according to the SHPM using the maximum likelihood method. Then, the goodness-of-fit of these data with the SHPM was evaluated. The log likelihood test and the modified Weibull plot tests rejected the SHPM hypothesis, while the standard chi 2 test did not. Thus, the standard chi 2 test is unable to discriminate sensitively between the SHPM and more complicated (non-single-hit) Poisson models. We concluded that the results of limiting dilution studies published thus far must be evaluated with caution. The statistical tests presented here should be routinely applied for each limiting dilution experiment.
有限稀释分析是免疫学中常用的一种技术，用于准确估计具有多种功能活性（如生长、细胞毒性和淋巴因子产生）的细胞频率。在文献中，大多数实验都能很好地拟合单打击泊松模型（SHPM），该模型假设对于阳性反应，仅一个定义细胞亚群中的一个细胞就足够了。这有点令人惊讶，因为可以设想其他模型，如多打击或多靶点模型，这些模型涉及一个或多个细胞亚群中的一个或多个细胞相互作用以产生或抑制阳性反应。由于SHPM的有效性通常通过基于观察到的和预期的阳性及阴性反应数量进行标准卡方检验来研究，我们在此质疑该检验与SHPM的其他有效性检验（Cox推导的对数似然检验和修正的威布尔图检验，其原理与标准卡方检验完全不同）相比的效率。我们采用了以下理论方法。首先，我们生成了对应于多打击和多靶点模型的人工数据。其次，考虑到这些数据来自真实实验，我们使用最大似然法根据SHPM计算所需细胞亚群的频率。然后，评估这些数据与SHPM的拟合优度。对数似然检验和修正的威布尔图检验拒绝了SHPM假设，而标准卡方检验没有。因此，标准卡方检验无法灵敏地区分SHPM和更复杂的（非单打击）泊松模型。我们得出结论，迄今为止发表的有限稀释研究结果必须谨慎评估。这里介绍的统计检验应该常规应用于每个有限稀释实验。
