Table 1.

Variance and covariance of estimated parameters for testing DM efficacy (Notice that the covariance becomes variance when two estimates are the same)

Estimate 1	Estimate 2	Covariance between Estimate 1 and Estimator 2
β̂tt	β̂tt	$\frac{c^2}{d_1^2}(\frac{{\sigma }_2^2}{n_{tt}}+\frac{s_1}{n})+\frac{s_4{(1-c)}^2}{d_2^2{n}_{tt}}+\frac{2c(1-c)}{d_1{d}_2}(\frac{{\sigma }_{23}-{\sigma }_2^2}{n_{tt}}-\frac{s_3}{n})$
β̂pp	β̂pp	$\frac{f^2}{d_1^2}(\frac{{\sigma }_2^2}{n-n_{tt}}+\frac{s_1}{n})+\frac{{(1-f)}^2}{d_2^2}(\frac{{\sigma }_3^2}{n_{pp}}+\frac{s_2}{n-n_{tt}})+\frac{2f(1-f)}{d_1{d}_2}(\frac{{\sigma }_{23}-{\sigma }_2^2}{n_{pp}+n_{pt}}-\frac{s_3}{n})$
β̂tt	β̂pp	$\frac{cf{s}_1}{n{d}_1^2}-\frac{(c+f-2cf)s_3}{n{d}_1{d}_2}$
β̂pt	β̂pt	$\frac{1}{d_2^2}(\frac{{\sigma }_3^2}{n_{pt}}+\frac{s_2}{n_{pp}+n_{pt}})$
β̂tt	β̂pt	$\frac{-c{s}_3}{n{d}_1{d}_2}$
β̂pt	β̂pp	$\frac{f}{d_1{d}_2}(\frac{{\sigma }_{23}-{\sigma }_2^2}{n_{pp}+n_{pt}}-\frac{s_3}{n})+\frac{(1-f)s_2}{(n_{pp}+n_{pt})d_2^2}$
δ̂	δ̂	${\sigma }_{{\mathrm{\beta ̂}}^{tt}}^2+{\sigma }_{{\mathrm{\beta ̂}}^{pt}}^2-2\text{cov}({\mathrm{\beta ̂}}^{tt},{\mathrm{\beta ̂}}^{pt})$
Δ̂	Δ̂	${\sigma }_{{\mathrm{\beta ̂}}^{pt}}^2+{\sigma }_{{\mathrm{\beta ̂}}^{pp}}^2-2\text{cov}({\mathrm{\beta ̂}}^{pt},{\mathrm{\beta ̂}}^{pp})$
δ̂	Δ̂	$\text{cov}({\mathrm{\beta ̂}}^{tt},{\mathrm{\beta ̂}}^{pt})+\text{cov}({\mathrm{\beta ̂}}^{pt},{\mathrm{\beta ̂}}^{pp})-{\sigma }_{{\mathrm{\beta ̂}}^{pt}}^2-\text{cov}({\mathrm{\beta ̂}}^{tt},{\mathrm{\beta ̂}}^{pp})$