Linear Combinations of Endpoints

Several statistics which are linear combinations of the endpoints have been suggested. Assume first that the underlying data have a normal distribution with known covariance matrix A and that there are nt = N patients assigned to each treatment. We consider three linear combination tests for testing H0{1, 2,..., k versus 2,..., ^j. Each test statistic has a standard normal distribution and H0{12,...,K} would be rejected for large values of the test statistic.

Let Y be the column vector of differences in means for the K endpoints (second sample minus first sample), R = (aim) the covariance matrix of Y, and amm = jm, the variance of the mth mean difference. The ordinary least squares (OLS) statistic (O'Brien, 1984) is a function of the average of Ym/am, which is then properly normalized:

The generalized least squares (GLS) statistic (O'Brien, 1984) is a weighted average of the Ym/am:

Was this article helpful?

0 0

Post a comment