TABLE 4A.

Performance of PT method using 10 000 simulations (r = 1 in all cases, one-sided test) when the proportional hazards assumption is true

Baseline Distribution (Control Group)	n/ΔHR/Power	Approximated ${\widehat{\mathrm{\Delta }}}_{\text{PT}}$	% Empirical Power
Exponential	12/0.35/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2.857$	78.90
λ = 1, σ = 1 d = 1	16/0.35/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2.857$	88.95
Generalized gammaa	15/0.40/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.501$	82.47
λ = 0.832, σ = 0.416 d = 1	21/0.40/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.501$	92.23
Generalized gammaa	15/0.40/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.215$	80.28
λ = 0.832, σ = 0.208 d = 1	21/0.40/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.215$	90.48
Inverse gamma	20/0.45/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.889$	78.89
λ = −0.8, σ = 0.8 d = 1	27/0.45/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.889$	88.95
Log-logisticc	26/0.50/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=3.251$	79.26
μlocation = 1.08, Sscale = 0.9882 d = 1	36/0.50/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=3.251$	88.85
Exponentiated Weibullc	35/0.55/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2.075$	79.30
λ = 1, σ = 2, αshape = 2 d = 1	48/0.55/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2.075$	88.86
Generalized gammaa	48/0.6/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.090$	80.30
λ = 0.832, σ = 0.166 d = 0.25	66/0.6/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.090$	90.41
Generalized gammab	54/0.62/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2$	80.62
λ = −1.992, σ = 1.414 d = 0.766	75/0.62/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2$	90.28
2-parameter gamma	97/0.70/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2.050$	79.48
λ = 2, σ = 2 d = 1	135/0.70/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=2.050$	89.40
Ammag	150/0.75/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.776$	79.76
λ = 0.5, σ = 2 d = 1	207/0.75/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.776$	90.33
Inverse Weibull	299/0.80/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.450$	79.59
λ = −1, σ = 1.667 d = 1	344/0.80/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.450$	89.38
Inverse Ammag	469/0.85/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.115$	80.20
λ = −0.817, σ = 1.225 d = 1	649/0.85/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.115$	89.99
Standard gamma	1114/0.9/0.8	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.427$	79.82
λ = 1.5, σ = 1 d = 1	1543/0.9/0.9	${\widehat{\mathrm{\Delta }}}_{\text{PT}}=1.427$	90.17

^aThese simulations represent the scenarios presented in Figure 4B–D.

^bThis scenario represents the motivating example discussed in the text.

^cBaseline distribution is not from the generalized gamma family.