The correlation coefficient of change from baseline of early and late response can be given by 7.7 If the correlation of post-baseline response (Y2 or Y3) and baseline is zero, Eqn 7.7 becomes Thus, the correlation of DAS28 change from baseline has a linear relationship to the correlation of raw DAS28 score with slope and intercept of . The correlation in change from baseline response is dependent of the correlations in raw score as well as the correlation of post-baseline and baseline and is equal to , when there are no correlations between the raw scores Y1, Y2, and Y3. Let be the ratio of ϒ2 σY2 and and to be the ratio of and = and = so the σY1, ϒ3 σY3 σY1.ϒ2 σY2 /σY1 ϒ3 σY3 /σY1, denominator can be written as . After replacing and with and the a, b, c, and d the above result is σY1, σY2, σY3 ϒ2 ϒ3, transformed to Let a=; b=; c=; and d=.
The correlation coefficient of change from baseline of early and late response can be given by 7.7 If the correlation of post-baseline response (Y2 or Y3) and baseline is zero, Eqn 7.7 becomes Thus, the correlation of DAS28 change from baseline has a linear relationship to the correlation of raw DAS28 score with slope and intercept of . The correlation in change from baseline response is dependent of the correlations in raw score as well as the correlation of post-baseline and baseline and is equal to , when there are no correlations between the raw scores Y1, Y2, and Y3. Let ϒ2 be the ratio of σY2 and σY1, and ϒ3 to be the ratio of σY3 and σY1.ϒ2 = σY2 /σY1 and ϒ3 = σY3 /σY1, so the denominator can be written as . After replacing σY1, σY2, and σY3 with ϒ2 and ϒ3, the a, b, c, and d the above result is transformed to Let a=; b=; c=; and d=.
PhD%20Dissertation%20Feng%20Liu%20Final%20Clean.docx