基于Excel的泊松分布可信区间算法在辐射生物剂量估算中的应用

  目的  建立泊松分布95%可信区间表，基于该可信区间表估算辐射生物剂量。
  方法  根据泊松分布累积概率和的算法，用Excel函数及迭代法建立计算变量X可信区间的方法，用宏代码循环计算得到95%可信区间表，基于该可信区间表建立辐射生物剂量估算的Excel应用，并验证可信区间表以及估算剂量的准确性。
  结果  利用Excel软件建立了X取值0 ~ 500的95%可信区间表，其结果与权威教材文献给出的可信区间一致；正态近似法与泊松分布表法估算辐射生物剂量95%可信区间在畸变数较小时差别明显，在畸变数较大时差别较小，泊松分布表法的95%可信区间与国际原子能机构（IAEA）推荐的专业估算软件CABAS 2.0的结果一致。
  结论  建立的估算程序可以准确计算泊松分布的可信区间，使用该可信区间表来估算辐射生物剂量的95%可信区间更合理；该程序应用范围更广、使用更方便，可满足辐射应急事故中对大量受照人员进行生物剂量估算的需求。

Calculation method of Poisson distribution confidence interval and its application in estimating radiation biological dose by using Excel

  Objective  A convenient table for calculating 95% confidence interval of data with Poisson distribution was designed to estimate confidence interval of radiation biological dose.  Methods  Based on the calculation methods of the cumulative probability sum of Poisson distribution, a method of calculating the confidence interval of variable X was established by using Excel function and iterative methods, and a 95% credible interval table was calculated by using the macro code loop. Then, an Excel application for estimating confidence interval of radiation biological dose was established based on this credible interval table, and finally the accuracy of this credible interval table and the estimated dose were verified.  Results  A 95% confidence interval table with the parameters X ranged from 0 - 500 was successfully established by using the Excel methods, and the results were consistent with the confidence intervals given by authoritative textbooks. Compared with the results of the 95% confidence intervals of radiation biological dose by using normal approximation method and Poisson distribution table method, the difference was significant when aberrations number was small, while the difference was small when aberrations number was large. The 95% confidence interval based on the Poisson distribution table method was consistent with the results using the professional estimation software CABAS 2.0 recommended by the International Atomic Energy Agency (IAEA).  Conclusions  The Excel method introduced in this article can be used to calculate the confidence interval of data with Poisson distribution and it is more reasonable to use this confidence interval table to estimate the 95% confidence interval of the biological radiation dose. Such convenient table can be used widely, and in particular can meet the needs of biological dose estimation in radiation emergency accidents.