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Table 4 Goodness-of-fit tests and estimated mean survival times for five parametric distributions, patients with metastatic colorectal cancer, Norway 1991-2005

From: Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

Period

Model

χ ob 1 s 2

d.f.

p

Mean

90% CI

1991-1996

Gamma

225.1

62

0.0000

-

-

 

Gompertz

75.9

55

0.0324

-

 

Log-Logistic

81.3

56

0.0151

2.29

(2.06; 2.58)

 

Log-Normal

116.9

58

0.0000

1.61

(1.49; 1.75)

 

Weibull

179.7

60

0.0000

1.19

(1.06; 1.34)

1997-2001

Gamma

154.2

60

0.0000

1.25

(0.91; 1.50)

 

Gompertz

79.2

53

0.0114

-

 

Log-Logistic

80.8

55

0.0135

3.20

(2.80; 3.79)

 

Log-Normal

98.2

56

0.0004

2.06

(1.92; 2.22)

 

Weibull

137.5

60

0.0000

1.71

(1.56; 1.87)

2002-2005

Gamma

46.9

36

0.1053

1.89

(1.77; 2.02)

 

Gompertz

44.5

35

0.1312

-

 

Log-Logistic

43.1

34

0.1358

3.14

(2.76; 3.65)

 

Log-Normal

45.3

35

0.1142

2.39

(2.24; 2.54)

 

Weibull

46.4

37

0.1392

1.92

(1.81; 2.05)

All

Gamma

319.7

81

0.0000

1.23

(1.06; 1.38)

 

Gompertz

135.8

70

0.0000

-

 

Log-Logistic

127.5

74

0.0001

2.87

(2.67; 3.11)

 

Log-Normal

170.0

77

0.0000

2.01

(1.93; 2.09)

 

Weibull

277.1

79

0.0000

1.64

(1.55; 1.73)

  1. Could not be meaningfully estimated due to unreliable parameter estimates (the estimated standard error of the α parameter approached infinity).
  2. Goodness-of-fit χ2 test statistics, degrees of freedom (d.f.), and p-value is given for each period and all data pooled. The mean survival times are based on 10,000 draws from a bivariate normal distribution given by the estimated parameters and their covariance. For each draw a mean is computed with the appropriate formula given in Table 2, and the median together with 5% and 95% percentiles of this posterior distribution are used as estimate and confidence interval, respectively.