Repeated-measures mixed models

Lindstrom MJ, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics, 1990 46 673-87. 

Biopharmaceutical research often involves the collection of repeated measures on experimental units (such as patients or healthy volunteers) in the form of longitudinal data and/or multilevel hierarchical data. Responses collected on the same experimental unit are typically correlated and, as a result, classical modeling methods that assume independent observations do not lead to valid inferences. Mixed effects models, which allow some or all of the parameters to vary with experimental unit through the inclusion of random effects, can flexibly account for the within-unit correlation often observed with repeated measures and provide proper inference. This chapter discusses the use of mixed effects models to analyze biopharmaceutical data, more specihcally pharmacokinetic (PK) and pharmacodynamic (PD) data. Different types of PK and PD data are considered to illustrate the use of the three most important classes of mixed effects models linear, nonlinear, and generalized linear. 

MMRM mixed effects model repeated measures... 

The basic experimental unit in a linear or nonlinear model is the observation itself—each observation is independent of the others. With a mixed model, the basic experimental unit is the subject that is being repeatedly sampled. For example, a patient s CD4-count may be measured monthly in an AIDS clinical trial. While a particular observation may be influential, of more interest is whether a particular subject is influential. Hence, influence analysis in a mixed effects model tends to focus on a set of observations within a subject, rather than at the observation level. That is not to say that particular observations are not of interest. Once an individual is identified as being influential, the next step then is to determine whether that subject s influence is due to a particular observation. 

Table 6.7 Summary of linear mixed effect model analysis to tumor growth data using a repeated measures analysis of covariance treating time as a categorical variable.

Cnaan, A., Laird, N.M., and Slasor, P. Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Statistics in Medicine 1997 16 2349-2380. 

Wolfinger, R.D. Heterogeneous variance-covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics 1996 1 205-230. Wolfinger, R.D. An example of using mixed models and PROC MIXED for longitudinal data. Journal of Biophar-maceutical Statistics 1997 7 481-500. 

Statistical Analysis. Analyses were performed for intent-to-treat and per protocol samples with SAS, version 8.0 software (Cary, NC). ANOVA models were generated utilizing the PROC MIXED procedure. Repeated-measures ANOVA was employed to assess effects of treatment, time (week), and treatment X time interactions for the percentage of change from baseline in body weight, fat mass, and lAF area. 

Where appropriate, models were developed with the joint goals of providing a parsimonious explanation of the data while maintaining maximum predictive power. Initial model screening and computation of the r statistic were handled using SAS/GLM. However, for many of the analyses the data contained observations on the same unit measured repeatedly over time. This created a violation of the assumptions for standard statistical techniques and the need to use methodologies for handling models with repeated measures. The tool used in this case was the SAS/MIXED procedure (Littell et al. 1996). 

An important part of the statistical and epidemiological assessments of Bunker HiU children was the impact of treatment modality on children s PbB levels. This was done using a mixed model repeat measures analysis comparing two exposure control methods over the period 1989—1998. Treatments consisted of either yard soil Pb reduction or public health interventions without soil removal by the Panhandle Health District, using the various methods described earlier. Table 23.5 notes comparative data for selected years plus data for aU years combined, and compares control pre-and post-PbB with exposed pre- and post-PbB values for the indicated year. 

TABLE 23.5 Mixed Model Repeat Measures Analyses Superfund Box Children 1988-1998 of PbB Changes Versus Exposure Control Methods for Bunker Hill, ID, ... 

Data were analyzed as a mixed model with repeated measures using the PROC MIXED of SAS (SAS Inst Inc., Cary, NC). The statistical model included Ml (SAB, LAB and protozoa), F C, FOR, period, MlxF C, MtxpOR, FiCxpOR, MlxpiCxpOR as fixed effects, and sheep as a random effect Effects were declared significant at P<0.05. 

Differences in BW and total feed intake in each experiment were analyzed using the PROC GLM procedure in SAS (2004) with main effects of phenotype, feeding program, trial, and their interactions included in the model. Intake of the HP and LP diets in pigs in the Choice treatment, were also analyzed as repeated measures using the PROC Mixed procedure in SAS (2004). The model included fixed effects of phenotype, day, and day x phenotype and the random effects of pig within phenotype and trial. 

While population PK analyses often involve the utilization of mixed effects models due to the repeated nature of the measurements collected from each individual and the desire to estimate and discriminate between the various sources of variability, PK/PD analyses of binary endpoint data may utilize either fixed or mixed effects models. Oftentimes, a single endpoint measurement is collected from each individual being studied and a model estimating only fixed effects is used. However, when multiple observations are collected from each individual (over time), we may wish to estimate the change in response probability over time while recognizing the correlation between observations from the same individual and also estimate the variation between individuals. This is accomplished through the use of a mixed effects model. 

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