Proc Mixed
本文为大家介绍广义线性模型Generalized linear models中的混合效应模型The Mixed Model。
先看下面这个例子：
“To evaluate the effect of treatment on serum aldosterone and plasma PRA, the linear mixed effect repeated measures models will be used to analyze the natural log-transformed AUEC (AUEC(0-24) and AUEC(0-8) separately), with treatment (including dose levels), day and treatment-by-day interaction as fixed effects, natural log-transformed AUECDay0 value as covariate and subject as a random effect. The different dose levels of PF-03882845 will be considered as different treatments in the model. The adjusted mean differences and 90% confidence intervals for the differences [AUEC(0-24)Day10 - AUEC(0-24)Day0, AUEC(0-24)Day1 - AUEC(0-24)Day0, AUEC(0-8)Day10 - AUEC(0-8)Day0, AUEC(0-8)Day1 -AUEC(0-8)Day0] will be obtained from the model and will be exponentiated to provide estimates of the ratio of adjusted geometric means [AUEC(0-24)Day10 / AUEC(0-24)Day0, AUEC(0-24)Day1 / AUEC(0-24)Day0, AUEC(0-8)Day10 / AUEC(0-8)Day0, AUEC(0-8)Day1 /AUEC(0-8)Day0] and 90% confidence intervals for the ratios for each treatment. The appropriate contrasts will be specified to compare the ratio of each PF-03882845 dose to the ratio of the placebo. The mixed effects model will be implemented using SAS Proc Mixed, with REML estimation method, variance-covariance structure of compound symmetry.”
我们通常把某个因素factor对结果变量variable的影响称为这个变量的效应effect。而这种效应分为固定效应fixed effect和随机效应random effect。
其实重复测量repeated measures数据分析就是一个混合效应模型，为什么呢？
1. 我们纳入模型的治疗组别一般是固定效应
2. 我们纳入模型的病人效应一般是随机效应
混合效应模型是由Mallinckrodt等人在2001年的一篇文章中提出的：
Mallinckrodt, C. H., Clark, W. S., David, S. R. (2001). Accounting for dropout bias using mixed-effects models. Journal of Biopharmaceutical Statistics 11:9–21.
现在已被广泛应用于重复测量数据的分析，在pfizer读到的的每个protocol里都有用到，到底它在处理重复测量数据方面有什么优势呢？
1. 混合效应模型不对compound symmetry做要求，允许每个病人测量次数不同和观测时间不同，并且解决了临床试验过程中最棘手的缺失值问题。可用于variance-covariance structure of compound symmetry（CS）或unstructured（UN）
2. 一般线性模型General linear models只能用于均数的比较，混合效应模型可用于协方差分析covariance analysis。关于协方差结构，我们通过上例中使用的SAS PROC MIXED程序来进一步介绍混合效应模型在重复测量数据中的应用。
proc mixed data=pd;
class trt subject day;
model lnAUEC =lnAUEC_bl trt day trt*day/ ddfm=KR;
repeated /subject=subject type=cs;
lsmeans trt*day/ cl alpha=0.1;
Note: baseline is defined as AUECDay0 value，因此将lnAUEC_bl作为协变量。ddfm=KR表示Kenward-Rogers degrees of freedom algorithm。CS即compound symmetric，表示测量时间点间距相同。lsmeans trt*day表示检验不同时间点治疗组间Least Squares Means的不同，LS-mean等于各个研究中心平均值加起来再除以中心数，即每个中心对治疗效应的贡献具有相同的权重。cl选项表示计算各Least Squares Means的可信区间，缺省值为95%置信区间confidence interval。
用MMRM检验不同剂量间修正均数和不同剂量间change的差异的显著性。
and will be exponentiated to provide estimates of the ratio of adjusted geometric means AUECDay10 / AUECDay0 and 90% confidence intervals for the ratios for each treatment.
Code：
estimate ‘Day10 vs. Day 0 in d1’ day -1 0 1
比较不同剂量下AUECDay10和AUECDay0在90%cl的差异的显著性。（检验完毕，转换回去，求几何均数的比值）
The appropriate contrasts will be specified to compare the ratio of each dose to the ratio of the placebo.
Code：
estimate '[Day10-Day0] in d1 vs [Day10-Day0] in PBO'
比较不同剂量下AUECDay10 - AUECDay0和placebo在90%cl的差异的显著性
/*协方差分析是将线性回归分析与方差分析结合起来的一种分析方法。利用回归关系把X值化为相等后再进行各组Y的修正均数adjust means间差别的假设检验。*/
/**AUC和AUEC的C涵义完全不同，前者指血“药”浓度，后者指血“biomarker”浓度**/
先看下面这个例子：
“To evaluate the effect of treatment on serum aldosterone and plasma PRA, the linear mixed effect repeated measures models will be used to analyze the natural log-transformed AUEC (AUEC(0-24) and AUEC(0-8) separately), with treatment (including dose levels), day and treatment-by-day interaction as fixed effects, natural log-transformed AUECDay0 value as covariate and subject as a random effect. The different dose levels of PF-03882845 will be considered as different treatments in the model. The adjusted mean differences and 90% confidence intervals for the differences [AUEC(0-24)Day10 - AUEC(0-24)Day0, AUEC(0-24)Day1 - AUEC(0-24)Day0, AUEC(0-8)Day10 - AUEC(0-8)Day0, AUEC(0-8)Day1 -AUEC(0-8)Day0] will be obtained from the model and will be exponentiated to provide estimates of the ratio of adjusted geometric means [AUEC(0-24)Day10 / AUEC(0-24)Day0, AUEC(0-24)Day1 / AUEC(0-24)Day0, AUEC(0-8)Day10 / AUEC(0-8)Day0, AUEC(0-8)Day1 /AUEC(0-8)Day0] and 90% confidence intervals for the ratios for each treatment. The appropriate contrasts will be specified to compare the ratio of each PF-03882845 dose to the ratio of the placebo. The mixed effects model will be implemented using SAS Proc Mixed, with REML estimation method, variance-covariance structure of compound symmetry.”
我们通常把某个因素factor对结果变量variable的影响称为这个变量的效应effect。而这种效应分为固定效应fixed effect和随机效应random effect。
其实重复测量repeated measures数据分析就是一个混合效应模型，为什么呢？
1. 我们纳入模型的治疗组别一般是固定效应
2. 我们纳入模型的病人效应一般是随机效应
混合效应模型是由Mallinckrodt等人在2001年的一篇文章中提出的：
Mallinckrodt, C. H., Clark, W. S., David, S. R. (2001). Accounting for dropout bias using mixed-effects models. Journal of Biopharmaceutical Statistics 11:9–21.
现在已被广泛应用于重复测量数据的分析，在pfizer读到的的每个protocol里都有用到，到底它在处理重复测量数据方面有什么优势呢？
1. 混合效应模型不对compound symmetry做要求，允许每个病人测量次数不同和观测时间不同，并且解决了临床试验过程中最棘手的缺失值问题。可用于variance-covariance structure of compound symmetry（CS）或unstructured（UN）
2. 一般线性模型General linear models只能用于均数的比较，混合效应模型可用于协方差分析covariance analysis。关于协方差结构，我们通过上例中使用的SAS PROC MIXED程序来进一步介绍混合效应模型在重复测量数据中的应用。
proc mixed data=pd;
class trt subject day;
model lnAUEC =lnAUEC_bl trt day trt*day/ ddfm=KR;
repeated /subject=subject type=cs;
lsmeans trt*day/ cl alpha=0.1;
Note: baseline is defined as AUECDay0 value，因此将lnAUEC_bl作为协变量。ddfm=KR表示Kenward-Rogers degrees of freedom algorithm。CS即compound symmetric，表示测量时间点间距相同。lsmeans trt*day表示检验不同时间点治疗组间Least Squares Means的不同，LS-mean等于各个研究中心平均值加起来再除以中心数，即每个中心对治疗效应的贡献具有相同的权重。cl选项表示计算各Least Squares Means的可信区间，缺省值为95%置信区间confidence interval。
用MMRM检验不同剂量间修正均数和不同剂量间change的差异的显著性。
and will be exponentiated to provide estimates of the ratio of adjusted geometric means AUECDay10 / AUECDay0 and 90% confidence intervals for the ratios for each treatment.
Code：
estimate ‘Day10 vs. Day 0 in d1’ day -1 0 1
比较不同剂量下AUECDay10和AUECDay0在90%cl的差异的显著性。（检验完毕，转换回去，求几何均数的比值）
The appropriate contrasts will be specified to compare the ratio of each dose to the ratio of the placebo.
Code：
estimate '[Day10-Day0] in d1 vs [Day10-Day0] in PBO'
比较不同剂量下AUECDay10 - AUECDay0和placebo在90%cl的差异的显著性
/*协方差分析是将线性回归分析与方差分析结合起来的一种分析方法。利用回归关系把X值化为相等后再进行各组Y的修正均数adjust means间差别的假设检验。*/
/**AUC和AUEC的C涵义完全不同，前者指血“药”浓度，后者指血“biomarker”浓度**/
