Gavan Sean P, Chang Sainan, Rivellese Felice, Ide Zoë, Stadler Michael, Payne Katherine, Plant Darren, Barton Anne, Pitzalis Costantino
Manchester Centre for Health Economics, Division of Population Health, Health Services Research and Primary Care, School of Health Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester, M13 9PL, UK.
Centre for Experimental Medicine and Rheumatology, Queen Mary University of London, London, UK.
Rheumatol Int. 2025 Jun 14;45(7):154. doi: 10.1007/s00296-025-05897-1.
To map from the health assessment questionnaire disability index (HAQ) to the pain visual analogue scale (VAS) for people with rheumatoid arthritis. The estimation sample comprised adults with rheumatoid arthritis and inadequate response to tumour necrosis factor-α inhibitors in a multicentre phase 4 randomised controlled trial. Beta mixture models were estimated with combinations of HAQ and its square, age and sex as independent variables. Bayesian Information Criteria informed the number of components. Model performance (root mean squared error; mean absolute error; pseudo-R) was estimated by k-fold cross validation. Graphs illustrated mean observed and predicted pain VAS, and cumulative distribution of observed and simulated pain VAS values. For face validity, a probabilistic analysis simulated 5000 pain VAS values at four HAQ scores. For external validation, the performance of the preferred specification was assessed using the Rheumatoid Arthritis Medication Study cohort. There were 1055 observations from 158 participants in the estimation sample (mean age: 55.8; 81% female; mean HAQ: 1.72). The preferred specification was a two-component beta mixture model (probability variables: HAQ, age, sex; main regression variable: HAQ). Visual plots illustrated good fit across the HAQ distribution, and a similar cumulative distribution of observed and predicted pain VAS values. Probabilistic analysis demonstrated that the preferred specification handled uncertainty appropriately. External validation demonstrated that the preferred specification performed well in an independent dataset. Beta mixture models provide accurate non-linear estimates of pain VAS from HAQ scores to support evidence synthesis and resource allocation decision-making for people with rheumatoid arthritis.
将类风湿性关节炎患者的健康评估问卷残疾指数（HAQ）映射到疼痛视觉模拟量表（VAS）。估计样本包括在一项多中心4期随机对照试验中对肿瘤坏死因子-α抑制剂反应不足的类风湿性关节炎成人患者。以HAQ及其平方、年龄和性别为自变量组合估计β混合模型。贝叶斯信息准则确定了成分数量。通过k折交叉验证估计模型性能（均方根误差、平均绝对误差、伪R）。图表展示了观察到的和预测的疼痛VAS均值，以及观察到的和模拟的疼痛VAS值的累积分布。为了进行表面效度分析，概率分析在四个HAQ分数下模拟了5000个疼痛VAS值。为了进行外部验证，使用类风湿性关节炎药物研究队列评估了首选规格的性能。估计样本中有158名参与者的1055条观察数据（平均年龄：55.8岁；81%为女性；平均HAQ：1.72）。首选规格是一个双成分β混合模型（概率变量：HAQ、年龄、性别；主要回归变量：HAQ）。可视化图表明在HAQ分布范围内拟合良好，观察到的和预测的疼痛VAS值的累积分布相似。概率分析表明首选规格能适当处理不确定性。外部验证表明首选规格在独立数据集中表现良好。β混合模型提供了从HAQ分数到疼痛VAS的准确非线性估计，以支持类风湿性关节炎患者的证据综合和资源分配决策。
