. Author manuscript; available in PMC: 2017 May 10.

Published in final edited form as: Stat Med. 2015 Dec 2;35(10):1637–1653. doi: 10.1002/sim.6820

Table 3.

Estimates, standard deviations (SD), and 95% confidence intervals (CI) using both the quantile method (Quantile) and Fieller's method (Fieller) for estimates of the proportion of treatment effect explained by each of three potential surrogate markers alone (walking distance, walking speed and stair climbing obtained from the WIQ) and the proportion explained by all three together, where the outcome of interest is change in 6 minute walking distance from baseline to 12 months using the proposed estimator, ${\hat{R}}_{S}$ , the flexible model-based estimator, ${\hat{R}}_{S}^{M}$ , and Freedman's estimator, ${\hat{R}}_{S}^{F}$

	R̂ _S	${\hat{R}}_{S}^{M}$	${\hat{R}}_{S}^{F}$

Potential surrogate: walking distance from the WIQ
Estimate	0.4403	0.1701	0.0753
SE	0.22	0.1771	0.0976
95% CI (Quantile)	(0.04,0.92)	(−0.07,0.57)	(−0.03,0.31)
95% CI (Fieller)	(0.01,1.01)	(−0.11,0.55)	(−0.08,0.27)
Potential surrogate: walking speed from the WIQ
Estimate	0.4808	0.3722	0.1726
SE	0.2437	0.2839	0.1618
95% CI (Quantile)	(0.13,1.04)	(0.04,1.06)	(−0.02,0.53)
95% CI (Fieller)	(0.08,1.05)	(−0.04,1.11)	(−0.06,0.52)
Potential surrogate: stair climbing from the WIQ
Estimate	0.122	0.1392	0.0695
SE	0.2099	0.1581	0.0913
95% CI (Quantile)	(−0.34,0.47)	(−0.08,0.52)	(−0.02,0.3)
95% CI (Fieller)	(−0.43,0.46)	(−0.17,0.51)	(−0.11,0.28)
All three potential surrogates
Estimate	0.4835	0.3801	0.1771
SE	0.3236	0.3095	0.1785
95% CI (Quantile)	(−0.21,1.06)	(0.04,1.12)	(−0.02,0.61)
95% CI (Fieller)	(−0.28,1.04)	(−0.06,1.07)	(−0.09,0.57)