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) 回归计算的致死剂量与使用 R 的任意斜率的比较

半数致死剂量 (LD50) 通常用于表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。通常有必要比较几种杀虫剂与一个种群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，但对于具有任意斜率的情况通常不可用。我们使用 R 中的 glm 函数来计算和比较致死剂量，而不假设斜率相等。使用 logit 模型拟合的文献中的生物测定数据集使用 Fieller 定理给出了致死剂量的 95% 置信限 (95% CL)，并结合了与使用 PoloPlus 软件确定的 95% CL 相同的异质性因子。delta 方法给出的 95% CL 与使用 R drc 包确定的 95% CL 相同。使用 probit 模型拟合的相同数据集给出的 95% CL 与使用 PoloPlus 和 drc 包确定的 95% CL 相似。使用雅培方程包括对照组的自然反应率。当使用效价比法和 z 检验来确定两种致死剂量之间的差异时，当使用 χ2 和对数似然比检验来确定回归线是否平行时，