Data on 863 kidney transplant patients
Variables: 
  Observation number 
  Time to death or on-study time 
  Death indicator (0=alive, 1=dead) 
  Gender (1=male, 2=female) 
  Race (1=white, 2=black) 
  Age in years 

Model

model{  
  # Set up the c[ j ]s
  #  We have t[1]=0, t [ j]: j = 2,...,k +1 are distinct death times if 
  #  last observation is a death;  else, t[k+1] is last censoring time.
  #  Dimension of vector t is k+1
 c[1] <- 0
 for(i in 2:k+1){c[i] <- (t[i-1] + t[i])/2}
 c[k+2] <- t[k+1] + (t[k+1] - t[k])/2 
  # jth interval has  t [ j] in (c[ j ], c[ j+1 ]) j=2,...,k+1
 for(i in 1:n){   
   for(j in 1:(k+1)){  
     HH[i,j] <- step(y[i] - c[j] )  #  Indicates which interval y[i] is in
     H[i,j] <- HH[i,j]*(min(y[i],c[j+1]) -c[j] )
     N[i, j] <- HH[i, j]*step( c[j + 1] - y[i])*delta[i]  
 # Equals 1 iff y[i] is in interval j and delta[i]=1 
   }     
 }
 # Likelihood Construction
 for(i in 1:n){ 
   mu[i] <-   beta[1]*(sex[i]-1) + beta[2]*(race[i] -1)+ beta[3]*(age[i] - mean(age[]))/sd(age[])     
   for(j in 1:k+1){
     N[i, j]   ~ dpois(theta[i, j])             
     theta[i, j] <-  exp(mu[i])*H[i,j]*lam[j]
   }
 }   
 #  Prior for Baseline Hazard
 lamm <-  (10000)*(0.01) # exp(-c[2]*0.01) = 0.99
 lam[1] ~ dgamma(lamm,10000)
 for(j in 2:(k+1)){  # prior on baseline hazard bits 
   e[j] <- (c[j+1] -c[j])*w
   d[j] <- lamstar*e[j]
   lam[j] ~ dgamma(d[j], e[j])  
 }
# lamstar ~ dgamma(mm,ww)
#lamstarstar <- 0.15
#mm <- lamstarstar*ww
#ww<-1
 lamstar <- .0001
#  Inferences for survival functions
 for(j in 1:(k+1)){
   dH0[j] <- (c[j+1]-c[j])* lam[j]   # (H_0(c[j+1]) -  H_0(c[j]))
 # Survivor function at c[j+1] = exp{-H_0(c[j+1])e^mu[j] }    
 # Surv Fn for M and F among whites of average age
   S.wm[j] <- pow(exp(-sum(dH0[1 : j])), 1);
   S.wf[j] <- pow(exp(-sum(dH0[1 : j])), exp(beta[1]))
   S.wdiff[j] <- S.wm[j] - S.wf[j]  # Diff in survival probabilities   
 #Surv Fn for M and F among blacks of average age
   S.bm[j] <- pow(exp(-sum(dH0[1 : j])), exp(beta[2]));
   S.bf[j] <- pow(exp(-sum(dH0[1 : j])), exp(beta[1]+beta[2] ))
   S.bdiff[j] <- S.bm[j] - S.bf[j]
#  Surv Fn for WF aged 2sd above the mean
   S.age.2.wf[j]  <-  pow(exp(-sum(dH0[1 : j])), exp(beta[1] +2*beta[3]))   
   S.agediff[j] <- S.wf[j] - S.age.2.wf[j]   
 }
#  Inferences for the HRs and prior on the betas
 for(j in 1:3){
   HR[j] <- exp(beta[ j ]) # relative hazards
   beta[ j ] ~ dnorm(0.0,0.000001)   
   prob[ j ] <- step(beta[ j ])
 }

# Junk in the data file
junk <- I[1]
}

INITS

list(beta = c(0,0,0),
lam =c(
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1 ,
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)   )

DATA

list(n = 863, k = 129, w= 0.001,   
 t =c(0,2, 3, 7, 10, 17, 21, 26, 28, 37, 40, 43, 44, 45, 50, 52, 56,
57, 59, 62, 68, 69, 78, 79, 88, 91, 97, 98, 104, 106, 119, 121,
135, 143, 150, 154, 158, 162, 190, 206, 209, 228, 229, 242, 248,
249, 252, 273, 291, 297, 311, 334, 340, 344, 346, 354, 366, 391,
402, 421, 439, 450, 470, 478, 481, 490, 495, 570, 583, 614, 615,
621, 652, 697, 730, 773, 776, 790, 793, 806, 840, 852, 864, 875,
929, 939, 943, 945, 946, 1001, 1013, 1016, 1105, 1164, 1186,
1191, 1196, 1210, 1275, 1326, 1331, 1357, 1384, 1388, 1418, 1473,
1509, 1734, 1777, 1820, 1835, 1877, 1940, 2034, 2056, 2108, 2171,
2276, 2291, 2301, 2313, 2369, 2414, 2421, 2489, 2557, 2567, 2650,
2795, 3146)   )

I[]       y[]    delta[]  sex[]  race[]  age[]
   1        1       0      1       1      46
   2        5       0      1       1      51
   3        7       1      1       1      55
   4        9       0      1       1      57
   5       13       0      1       1      45
   6       13       0      1       1      43
   7       17       1      1       1      47
   8       20       0      1       1      65
   9       26       1      1       1      55
  10       26       1      1       1      44
  11       28       1      1       1      49
  12       32       0      1       1      52
  13       32       0      1       1      31
  14       43       0      1       1      63
  15       43       1      1       1      55
  16       44       1      1       1      50
  17       51       0      1       1      49
  18       51       0      1       1      35
  19       51       0      1       1      23
  20       56       1      1       1      57
  21       57       1      1       1      45
  22       59       1      1       1      41
  23       62       1      1       1      38
  24       66       0      1       1      55
  25       66       0      1       1      45
  26       67       0      1       1      44
  27       68       1      1       1      45
  28       69       1      1       1      65
  29       79       0      1       1      66
  30       79       1      1       1      57
  31       79       0      1       1      52
  32       87       0      1       1      38
  33       88       1      1       1      49
  34       91       1      1       1      44
  35       93       0      1       1      28
  36       98       1      1       1      64
  37       98       1      1       1      43
  38      104       0      1       1      11
  39      105       0      1       1      45
  40      106       1      1       1      59
  41      112       0      1       1      40
  42      116       0      1       1      65
  43      116       0      1       1      33
  44      118       0      1       1      53
  45      119       1      1       1      42
  46      121       0      1       1      51
  47      121       0      1       1      25
  48      135       1      1       1      33
  49      144       0      1       1      65
  50      150       1      1       1      42
  51      150       0      1       1      41
  52      162       1      1       1      68
  53      162       0      1       1      61
  54      167       0      1       1      19
  55      183       0      1       1      61
  56      186       0      1       1      42
  57      190       1      1       1      54
  58      198       0      1       1      43
  59      198       0      1       1      42
  60      200       0      1       1      37
  61      211       0      1       1      46
  62      215       0      1       1      42
  63      223       0      1       1      45
  64      224       0      1       1      28
  65      228       1      1       1      52
  66      236       0      1       1      32
  67      238       0      1       1      38
  68      242       1      1       1      35
  69      243       0      1       1      24
  70      248       1      1       1      46
  71      249       1      1       1      49
  72      251       0      1       1      49
  73      252       1      1       1      48
  74      253       0      1       1      62
  75      256       0      1       1      65
  76      257       0      1       1      38
  77      259       0      1       1      75
  78      261       0      1       1      48
  79      271       0      1       1      68
  80      271       0      1       1      39
  81      277       0      1       1      42
  82      283       0      1       1      37
  83      284       0      1       1      45
  84      289       0      1       1      33
  85      291       1      1       1      66
  86      311       1      1       1      66
  87      312       0      1       1      53
  88      316       0      1       1      52
  89      316       0      1       1      51
  90      331       0      1       1      58
  91      334       1      1       1      63
  92      338       0      1       1      27
  93      340       0      1       1      48
  94      340       1      1       1      41
  95      341       0      1       1      28
  96      346       1      1       1      49
  97      347       0      1       1      42
  98      354       1      1       1      45
  99      361       0      1       1      44
 100      367       0      1       1      37
 101      370       0      1       1      56
 102      370       0      1       1      55
 103      386       0      1       1      42
 104      391       1      1       1      60
 105      392       0      1       1      66
 106      403       0      1       1      61
 107      406       0      1       1      57
 108      410       0      1       1      44
 109      421       1      1       1      67
 110      428       0      1       1      62
 111      432       0      1       1      54
 112      432       0      1       1      26
 113      439       1      1       1      57
 114      452       0      1       1      55
 115      478       1      1       1      54
 116      481       1      1       1      58
 117      485       0      1       1      56
 118      486       0      1       1      23
 119      490       0      1       1      21
 120      494       0      1       1      58
 121      495       1      1       1      47
 122      512       0      1       1      60
 123      512       0      1       1      55
 124      535       0      1       1      44
 125      543       0      1       1      50
 126      545       0      1       1      58
 127      545       0      1       1      53
 128      545       0      1       1      43
 129      563       0      1       1      40
 130      570       0      1       1      65
 131      570       1      1       1      34
 132      572       0      1       1      52
 133      579       0      1       1      62
 134      582       0      1       1      11
 135      583       1      1       1      70
 136      590       0      1       1      59
 137      596       0      1       1      53
 138      615       1      1       1      48
 139      621       1      1       1      25
 140      630       0      1       1      62
 141      631       0      1       1      17
 142      633       0      1       1      53
 143      652       1      1       1      57
 144      654       0      1       1      43
 145      655       0      1       1      45
 146      659       0      1       1      49
 147      670       0      1       1      24
 148      670       0      1       1      62
 149      692       0      1       1      48
 150      697       1      1       1      41
 151      701       0      1       1      42
 152      719       0      1       1      35
 153      723       0      1       1      46
 154      725       0      1       1      23
 155      730       1      1       1      56
 156      734       0      1       1      51
 157      753       0      1       1      45
 158      757       0      1       1      20
 159      773       1      1       1      34
 160      776       1      1       1      43
 161      790       1      1       1      62
 162      806       1      1       1      64
 163      834       0      1       1      18
 164      835       0      1       1      63
 165      864       0      1       1      54
 166      864       0      1       1      40
 167      875       1      1       1      51
 168      888       0      1       1      67
 169      890       0      1       1      40
 170      903       0      1       1      59
 171      909       0      1       1      46
 172      915       0      1       1      46
 173      932       0      1       1      36
 174      939       1      1       1      54
 175      945       1      1       1      42
 176      945       1      1       1      41
 177      946       1      1       1      67
 178      951       0      1       1      61
 179      961       0      1       1      38
 180      965       0      1       1      19
 181      968       0      1       1      27
 182     1016       0      1       1      54
 183     1028       0      1       1      26
 184     1050       0      1       1      42
 185     1058       0      1       1      58
 186     1058       0      1       1      54
 187     1092       0      1       1      45
 188     1092       0      1       1      40
 189     1105       1      1       1      57
 190     1110       0      1       1      46
 191     1110       0      1       1      37
 192     1114       0      1       1      41
 193     1115       0      1       1      51
 194     1118       0      1       1      34
 195     1124       0      1       1      53
 196     1124       0      1       1      40
 197     1125       0      1       1      38
 198     1128       0      1       1      23
 199     1128       0      1       1      21
 200     1145       0      1       1      43
 201     1149       0      1       1      40
 202     1154       0      1       1      67
 203     1154       0      1       1      36
 204     1165       0      1       1      52
 205     1186       1      1       1      37
 206     1191       1      1       1      44
 207     1196       0      1       1      33
 208     1208       0      1       1      38
 209     1208       0      1       1      25
 210     1210       1      1       1      66
 211     1224       0      1       1      49
 212     1224       0      1       1      39
 213     1229       0      1       1      45
 214     1230       0      1       1      48
 215     1252       0      1       1      58
 216     1256       0      1       1      40
 217     1274       0      1       1      48
 218     1291       0      1       1      31
 219     1297       0      1       1      45
 220     1297       0      1       1      44
 221     1302       0      1       1      33
 222     1313       0      1       1      63
 223     1316       0      1       1      33
 224     1350       0      1       1      46
 225     1357       1      1       1      64
 226     1383       0      1       1      56
 227     1383       0      1       1      56
 228     1383       0      1       1      53
 229     1383       0      1       1      30
 230     1386       0      1       1      68
 231     1388       1      1       1      48
 232     1395       0      1       1       3
 233     1418       1      1       1      67
 234     1428       0      1       1      27
 235     1429       0      1       1      33
 236     1435       0      1       1      58
 237     1449       0      1       1      61
 238     1449       0      1       1      42
 239     1450       0      1       1      41
 240     1457       0      1       1      37
 241     1463       0      1       1      38
 242     1470       0      1       1      63
 243     1497       0      1       1      46
 244     1497       0      1       1      35
 245     1500       0      1       1      22
 246     1509       1      1       1      57
 247     1522       0      1       1      49
 248     1527       0      1       1      54
 249     1527       0      1       1      30
 250     1541       0      1       1      39
 251     1567       0      1       1      28
 252     1571       0      1       1      38
 253     1578       0      1       1      46
 254     1586       0      1       1      43
 255     1594       0      1       1      35
 256     1610       0      1       1      67
 257     1610       0      1       1      60
 258     1611       0      1       1      62
 259     1617       0      1       1      53
 260     1624       0      1       1      24
 261     1638       0      1       1      34
 262     1641       0      1       1      38
 263     1655       0      1       1      31
 264     1668       0      1       1      31
 265     1674       0      1       1      34
 266     1699       0      1       1      38
 267     1700       0      1       1      49
 268     1700       0      1       1      34
 269     1707       0      1       1      41
 270     1717       0      1       1      31
 271     1717       0      1       1      31
 272     1718       0      1       1      54
 273     1718       0      1       1      40
 274     1734       1      1       1      55
 275     1736       0      1       1      42
 276     1736       0      1       1      42
 277     1739       0      1       1      34
 278     1739       0      1       1      27
 279     1739       0      1       1      25
 280     1745       0      1       1      64
 281     1745       0      1       1      52
 282     1746       0      1       1      53
 283     1749       0      1       1      55
 284     1770       0      1       1      45
 285     1770       0      1       1      32
 286     1795       0      1       1      30
 287     1802       0      1       1      56
 288     1802       0      1       1      31
 289     1803       0      1       1      38
 290     1808       0      1       1      43
 291     1808       0      1       1      41
 292     1815       0      1       1      57
 293     1820       1      1       1      44
 294     1839       0      1       1      31
 295     1861       0      1       1      38
 296     1861       0      1       1      20
 297     1893       0      1       1      20
 298     1900       0      1       1      48
 299     1920       0      1       1      40
 300     1937       0      1       1      31
 301     1947       0      1       1      61
 302     1947       0      1       1      37
 303     1959       0      1       1      41
 304     1959       0      1       1      30
 305     1975       0      1       1      31
 306     1988       0      1       1      55
 307     1988       0      1       1      32
 308     1995       0      1       1      59
 309     1995       0      1       1      57
 310     2001       0      1       1      55
 311     2016       0      1       1      52
 312     2025       0      1       1      23
 313     2032       0      1       1      59
 314     2035       0      1       1      30
 315     2038       0      1       1      25
 316     2041       0      1       1      29
 317     2043       0      1       1      30
 318     2048       0      1       1      44
 319     2049       0      1       1      40
 320     2056       1      1       1      62
 321     2060       0      1       1      32
 322     2090       0      1       1      41
 323     2090       0      1       1      38
 324     2095       0      1       1      44
 325     2096       0      1       1      47
 326     2096       0      1       1      41
 327     2098       0      1       1      38
 328     2102       0      1       1      44
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 330     2135       0      1       1      42
 331     2135       0      1       1      31
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 333     2190       0      1       1      38
 334     2211       0      1       1      36
 335     2221       0      1       1      47
 336     2223       0      1       1      24
 337     2253       0      1       1      45
 338     2253       0      1       1      18
 339     2264       0      1       1      28
 340     2267       0      1       1      36
 341     2270       0      1       1      55
 342     2291       1      1       1      56
 343     2291       0      1       1      20
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 345     2313       0      1       1      47
 346     2313       0      1       1      30
 347     2330       0      1       1      37
 348     2332       0      1       1      26
 349     2335       0      1       1      61
 350     2356       0      1       1      33
 351     2367       0      1       1      38
 352     2384       0      1       1      31
 353     2418       0      1       1      34
 354     2421       0      1       1      55
 355     2421       1      1       1      40
 356     2430       0      1       1      35
 357     2433       0      1       1      36
 358     2434       0      1       1      59
 359     2462       0      1       1      40
 360     2462       0      1       1      35
 361     2488       0      1       1      12
 362     2489       1      1       1      61
 363     2497       0      1       1      44
 364     2516       0      1       1      32
 365     2531       0      1       1      12
 366     2533       0      1       1      63
 367     2575       0      1       1      32
 368     2585       0      1       1      61
 369     2589       0      1       1      35
 370     2601       0      1       1      38
 371     2607       0      1       1      55
 372     2625       0      1       1      56
 373     2630       0      1       1      38
 374     2646       0      1       1      50
 375     2654       0      1       1       2
 376     2690       0      1       1      23
 377     2696       0      1       1      51
 378     2700       0      1       1      35
 379     2712       0      1       1      38
 380     2714       0      1       1      36
 381     2716       0      1       1      25
 382     2716       0      1       1      20
 383     2740       0      1       1      36
 384     2761       0      1       1      51
 385     2762       0      1       1      51
 386     2765       0      1       1      42
 387     2789       0      1       1      39
 388     2789       0      1       1      35
 389     2812       0      1       1      24
 390     2815       0      1       1      34
 391     2827       0      1       1      37
 392     2831       0      1       1      56
 393     2846       0      1       1      25
 394     2867       0      1       1      38
 395     2871       0      1       1      41
 396     2889       0      1       1      48
 397     2909       0      1       1      25
 398     2922       0      1       1      28
 399     2936       0      1       1      56
 400     2948       0      1       1      58
 401     2955       0      1       1      45
 402     2957       0      1       1      41
 403     2994       0      1       1      47
 404     2994       0      1       1      26
 405     2999       0      1       1      65
 406     3007       0      1       1      54
 407     3045       0      1       1      51
 408     3060       0      1       1      33
 409     3078       0      1       1      53
 410     3078       0      1       1      44
 411     3084       0      1       1      55
 412     3084       0      1       1      35
 413     3110       0      1       1      59
 414     3130       0      1       1      23
 415     3131       0      1       1      39
 416     3146       1      1       1      37
 417     3147       0      1       1      45
 418     3172       0      1       1      61
 419     3179       0      1       1      44
 420     3187       0      1       1      36
 421     3187       0      1       1      26
 422     3255       0      1       1      46
 423     3260       0      1       1      30
 424     3287       0      1       1      42
 425     3289       0      1       1      22
 426     3300       0      1       1      41
 427     3301       0      1       1       6
 428     3319       0      1       1      29
 429     3361       0      1       1      42
 430     3402       0      1       1      40
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END