Table 2.

Estimates of the hazard and its standard error for seven commonly used statistical time-to-event models studies in four hypothetical datasets

Dataset and model	Time period (years)
	0.5	1	1.5	2	2.5	3	3.5	4
Flat hazard
Empirical (smooth)	1.09 (0.35)	0.93 (1.11)
Exponential	1.16 (0.14)	1.16 (0.14)	1.16 (0.14)	1.16 (0.14)	1.16 (0.14)	1.16 (0.14)	1.16 (0.14)	1.16 (0.14)
Weibull	1.14 (0.16)	1.11 (0.21)	1.09 (0.24)	1.08 (0.27)	1.07 (0.28)	1.06 (0.30)	1.05 (0.31)	1.05 (0.33)
Gompertz	1.12 (0.14)	0.93 (0.27)	0.77 (0.38)	0.64 (0.47)	0.53 (0.53)	0.44 (0.58)	0.36 (0.61)	0.30 (0.64)
Gamma	1.15 (0.16)	1.14 (0.19)	1.13 (0.21)	1.13 (0.22)	1.13 (0.22)	1.13 (0.23)	1.13 (0.23)	1.12 (0.23)
Log-logistic	1.14 (0.17)	0.82 (0.13)	0.62 (0.09)	0.50 (0.07)	0.42 (0.06)	0.36 (0.05)	0.31 (0.04)	0.28 (0.04)
Log-normal	1.03 (0.14)	0.73 (0.11)	0.58 (0.09)	0.49 (0.08)	0.42 (0.07)	0.37 (0.06)	0.34 (0.06)	0.31 (0.05)
Gen. Gamma	1.12 (0.16)	0.94 (0.21)	0.83 (0.26)	0.75 (0.28)	0.69 (0.29)	0.64 (0.30)	0.61 (0.31)	0.57 (0.32)
Increasing hazard
Empirical (smooth)	0.80 (0.27)	2.73 (1.95)
Exponential	0.77 (0.09)	0.77 (0.09)	0.77 (0.09)	0.77 (0.09)	0.77 (0.09)	0.77 (0.09)	0.77 (0.09)	0.77 (0.09)
Weibull	0.72 (0.12)	3.01 (0.58)	6.94 (2.25)	12.53 (5.33)	19.83 (9.98)	28.86 (16.44)	39.63 (25.37)	52.15 (36.08)
Gompertz	0.58 (0.10)	4.02 (0.84)	28.02 (12.87)	195.31 (144.58)	1361.3 (1,497.7)	9488 (14,576)	66,130 (137,480)	460,913 (1,274,871)
Gamma	0.85 (0.13)	2.30 (0.38)	3.18 (0.57)	3.71 (0.71)	4.06 (0.80)	4.30 (0.85)	4.48 (0.89)	4.62 (0.92)
Log-logistic	0.79 (0.13)	2.28 (0.34)	2.18 (0.30)	1.78 (0.22)	1.46 (0.17)	1.23 (0.14)	1.06 (0.12)	0.93 (0.10)
Log-normal	0.96 (0.14)	1.86 (0.29)	2.01 (0.36)	1.96 (0.36)	1.86 (0.35)	1.76 (0.33)	1.66 (0.32)	1.57 (0.30)
Gen. Gamma	0.72 (0.13)	3.07 (0.78)	7.51 (7.56)	14.4 (35.33)	23.97 (113.17)	36.43 (260.86)	51.93 (330.16)	70.63 (370.34)
Decreasing hazard
Empirical (smooth)	1.05 (0.45)	1.18 (2.10)
Exponential	1.72 (0.20)	1.72 (0.20)	1.72 (0.20)	1.72 (0.20)	1.72 (0.20)	1.72 (0.20)	1.72 (0.20)	1.72 (0.20)
Weibull	1.01 (0.15)	0.73 (0.13)	0.60 (0.12)	0.53 (0.11)	0.47 (0.10)	0.43 (0.10)	0.4 (0.09)	0.38 (0.09)
Gompertz	1.14 (0.19)	0.36 (0.15)	0.11 (0.08)	0.04 (0.04)	0.01 (0.02)	< 0.01 (0.01)	< 0.01 (< 0.01)	< 0.01 (< 0.01)
Gamma	1.08 (0.16)	0.89 (0.15)	0.81 (0.15)	0.77 (0.15)	0.74 (0.15)	0.72 (0.15)	0.7 (0.15)	0.69 (0.15)
Log-logistic	0.82 (0.12)	0.48 (0.07)	0.34 (0.05)	0.27 (0.04)	0.22 (0.03)	0.19 (0.02)	0.16 (0.02)	0.15 (0.02)
Log-normal	0.68 (0.09)	0.40 (0.06)	0.29 (0.04)	0.23 (0.03)	0.19 (0.03)	0.17 (0.02)	0.15 (0.02)	0.13 (0.02)
Gen. Gamma	1.04 (0.17)	0.80 (0.20)	0.68 (0.23)	0.62 (0.25)	0.57 (0.27)	0.53 (0.29)	0.51 (0.30)	0.48 (0.31)
Unimodal hazard
Empirical (smooth)	1.33 (0.42)	1.41 (1.41)
Exponential	1.03 (0.12)	1.03 (0.12)	1.03 (0.12)	1.03 (0.12)	1.03 (0.12)	1.03 (0.12)	1.03 (0.12)	1.03 (0.12)
Weibull	1.27 (0.16)	2.04 (0.38)	2.69 (0.67)	3.28 (0.96)	3.82 (1.28)	4.33 (1.60)	4.81 (1.92)	5.27 (2.24)
Gompertz	1.09 (0.13)	2.26 (0.52)	4.69 (1.94)	9.73 (6.12)	20.17 (17.75)	41.81 (48.32)	86.68 (128.88)	179.69 (337.89)
Gamma	1.36 (0.18)	1.88 (0.31)	2.13 (0.38)	2.28 (0.43)	2.38 (0.46)	2.45 (0.48)	2.50 (0.49)	2.54 (0.50)
Log-logistic	1.47 (0.21)	1.52 (0.22)	1.23 (0.17)	0.99 (0.13)	0.82 (0.10)	0.70 (0.08)	0.60 (0.07)	0.53 (0.06)
Log-normal	1.45 (0.19)	1.46 (0.23)	1.31 (0.22)	1.18 (0.20)	1.07 (0.19)	0.98 (0.17)	0.90 (0.16)	0.84 (0.15)
Gen. Gamma	1.46 (0.19)	1.36 (0.31)	1.16 (0.39)	1.01 (0.43)	0.89 (0.44)	0.80 (0.44)	0.72 (0.44)	0.66 (0.43)

Gen. Gamma generalised gamma