The median lethal dose (LD50) is commonly used to indicate acute toxicity of an insecticide to an insect species. Approximate confidence intervals for LD50s are often calculated using the Fieller and delta methods. It is often necessary to compare the relative potencies of several insecticides with a population or of one insecticide with different populations. Comparing the LD50s using probit/logit-log(dose) regressions with parallel slopes can be implemented in many software packages, but for the cases with arbitrary slopes are not generally available. We used the glm function in R to calculate and compare lethal doses without assuming equal slopes. Bioassay datasets from the literature fitted using the logit model gave the 95% confidence limits (95% CLs) for the lethal doses using Fieller's theorem and incorporating a heterogeneity factor identical to the 95% CLs determined using the PoloPlus software. The delta method gave 95% CLs identical to the 95% CLs determined using the R drc package. The same datasets fitted using the probit model gave 95% CLs similar to the 95% CLs determined using PoloPlus and the drc package. The natural response rates for the control group were included using Abbott's equation. When the potency ratio method and the z-test were used to identify differences between two lethal doses, and when the χ2 and log likelihood ratio tests were used to determine whether the regression lines were parallel, the conclusions were the same as those gave by PoloPlus and the drc package.

中文翻译：

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使用Logit / Probit-Log（Dose）回归与任意斜率使用R计算的致死剂量的比较。

中位数致死剂量（LD50）通常用于指示杀虫剂对昆虫物种的急性毒性。LD50的近似置信区间通常使用Fieller和delta方法计算。通常需要比较几种杀虫剂与种群的相对效力或一种杀虫剂与不同种群的相对效力。使用probit / logit-log（dose）回归与平行斜率比较LD50可以在许多软件包中实现，但是对于任意斜率的情况通常不可用。我们在R中使用glm函数来计算和比较致死剂量，而无需假设斜率相等。使用Logit模型拟合的文献中的生物测定数据集使用Fieller'得出了致命剂量的95％置信限（95％CL）。s定理，并引入与使用PoloPlus软件确定的95％CL相同的异质性因子。增量法得出的95％CL与使用R drc软件包确定的95％CL相同。使用概率模型拟合的相同数据集给出了95％的CL，与使用PoloPlus和drc软件包确定的95％的CL相似。对照组的自然反应率采用雅培方程。当使用效价比方法和z检验确定两个致死剂量之间的差异时，当使用χ2和对数似然比检验确定回归线是否平行时，结论与PoloPlus得出的结论相同。和drc软件包。增量法得出的95％CL与使用R drc软件包确定的95％CL相同。使用概率模型拟合的相同数据集给出了95％的CL，与使用PoloPlus和drc软件包确定的95％的CL相似。对照组的自然反应率采用雅培方程。当使用效价比方法和z检验确定两个致死剂量之间的差异时，当使用χ2和对数似然比检验确定回归线是否平行时，结论与PoloPlus得出的结论相同。和drc软件包。增量法得出的95％CL与使用R drc软件包确定的95％CL相同。使用概率模型拟合的相同数据集给出了95％的CL，与使用PoloPlus和drc软件包确定的95％的CL相似。对照组的自然反应率包括雅培方程式。当使用效价比方法和z检验确定两个致死剂量之间的差异时，当使用χ2和对数似然比检验确定回归线是否平行时，结论与PoloPlus得出的结论相同。和drc软件包。