Ribaudo H J, Thompson S G, Allen-Mersh T G
Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA.
Stat Med. 2000 Dec 15;19(23):3237-50. doi: 10.1002/1097-0258(20001215)19:23<3237::aid-sim624>3.0.co;2-q.
In studies of patients with advanced disease, longitudinal quality of life data may be truncated as a result of early death. Since survival and quality of life are likely to be related, modelling of the quality of life response needs to account for these different survival patterns. Here we discuss the application of a random effect selection model, in the form of a trivariate Normal model for the joint analysis of quality of life response (intercept and slope) and log survival time. Under certain assumptions this can give an unbiased description of the quality of life responses and valid inferences comparing treatment strategies in a clinical trial. It also indicates how quality of life and survival are related, by estimating the expected quality of life responses conditional on different survival times. Model parameters can be estimated using a restricted iterative generalized least-squares (RIGLS) procedure within standard software, extended to handle censoring of survival outcome using an EM algorithm. The model is applied to a physical quality of life score and survival data from a trial of treatment for patients with colorectal hepatic metastases. Survival differed between the treatment groups, and quality of life repsonse tended to be worse, both in initial level and change over time, for those patients who died earlier. The parameter estimates obtained agreed well with those from analysing the extended trial data set with complete survival information. Residual diagnostics used to check the necessary underlying assumptions of the model are exemplified. We conclude that such models can give an informative description of longitudinal responses when these are truncated by differential survival patterns.
在对晚期疾病患者的研究中，由于早期死亡，纵向生活质量数据可能会被截断。由于生存和生活质量可能相关，生活质量反应的建模需要考虑这些不同的生存模式。在此，我们讨论一种随机效应选择模型的应用，该模型采用三变量正态模型的形式，用于联合分析生活质量反应（截距和斜率）和对数生存时间。在某些假设下，这可以对生活质量反应给出无偏描述，并在临床试验中对比较治疗策略进行有效推断。它还通过估计不同生存时间条件下的预期生活质量反应，表明生活质量与生存之间的关系。模型参数可以使用标准软件中的受限迭代广义最小二乘法（RIGLS）程序进行估计，并通过期望最大化（EM）算法进行扩展以处理生存结局的删失情况。该模型应用于一项针对结直肠癌肝转移患者治疗试验的身体生活质量评分和生存数据。治疗组之间的生存情况不同，对于那些较早死亡的患者，生活质量反应在初始水平和随时间变化方面往往更差。获得的参数估计值与分析具有完整生存信息的扩展试验数据集所得结果吻合良好。文中举例说明了用于检验模型必要基本假设的残差诊断方法。我们得出结论，当纵向反应因不同的生存模式而被截断时，此类模型可以对其给出有价值的描述。
