Additional file 1 of Group sequential designs for pragmatic clinical trials with early outcomes: methods and guidance for planning and implementation
Creators: name: Parsons, Nick R.
name: Basu, Joydeep
name: Stallard, Nigel
Publisher: name: figshare
Year: 2024
Subjects: subject: Medicine
subject: Genetics
subject: FOS: Biological sciences
subject: Biological Sciences not elsewhere classified
subject: Information Systems not elsewhere classified
subject: Inorganic Chemistry
subject: FOS: Chemical sciences

description: Additional file 1: Figure S1. The feasible region of $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif  for s = 2 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S2. The feasible region of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif   for s = 3 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S3. The empirical distribution (nsim = 10000) of Δ $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif   , the difference from the median value of $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif , with varying 1 &lt; dr &lt; 2 (r = 2) for s = 3, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models. Figure S4. The feasible region of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif for s = 4 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3, 4; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S5. The empirical distribution (nsim = 10000) of Δ  , the difference from the median value of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif , with varying 1 &lt; dr &lt; 2 (r = 2, 3) for s = 4, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models. Figure S6. The feasible region of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif for s = 5 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3, 4, 5; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses.Figure S7. The empirical distribution (nsim = 10000) of Δ $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif , the difference from the median value of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif , with varying 1 &lt; dr &lt; 2 (r = 2, 3, 4) for s = 5, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models. Figure S8. The feasible region of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif for s = 6 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3, 4, 5, 6; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S9. The empirical distribution (nsim = 10000) of Δ $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif   , the difference from the median value of  $$\mathrm V_{\mathrm s}^{\mathrm{unif}}$$ V s unif , with varying 1 &lt; dr &lt; 2 (r = 2, 3, 4, 5) for s = 6, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ α &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models.Figure S10. The feasible region of Vexp s for s = 2 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2) for [a] early (τ 01= 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S11. The feasible region of Vexp s for s = 3 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S12. The empirical distribution (nsim = 10000) of ΔVexp s , the difference from the median value of Vexp s , with varying 1 &lt; dr &lt; 2 (r = 2) for s = 3, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models. Figure S13. The feasible region of Vexp s for s = 4 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3, 4; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S14. The empirical distribution (nsim = 10000) of ΔVexp s , the difference from the median value of Vexp s , with varying 1 &lt; dr &lt; 2 (r = 2, 3) for s = 4, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models. Figure S15. The feasible region of Vexp s for s = 5 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3, 4, 5; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S16. The empirical distribution (nsim = 10000) of ΔVexp s , the difference from the median value of Vexp s , with varying 1 &lt; dr &lt; 2 (r = 2, 3, 4) for s = 5, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models. Figure S17. The feasible region of Vexps for s = 6 (shaded areas), bounded above by the maximum and below by the minimum, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for the decreasing, fixed and increasing rate recruitment models with lines for the setting where the time-points are given by dr = 1+(r−1)/(s−1) (r = 1, 2, 3, 4, 5, 6; i.e. equal spacing) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses. Figure S18. The empirical distribution (nsim = 10000) of ΔVexp s , the difference from the median value of Vexp s , with varying 1 &lt; dr &lt; 2 (r = 2, 3, 4, 5) for s = 6, with shading showing quantiles 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, for correlations in the range 0 ≤ γ &lt; 1 and equal group sizes (ϕ = 0.5) for [a] early (τ 01 = 0.15), [b] mid (τ 02 = 0.30) and [c] late (τ 03 = 0.45) interim analyses, for the (i) increasing, (ii) fixed and (iii) decreasing rate recruitment models.