Table 5 Results summary for the data application of the PCR under M2 and M3 with Weibull and log-logistic AFT models. Note that the priors with \(\sigma ^2\sim IG(0.001, 0.001)\) and \({\textbf {R}}=Diag\{100,\dots ,100\}\) are used except that for M3\(^{*}\) with \(\sigma ^2\sim IG(0.001, 0.001)\) and \({\textbf {R}}=Diag\{10,\dots ,10\}\). EST: parameter estimate; CL: credible limit; IG: inverse gamma

Serum PSA

-0.167(-0.180, -0.152)

-0.155(-0.177, -0.121)

-0.202(-0.218, -0.179)

-0.203(-0.236, -0.167)

-0.229 (-0.232, -0.190)

Age at diagnosis

 >=65

REF

REF

REF

REF

REF

 <65

0.386(0.352, 0.414)

0.395(0.359, 0.428)

0.460(0.403, 0.494)

0.450(0.401, 0.489)

0.474 (0.472, 0.543)

Insurance

 Yes

REF

REF

REF

REF

REF

 No

0.057(0.009, 0.097)

-0.092(-0.155, -0.013)

0.036(-0.026, 0.088)

-0.167(-0.235, -0.069)

-0.151 (-0.142, -0.030)

Appalachian

 No

REF

REF

REF

REF

REF

 Yes

0.106(-0.068, 0.418)

-0.031(-0.153, 0.073)

0.061(-0.092, 0.547)

-0.107(-0.165, -0.081)

3.671 (4.003, 6.009)

Treatment at diagnosis

 Neither Surgery or Radiation

REF

REF

REF

REF

REF

 Surgery only

0.974(0.909, 1.039)

0.978(0.917, 1.043)

1.097(1.049, 1.175)

1.106(1.054, 1.168)

1.152 (1.129, 1.237)

 Radiation only

0.446(0.408, 0.483)

0.453(0.412, 0.493)

0.588(0.558, 0.616)

0.571(0.542, 0.614)

0.607 (0.610, 0.687)

 Surgery and Radiation

1.071(0.963, 1.205)

1.015(0.911, 1.158)

1.279(1.077, 1.471)

1.240(1.081, 1.399)

1.328 (1.307, 1.512)

 Others/Unknown

-0.246(-0.352, -0.125)

-0.102(-0.188, 0.054)

-0.312(-0.457, -0.101)

-0.224(-0.448, -0.057)

-0.294 (-0.281, -0.129)

Race

 White

REF

REF

REF

REF

REF

 Black

-0.109(-0.150, -0.068)

-0.217(-0.285, -0.123)

-0.116(-0.170, -0.044)

-0.184(-0.234, -0.114)

-0.150 (-0.140, -0.061)

 Others/Unknown

0.601(0.497, 0.696)

0.537(0.322, 0.724)

0.644(0.459, 0.809)

0.665(0.563, 0.784)

0.712 (0.710, 0.868)

Stage of Aggressiveness

 Less Aggressive

REF

REF

REF

REF

REF

 More Aggressive

-0.435(-0.469, -0.408)

-0.453(-0.516, -0.409)

-0.528(-0.554, -0.499)

-0.525(-0.553, -0.486)

-0.593 (-0.594, -0.544)

 Unknown

-0.117(-0.161, -0.071)

-0.129(-0.231, -0.057)

-0.117(-0.202, -0.068)

-0.072(-0.136, -0.017)

-0.155 (-0.138, -0.071)

Year(Cont)

0.044(0.039, 0.052)

-

0.075(0.068, 0.086)

-

-

 Year=2004

-

REF

-

REF

REF

 Year=2005

-

-0.661(-1.413, -0.056)

-

-0.036(-0.107, 0.078)

-1.034 (-1.076, -0.099)

 Year=2006

-

0.106(-0.084, 0.224)

-

-0.114(-0.157, 0.022)

-0.374 (-0.419, -0.090)

 Year=2007

-

-0.192(-0.495, 0.131)

-

-0.112(-0.165, 0.037)

-1.091 (-1.155, -0.361)

 Year=2008

-

-0.529(-0.900, -0.221)

-

-0.103(-0.165, 0.050)

-1.706 (-1.782, -0.620)

 Year=2009

-

0.095(-0.570, 0.781)

-

-0.053(-0.159, 0.110)

0.453 (0.474, 0.776)

 Year=2010

-

0.416(-0.026, 0.741)

-

0.052(-0.030, 0.191)

0.977 (0.993, 1.244)

 Year=2011

-

1.526(0.761, 1.891)

-

0.277(0.193, 0.407)

2.028 (1.653, 3.679)

 Year=2012

-

1.495(0.754, 1.901)

-

0.267(0.193, 0.403)

1.997 (1.653, 3.633)

 Year=2013

-

2.214(1.514, 2.996)

-

0.619(0.536, 0.765)

2.470 (2.242, 3.888)

 Year=2014

-

5.375(2.499, 7.816)

-

1.271(1.018, 1.553)

5.167 (5.337, 7.368)

Model Diagnosis

 DIC

80202.51

89965.28

35360.85

34867.03

16397.44