UCLA Academic Technology Services HomeServicesClassesContactJobs
Search

Stata Textbook Examples
Applied Survival Analysis by Hosmer and Lemeshow
Chapter 5: Model Development

The data files used for the examples in this text can be downloaded in a zip file from the Wiley FTP website or the Stata Web site.  You can then use a program such as WinZip to unzip the data files.  If you need assistance getting data into Stata, please see our Stata Class Notes, especially the unit on Entering Data.  (NOTE:  The *.dat files are the data files, and the *.txt files contain the codebook information.)
Partial likelihood ratio test from Table 5.1, page 166.
Note: Much of the output is omitted since only the p-value for the likelihood ratio chi-square is needed.
use uis, clear

stset time, failure(censor)
xi: stcox i.hercoc, nohr

                                                   LR chi2(3)      =      7.76
Log likelihood  =   -2855.2457                     Prob > chi2     =    0.0513

stci, by(hercoc)

             |    no. of
hercoc       |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           1 |       111         150      10.19877          106        196
           2 |       114         142      8.867892          110        184
           3 |       178         183      11.40735          147        226
           4 |       207         181      8.826439          153        220
-------------+-------------------------------------------------------------
       total |       610         168      9.223978          153        186

xi: stcox i.ivhx, nohr

                                                   LR chi2(2)      =     14.64
Log likelihood  =   -2851.8054                     Prob > chi2     =    0.0007


stci, by(ivhx)

             |    no. of
ivhx         |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           1 |       233         194      8.682577          171        228
           2 |       115         170      13.43096          129        226
           3 |       262         147      9.493609          113        168
-------------+-------------------------------------------------------------
       total |       610         168      9.223978          153        186

xi: stcox i.race, nohr

                                                   LR chi2(1)      =      7.57
Log likelihood  =   -2927.6972                     Prob > chi2     =    0.0059

stci, by(race)

             |    no. of
race         |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           0 |       467         152      10.46316          124        174
           1 |       155         193      9.202173          162        232
-------------+-------------------------------------------------------------
       total |       622         166      9.025591          147        183

xi: stcox i.treat, nohr

                                                   LR chi2(1)      =      6.75
Log likelihood  =   -2957.1293                     Prob > chi2     =    0.0094

stci, by(treat)

             |    no. of
treat        |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           0 |       320         131      7.477745          113        154
           1 |       308         190      8.618466          175        224
-------------+-------------------------------------------------------------
       total |       628         166      9.112655          144        183

xi: stcox i.site, nohr

                                                   LR chi2(1)      =      2.40
Log likelihood  =   -2959.3033                     Prob > chi2     =    0.1211

stci, by(site)

             |    no. of
site         |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           0 |       444         156      9.039492          130        174
           1 |       184         198      10.03484          159        228
-------------+-------------------------------------------------------------
       total |       628         166      9.112655          144        183

generate age2 = recode(age,27,32,37,56)
recode age2 27=1 32=2 37=3 56=4
xi: stcox i.age2, nohr

                                                   LR chi2(3)      =      3.81
Log likelihood  =   -2931.2058                     Prob > chi2     =    0.2823

stci, by(age2)

             |    no. of
age2         |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           1 |       158         159      11.22693          121        194
           2 |       158         148      8.254827          123        177
           3 |       184         162      10.46207          121        200
           4 |       123         189      9.008079          162        237
-------------+-------------------------------------------------------------
       total |       623         167      9.075607          148        184

generate beckt2 = recode(becktota,9.99,14.9,24.9,55)
recode beckt2 9.99=1 14.9=2 24.9=3 55=4
xi: stcox i.beckt2, nohr

                                                   LR chi2(3)      =      4.41
Log likelihood  =   -2760.8369                     Prob > chi2     =    0.2208

stci, by(beckt2)


             |    no. of
beckt2       |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           1 |       135         211      9.888823          166        246
           2 |       102         169      8.607335          124        220
           3 |       226         168      9.391813          136        199
           4 |       132         144         8.051          110        187
-------------+-------------------------------------------------------------
       total |       595         170      8.557824          156        189

generate ndrugt2 = ndrugtx
recode ndrugt2 0/1=1 2/3=2 4/6=3 7/40=4
xi: stcox i.ndrugtx2, nohr

                                                   LR chi2(3)      =     14.50
Log likelihood  =   -2867.7232                     Prob > chi2     =    0.0023

stci, by(ndrugt2)

             |    no. of
ndrugt2      |  subjects         50%     Std. Err.     [95% Conf. Interval]
-------------+-------------------------------------------------------------
           1 |       183         170       12.6755          140        227
           2 |       165         177      5.798958          161        207
           3 |       138         127      9.139421          106        183
           4 |       125         123      10.21114          106        184
-------------+-------------------------------------------------------------
       total |       611         166      8.952557          144        182
Table 5.2, page 167.
generate age3 =  qge/5
stcox age

Cox regression -- Breslow method for ties

No. of subjects =          623                     Number of obs   =       623
No. of failures =          504
Time at risk    =       146816
                                                   LR chi2(1)      =      3.24
Log likelihood  =   -2931.4929                     Prob > chi2     =    0.0719

------------------------------------------------------------------------------
          _t |
          _d | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        age3 |   .9377044   .0337048    -1.79   0.074     .8739175    1.006147
------------------------------------------------------------------------------

generate beckt3 = becktota/10
stcox beckt3

Cox regression -- Breslow method for ties

No. of subjects =          595                     Number of obs   =       595
No. of failures =          478
Time at risk    =       144013
                                                   LR chi2(1)      =      5.32
Log likelihood  =   -2760.3812                     Prob > chi2     =    0.0211

------------------------------------------------------------------------------
          _t |
          _d | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      beckt3 |   1.115852   .0526159     2.32   0.020     1.017348    1.223892
------------------------------------------------------------------------------

generate ndrugt3 = ndrugtx/5
stcox ndrugt3

Cox regression -- Breslow method for ties

No. of subjects =          611                     Number of obs   =       611
No. of failures =          496
Time at risk    =       143002
                                                   LR chi2(1)      =     13.35
Log likelihood  =    -2868.299                     Prob > chi2     =    0.0003

------------------------------------------------------------------------------
          _t |
          _d | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     ndrugt3 |   1.158192     .04342     3.92   0.000     1.076141    1.246498
------------------------------------------------------------------------------
Table 5.3, page 168.
xi: stcox age becktota ndrugtx i.hercoc i.ivhx race treat site, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(11)     =     47.91
Log likelihood  =   -2640.0305                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0288716   .0081716    -3.53   0.000    -.0448876   -.0128556
    becktota |    .008342   .0049756     1.68   0.094      -.00141    .0180939
     ndrugtx |   .0283735   .0083064     3.42   0.001     .0120934    .0446537
  _Ihercoc_2 |   .0653182   .1500091     0.44   0.663    -.2286942    .3593307
  _Ihercoc_3 |  -.0936223   .1654656    -0.57   0.572    -.4179288    .2306843
  _Ihercoc_4 |   .0279784   .1602768     0.17   0.861    -.2861584    .3421152
    _Iivhx_2 |   .1743865   .1386377     1.26   0.208    -.0973384    .4461115
    _Iivhx_3 |   .2807122   .1469297     1.91   0.056    -.0072648    .5686891
        race |  -.2028896   .1166875    -1.74   0.082    -.4315929    .0258137
       treat |  -.2399473   .0943704    -2.54   0.011    -.4249099   -.0549847
        site |  -.1024875   .1092668    -0.94   0.348    -.3166465    .1116716
------------------------------------------------------------------------------
Table 5.4, page 168.
lrtest, saving(0)

xi: stcox age becktota ndrugtx i.ivhx race treat site, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(8)      =     46.51
Log likelihood  =   -2640.7278                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   -.028217     .00817    -3.45   0.000    -.0442298   -.0122042
    becktota |   .0079385   .0049673     1.60   0.110    -.0017972    .0176741
     ndrugtx |   .0277628   .0082863     3.35   0.001      .011522    .0440035
    _Iivhx_2 |   .1959922   .1372134     1.43   0.153    -.0729412    .4649255
    _Iivhx_3 |   .3327979    .119912     2.78   0.006     .0977746    .5678212
        race |  -.2092451   .1158944    -1.81   0.071    -.4363939    .0179037
       treat |  -.2317746    .093713    -2.47   0.013    -.4154487   -.0481006
        site |  -.0994619   .1085414    -0.92   0.359    -.3121991    .1132753
------------------------------------------------------------------------------

lrtest  /* shown on page 167 */

Cox:  likelihood-ratio test                           chi2(3)     =       1.39
                                                      Prob > chi2 =     0.7068
Table 5.5, page 169.
lrtest, saving(0)
rename _livhx_3 ivhx3

stcox age becktota ndrugtx ivhx3 race treat site, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(7)      =     44.51
Log likelihood  =   -2641.7294                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0261517   .0080491    -3.25   0.001    -.0419276   -.0103758
    becktota |   .0083976   .0049516     1.70   0.090    -.0013074    .0181025
     ndrugtx |   .0290737   .0082126     3.54   0.000     .0129773      .04517
       ivhx3 |   .2561209   .1062996     2.41   0.016     .0477776    .4644642
        race |   -.224462   .1152656    -1.95   0.051    -.4503784    .0014544
       treat |  -.2324266   .0937326    -2.48   0.013    -.4161392    -.048714
        site |  -.0866855   .1078637    -0.80   0.422    -.2980944    .1247233
------------------------------------------------------------------------------

lrtest

Cox:  likelihood-ratio test                           chi2(1)     =       2.00
                                                      Prob > chi2 =     0.1570
Table 5.6, page 170.
xi: stcox i.age2 i.beckt2 i.ndrugt2 ivhx3 race treat site, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(13)     =     47.24
Log likelihood  =   -2640.3652                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _Iage2_2 |   .0374926   .1316518     0.28   0.776    -.2205402    .2955254
    _Iage2_3 |  -.2408561   .1312281    -1.84   0.066    -.4980584    .0163462
    _Iage2_4 |  -.4002157   .1506788    -2.66   0.008    -.6955408   -.1048906
  _Ibeckt2_2 |   .0464099   .1526759     0.30   0.761    -.2528293    .3456491
  _Ibeckt2_3 |   .1077921    .124958     0.86   0.388     -.137121    .3527052
  _Ibeckt2_4 |   .2096867   .1402925     1.49   0.135    -.0652817     .484655
 _Indrugt2_2 |  -.0914484   .1294441    -0.71   0.480    -.3451542    .1622575
 _Indrugt2_3 |   .2427763   .1336843     1.82   0.069    -.0192401    .5047927
 _Indrugt2_4 |   .3704249   .1404316     2.64   0.008      .095184    .6456657
       ivhx3 |   .2417153   .1067796     2.26   0.024     .0324311    .4509995
        race |  -.2511075   .1163678    -2.16   0.031    -.4791841   -.0230309
       treat |  -.2173453   .0941389    -2.31   0.021    -.4018541   -.0328365
        site |  -.0835198   .1084607    -0.77   0.441    -.2960989    .1290593
------------------------------------------------------------------------------
Figure 5.1, page 171.
preserve

input mp1 c1 mp2 c2 mp3 c3
  24     0    5      0   .5      0
30.5  .037 12.5   .046  2.5  -.091
35.5 -.241   20   .108    5   .243
47.5 -.400   40   .210 23.5   .370
end
Figure 5.1a, page 171.
graph twoway scatter c1 mp1, connect(l) xlabel(24 30.5 35.5 47.5)
Figure 5.1b, page 171.
graph twoway scatter c2 mp2, connect(l) ylabel(0 .25) xlabel(5 12.5 20 40)
Figure 5.1c, page 171.
graph twoway scatter c3 mp3, connect(l) ylabel(-.07 .4) xlabel(.5 2.5 5 23.5)
Table 5.7, page 172 and Table 5.8, page 173.
restore
fracpoly cox time ndrugtx age becktota ivhx3 race treat site, dead(censor) nohr degree(2) compare

Cox regression -- Breslow method for ties
Entry time 0                                      Number of obs   =        575
                                                  LR chi2(8)      =      51.43
                                                  Prob > chi2     =     0.0000
Log likelihood = -2638.2717                       Pseudo R2       =     0.0097

------------------------------------------------------------------------------
        time |
      censor |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    Indru__1 |  -.5226671   .1244122    -4.20   0.000    -.7665105   -.2788238
    Indru__2 |  -.1947183   .0482466    -4.04   0.000    -.2892799   -.1001566
     Iage__1 |  -.0281541   .0081328    -3.46   0.000     -.044094   -.0122141
    Ibeck__1 |   .0091589    .004987     1.84   0.066    -.0006154    .0189333
       ivhx3 |   .2585973   .1080215     2.39   0.017      .046879    .4703156
        race |  -.2421462   .1154647    -2.10   0.036    -.4684528   -.0158396
       treat |  -.2108924   .0936877    -2.25   0.024     -.394517   -.0272678
        site |  -.1053157    .109154    -0.96   0.335    -.3192536    .1086223
------------------------------------------------------------------------------
Deviance: 5276.543. Best powers of ndrugtx among 44 models fit: -1 -1.

Fractional polynomial model comparisons:
---------------------------------------------------------------
ndrugtx          df       Deviance      Gain   P(term) Powers
---------------------------------------------------------------
Not in model      0       5294.497        --     --
Linear            1       5283.459     0.000    0.001  1
m = 1             2       5283.088     0.371    0.543  .5
m = 2             4       5276.543     6.915    0.038  -1 -1
---------------------------------------------------------------

fracgen ndrugtx -1 -1
Figure 5.1d, page 171.
fracpred fp, for(ndrugtx)
graph twoway scatter fp ndrugtx, msymbol(i) connect(l) sort
Figure 5.2a, page 175.
stcox becktota ndrugtx ivhx3 race treat site, nohr mgale(mgale)

[...output omitted...]

graph twoway (lowess mgale age) (scatter mgale age), ylabel(-2.642 .997) xlabel(20 56)
Figure 5.3a, page 176.
drop mgale
stcox age ndrugtx ivhx3 race treat site, nohr mgale(mgale)

[...output omitted...]

graph twoway (lowess mgale becktota) (scatter mgale becktota), ///
	ylabel(-3.211 .998) xlabel(0 54)
Figure 5.4a, page 177.
drop mgale
stcox age becktota ivhx3 race treat site, nohr mgale(mgale)

[...output omitted...]

graph twoway (lowess mgale ndrugtx) (scatter mgale ndrugtx), ///
	ylabel(-3.201 1) xlabel(0 40)
Figure 5.2b, page 175; Figure 53b, page 176; Figure 5.4b, page 177.
drop mgale
stcox age becktota ndrugtx ivhx3 race treat site, nohr mgale(mgale)

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(7)      =     44.51
Log likelihood  =   -2641.7294                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0261517   .0080491    -3.25   0.001    -.0419276   -.0103758
    becktota |   .0083976   .0049516     1.70   0.090    -.0013074    .0181025
     ndrugtx |   .0290737   .0082126     3.54   0.000     .0129773      .04517
       ivhx3 |   .2561209   .1062996     2.41   0.016     .0477776    .4644642
        race |   -.224462   .1152656    -1.95   0.051    -.4503784    .0014544
       treat |  -.2324266   .0937326    -2.48   0.013    -.4161392    -.048714
        site |  -.0866855   .1078637    -0.80   0.422    -.2980944    .1247233
------------------------------------------------------------------------------

lowess censor age, gen(cism) nodraw
generate hi = censor - mgale
lowess hi age, gen(hism) nodraw
generate fi = log(cism/hism) -.0261517*age
graph twoway scatter fi age, msymbol(i) connect(l) sort ylabel(-.499 -2.003) xlabel(20 56)
drop cism hism fi
lowess censor becktota, gen(cism) nodraw
lowess hi becktota, gen(hism) nodraw
generate fi = log(cism/hism) + .0083976*becktota
graph twoway scatter fi becktota, msymbol(i) connect(l) sort ylabel(-.077 .389) xlabel(0 54)
drop cism hism fi
lowess censor ndrugtx, gen(cism) nodraw
lowess hi ndrugtx, gen(hism) nodraw
generate fi = log(cism/hism) + .0290737*ndrugtx
graph twoway scatter fi ndrugtx, msymbol(i) connect(l) sort ylabel(-.034 1.001) xlabel(0 40)
Table 5.10, page 179.
generate agexsite = age*site
generate racexsite = race*site
generate agexndrugfp1=age*ndrugt_1
generate agexndrugfp2=age*ndrugt_2

stcox age becktota ndrugt_1 ndrugt_2 ivhx3 race treat site agexsite racexsite agexndrugfp1 agexndrugfp2, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(12)     =     73.12
Log likelihood  =   -2627.4236                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0543081    .028035    -1.94   0.053    -.1092556    .0006395
    becktota |   .0100496   .0049925     2.01   0.044     .0002644    .0198347
    ndrugt_1 |  -.6743511   .6444652    -1.05   0.295     -1.93748    .5887775
    ndrugt_2 |  -.1721687   .2523393    -0.68   0.495    -.6667447    .3224072
       ivhx3 |     .22935   .1079297     2.12   0.034     .0178116    .4408884
        race |  -.4877383   .1346109    -3.62   0.000    -.7515709   -.2239057
       treat |  -.2420527   .0945533    -2.56   0.010    -.4273738   -.0567316
        site |  -1.119396   .5460698    -2.05   0.040    -2.189674   -.0491192
    agexsite |    .026438   .0165766     1.59   0.111    -.0060515    .0589275
   racexsite |   .8627388   .2481027     3.48   0.000     .3764666    1.349011
agexndrugfp1 |   .0016289   .0194482     0.08   0.933    -.0364889    .0397467
agexndrugfp2 |  -.0019831   .0076598    -0.26   0.796    -.0169961      .01303
------------------------------------------------------------------------------
Table 5.11, page 179.
stcox age becktota ndrugt_1 ndrugt_2 ivhx3 race treat site agexsite racexsite, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(10)     =     67.13
Log likelihood  =   -2630.4179                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0413963   .0099128    -4.18   0.000     -.060825   -.0219676
    becktota |    .008738   .0049654     1.76   0.078     -.000994    .0184701
    ndrugt_1 |  -.5744565   .1251879    -4.59   0.000    -.8198202   -.3290928
    ndrugt_2 |  -.2145783    .048587    -4.42   0.000    -.3098071   -.1193495
       ivhx3 |    .227748    .108563     2.10   0.036     .0149684    .4405276
        race |  -.4668853   .1347564    -3.46   0.000    -.7310029   -.2027677
       treat |  -.2467592     .09434    -2.62   0.009    -.4316621   -.0618562
        site |  -1.316987   .5314407    -2.48   0.013    -2.358592   -.2753827
    agexsite |   .0324002   .0160807     2.01   0.044     .0008827    .0639178
   racexsite |   .8502773   .2477582     3.43   0.000     .3646801    1.335875
------------------------------------------------------------------------------
Table 5.13, page 186.
stcox age becktota race treat site ivhx3 ndrugt_1 ndrugt_2 racexsite agexndrugfp1, nohr

Cox regression -- Breslow method for ties

No. of subjects =          575                     Number of obs   =       575
No. of failures =          464
Time at risk    =       138900
                                                   LR chi2(10)     =     70.49
Log likelihood  =    -2628.739                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0538471   .0118803    -4.53   0.000     -.077132   -.0305622
    becktota |   .0103485   .0049966     2.07   0.038     .0005554    .0201417
        race |  -.4829437   .1344923    -3.59   0.000    -.7465438   -.2193435
       treat |  -.2223822   .0937517    -2.37   0.018    -.4061322   -.0386321
        site |  -.2781853   .1220049    -2.28   0.023    -.5173106     -.03906
       ivhx3 |   .2339795   .1077173     2.17   0.030     .0228575    .4451015
    ndrugt_1 |  -.8377904   .1595497    -5.25   0.000    -1.150502   -.5250788
    ndrugt_2 |   -.229083   .0487574    -4.70   0.000    -.3246458   -.1335202
   racexsite |   .8968524   .2473127     3.63   0.000     .4121284    1.381576
agexndrugfp1 |   .0072271   .0026092     2.77   0.006     .0021131     .012341
------------------------------------------------------------------------------

How to cite this page

Report an error on this page

UCLA Researchers are invited to our Statistical Consulting Services
We recommend others to our list of Other Resources for Statistical Computing Help
These pages are Copyrighted (c) by UCLA Academic Technology Services


The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California