Least square mean

Least squares means (marginal means) vs. means Least square means is actually referred to as marginal means. In an analysis of covariance model, they are the group means after having controlled for a covariate (i.e. holding it constant at some typical value of the covariate, such as its mean value).

I made up the data in Table 1 above. There are two treatment groups (treatment A and treatment B) that are measured at two centers (Center 1 and Center 2). The mean value for Treatment A is simply the summation of all measures divided by the total number of observations (Mean for treatment A = 24/5 = 4.8); similarly the Mean for treatment B = 26/5 = 5.2. Mean for treatmeng A > Mean for treatment B. Table 2 shows the calculation of least squares means. First step is to calculate the means for each cell of treatment and center combination. The mean 9/3=3 for treatment A and center 1 combination; 7.5 for treatment A and center 2 combination; 5.5 for treatment B and center 1 combination; and 5 for treatment B and center 2 combination. After the mean for each cell is calculated, the least squares means are simply the average of these means. For treatment A, the LS mean is (3+7.5)/2 = 5.25; for treatment B, it is (5.5+5)/2=5.25. The LS Mean for both treatment groups are identical. It is easy to show the simple calculation of means and LS means in the above table with two factors. In clinical trials, the statistical model often needs to be adjusted for multiple factors including both categorical (treatment, center, gender) and continuous covariates (baseline measures). The calculation of LS mean is not easy to demonstrate. However, the LS mean should be used when the inferential comparison needs to be made. Typically, the means and LS means should point to the same direction (while with different values) for treatment comparison. Occasionally, they could point to the different directions (treatment A better than treatment B according to mean values; treatment B better than treatment A according to LS Mean).