Mukhopadhyay Nitai D, Sampson Andrew J, Deniz Daniel, Alm Carlsson Gudrun, Williamson Jeffrey, Malusek Alexandr
Department of Biostatistics, Virginia Commonwealth University, Richmond, VA 23298, USA.
Appl Radiat Isot. 2012 Jan;70(1):315-23. doi: 10.1016/j.apradiso.2011.09.015. Epub 2011 Sep 29.
Correlated sampling Monte Carlo methods can shorten computing times in brachytherapy treatment planning. Monte Carlo efficiency is typically estimated via efficiency gain, defined as the reduction in computing time by correlated sampling relative to conventional Monte Carlo methods when equal statistical uncertainties have been achieved. The determination of the efficiency gain uncertainty arising from random effects, however, is not a straightforward task specially when the error distribution is non-normal. The purpose of this study is to evaluate the applicability of the F distribution and standardized uncertainty propagation methods (widely used in metrology to estimate uncertainty of physical measurements) for predicting confidence intervals about efficiency gain estimates derived from single Monte Carlo runs using fixed-collision correlated sampling in a simplified brachytherapy geometry. A bootstrap based algorithm was used to simulate the probability distribution of the efficiency gain estimates and the shortest 95% confidence interval was estimated from this distribution. It was found that the corresponding relative uncertainty was as large as 37% for this particular problem. The uncertainty propagation framework predicted confidence intervals reasonably well; however its main disadvantage was that uncertainties of input quantities had to be calculated in a separate run via a Monte Carlo method. The F distribution noticeably underestimated the confidence interval. These discrepancies were influenced by several photons with large statistical weights which made extremely large contributions to the scored absorbed dose difference. The mechanism of acquiring high statistical weights in the fixed-collision correlated sampling method was explained and a mitigation strategy was proposed.
相关抽样蒙特卡罗方法可以缩短近距离放射治疗治疗计划中的计算时间。蒙特卡罗效率通常通过效率增益来估计，效率增益定义为在达到相等统计不确定性时，相关抽样相对于传统蒙特卡罗方法计算时间的减少量。然而，确定由随机效应引起的效率增益不确定性并非易事，特别是当误差分布为非正态时。本研究的目的是评估F分布和标准化不确定度传播方法（在计量学中广泛用于估计物理测量的不确定度）在预测使用简化近距离放射治疗几何结构中的固定碰撞相关抽样从单次蒙特卡罗运行得出的效率增益估计值的置信区间方面的适用性。使用基于自助法的算法来模拟效率增益估计值的概率分布，并从该分布中估计最短的95%置信区间。结果发现，对于这个特定问题，相应的相对不确定度高达37%。不确定度传播框架对置信区间的预测相当不错；然而，其主要缺点是输入量的不确定度必须通过蒙特卡罗方法在单独的运行中计算。F分布明显低估了置信区间。这些差异受到几个具有大统计权重的光子的影响，这些光子对计分吸收剂量差异有极大贡献。解释了在固定碰撞相关抽样方法中获得高统计权重的机制，并提出了一种缓解策略。
