Analysis of 2x2x2 crossover design data: Proc Mixed or Proc GLM

In an early article "Cookbook SAS Codes for Bioequivalence Test in 2x2x2 Crossover Design", I provided the analysis using Proc Mixed model. There is a question about the necessity of using Proc Mixed while the Proc GLM can be used for analyzing the data from a 2x2x2 crossover design. As a matter of fact, FDA guidance  "Statistical Approaches to Establishing Bioequivalence” indeed mentioned the use of Proc GLM for analyzing the non-replicated Crossover Design:

b. Nonreplicated Crossover Designs

For nonreplicated crossover designs, this guidance recommends parametric (normal-theory) procedures to analyze log-transformed BA measures. General linear model procedures available in PROC GLM in SAS or equivalent software are preferred, although linear mixed-effects model procedures can also be indicated for analysis of nonreplicated crossover studies. For example, for a conventional two-treatment, two-period, two-sequence (2 x2) randomized crossover design, the statistical model typically includes factors accounting for the following sources of variation: sequence, subjects nested in sequences, period, and treatment. The Estimate statement in SAS PROC GLM, or equivalent statement in other software, should be used to obtain estimates for the adjusted differences between treatment means and the standard error associated with these differences.

Put it into the SAS statements, the SAS codes will be something like the following:

 PROC GLM data=pk;
    CLASS SEQUENCE PERIOD TREATMENT PATIENT;
    MODEL LogAUC = SEQUENCE PATIENT(SEQUENCE) PERIOD TREATMENT; 
    LSMEANS TREATMENT / PDIFF CL ALPHA=0.1;
RUN;

The SAS output below will provide the mean difference and its 90% confidence interval. Since the data is in log scale, anti-log of the mean difference (1.076) is the ratio of the geometric mean and anti-log of the 90% confidence interval is our 90% confidence interval for the geometric mean ratio (0.860, 1.346). 

Least Squares Means for Effect TREATMENT
i	j	Difference Between Means	90% Confidence Limits for LSMean(i)-LSMean(j)
1	2	0.073113	-0.150925	0.297152

If it is balanced design (i.e., there is no missing value) and all subjects have data available for period 1 and period 2, the results from the Proc GLM will be identical to teh results obtained from Proc Mixed as described in my previous article "Cookbook SAS Codes for Bioequivalence Test in 2x2x2 Crossover Design".

However, it is very often, there is possibility of missing data in one of the periods. In this case, if Proc GLM is used, the entire subject will be excluded from the analysis. If Proc Mixed is used, the subject who contributes only the data for one of the two periods will still be included in the analysis.