Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL.

致命的车祸是美国青少年死亡的主要原因。分级驾驶执照（GDL）计划是减少青少年致命车祸次数的一项有效政策。我们的研究重点是1990-2004年（不包括1997年GDL启动时）在密歇根州发生的致命车祸数量。我们将Poisson回归与空间相关的随机效应结合使用，以对县级青少年车祸计数进行建模。我们开发了一个测量误差模型，以说明县级青少年总人口被用作青少年驾驶员人口的代表这一事实。据我们所知，没有现有的文献考虑对偏移变量中的测量误差进行调整。此外，有限的工作已经解决了空间数据方面的测量误差。在我们的建模中 应用具有空间随机效应的Berkson测量误差模型来调整贝叶斯范式中易于出错的偏移变量。贝氏马尔可夫链蒙特卡洛（MCMC）采样是在Rstan中实现的。为了评估调整测量误差的结果，我们比较了有和没有调整测量误差的两个模型。我们发现，随着测量误差的调整，时间指示器的影响变得不那么显着。由此得出的结论是，青少年驾驶员数量的减少可以在一定程度上帮助解释GDL的有效性。为了评估调整测量误差的结果，我们比较了有和没有调整测量误差的两个模型。我们发现，随着测量误差的调整，时间指示器的影响变得不那么显着。由此得出的结论是，青少年驾驶员数量的减少可以在一定程度上帮助解释GDL的有效性。为了评估调整测量误差的结果，我们比较了有和没有调整测量误差的两个模型。我们发现，随着测量误差的调整，时间指示器的影响变得不那么显着。由此得出的结论是，青少年驾驶员数量的减少可以在一定程度上帮助解释GDL的有效性。