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Table 1 Clinical significance and precision of the log-hazard ratio according to the initial and final sample sizes

From: A sample size planning approach that considers both statistical significance and clinical significance

Δ loge(Δ) bλ c N Pr(LCL>δ/2 |H1) eCIW1 Pr(UCL<δ/2 |H0) dCIW0
1.25 0.22 1.12 aInitial 1264 0.2925 0.322 0.2651 0.314
    cFinal 5402 0.8241 0.155 0.8016 0.151
1.50 0.41 1.22 aInitial 384 0.2759 0.602 0.2658 0.577
    cFinal 1694 0.8349 0.285 0.8039 0.273
1.75 0.56 1.32 aInitial 204 0.2766 0.850 0.2536 0.804
    cFinal 938 0.8496 0.392 0.8021 0.371
2.00 0.69 1.41 aInitial 132 0.2700 1.087 0.2344 1.018
    cFinal 632 0.8503 0.487 0.8052 0.457
  1. The ainitial N calculated using equation (5), Schoenfeld’s [14] formula, is the total sample size required to detect a hazard ratio Δ at the 5% level with 80% power, assuming equal subject allocation and a 0.5 overall censoring proportion. b λ c is the hazard rate for the exponential censoring time given by equation (7), and δ. = loge(Δ). The cfinal N is the total sample size such that both Pr(LCL > δ /2 | H1) and Pr(UCL < δ /2 | H0) are at least 0.8 as estimated by the proportion of times LCL and UCL are bounded by δ /2 in 10,000 iterations. dCIW0 and eCIW1 are the mean width of the 95% confidence intervals under H0 and H1, respectively.