Akaishi Tetsuya, Ishii Tadashi, Aoki Masashi, Nakashima Ichiro
Department of Education and Support for Regional Medicine, Tohoku University Hospital, Sendai, Japan.
Division of General Medicine, Tohoku University Hospital, Sendai, Japan.
Front Neurol. 2022 Jun 10;13:875456. doi: 10.3389/fneur.2022.875456. eCollection 2022.
Calculating the crude or adjusted annualized relapse rate (ARR) and its confidence interval (CI) is often required in clinical studies to evaluate chronic relapsing diseases, such as multiple sclerosis and neuromyelitis optica spectrum disorders. However, accurately calculating ARR and estimating the 95% CI requires careful application of statistical approaches and basic familiarity with the exponential family of distributions. When the relapse rate can be regarded as constant over time or by individuals, the crude ARR can be calculated using the person-years method, which divides the number of all observed relapses among all participants by the total follow-up period of the study cohort. If the number of relapses can be modeled by the Poisson distribution, the 95% CI of ARR can be obtained by finding the 2.5% upper and lower critical values of the parameter λ as the mean. Basic familiarity with F-statistics is also required when comparing the ARR between two disease groups. It is necessary to distinguish the observed relapse rate ratio (RR) between two sample groups (sample RR) from the unobserved RR between their originating populations (population RR). The ratio of population RR to sample RR roughly follows the F distribution, with degrees of freedom obtained by doubling the number of observed relapses in the two sample groups. Based on this, a 95% CI of the population RR can be estimated. When the count data of the response variable is overdispersed, the negative binomial distribution would be a better fit than the Poisson. Adjusted ARR and the 95% CI can be obtained by using the generalized linear regression models after selecting appropriate error structures (e.g., Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial) according to the overdispersion and zero-inflation in the response variable.
在临床研究中，为评估慢性复发性疾病，如多发性硬化症和视神经脊髓炎谱系障碍，常常需要计算粗年化复发率（ARR）或调整年化复发率及其置信区间（CI）。然而，准确计算ARR并估计95%CI需要谨慎应用统计方法，并对指数分布族有基本的了解。当复发率在时间上或个体间可视为恒定时，可使用人年法计算粗ARR，即将所有参与者观察到的复发总数除以研究队列的总随访期。如果复发数可由泊松分布建模，则可通过将参数λ的2.5%上下临界值作为均值来获得ARR的95%CI。在比较两个疾病组的ARR时，还需要对F统计量有基本的了解。有必要区分两个样本组之间观察到的复发率比（RR）（样本RR）与其总体之间未观察到的RR（总体RR）。总体RR与样本RR的比值大致遵循F分布，其自由度通过将两个样本组中观察到的复发数加倍获得。基于此，可估计总体RR的95%CI。当响应变量的计数数据过度离散时，负二项分布比泊松分布更合适。根据响应变量中的过度离散和零膨胀情况选择适当的误差结构（如泊松、负二项、零膨胀泊松和零膨胀负二项）后，可使用广义线性回归模型获得调整后的ARR和95%CI。
