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Stata Textbook Examples
Applied Survival Analysis by Hosmer and Lemeshow
Chapter 4: Interpretation of a Fitted Proportional Hazards Regression Model

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.)
use hmohiv, clear

stset time, failure(censor)
Table 4.2, page 119.
stcox drug, nohr

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(1)      =     10.20
Log likelihood  =   -294.09639                     Prob > chi2     =    0.0014

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drug |   .7792305   .2422582     3.22   0.001     .3044132    1.254048
------------------------------------------------------------------------------
Table 4.3, page 121.
generate agegrp = age
recode agegrp 20/29=1 30/34=2 35/39=3 40/54=4
tab agegrp, gen(age)

     agegrp |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |         12       12.00       12.00
          2 |         34       34.00       46.00
          3 |         25       25.00       71.00
          4 |         29       29.00      100.00
------------+-----------------------------------
      Total |        100      100.00
Table 4.4, page 122.
stcox age2 age3 age4, nohr

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(3)      =     19.56
Log likelihood  =   -289.41333                     Prob > chi2     =    0.0002

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        age2 |   1.196962   .4510352     2.65   0.008     .3129497    2.080975
        age3 |   1.313291   .4588966     2.86   0.004     .4138706    2.212712
        age4 |     1.8604    .469308     3.96   0.000     .9405736    2.780227
------------------------------------------------------------------------------
Table 4.5, page 123.
stcox age2 age3 age4

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(3)      =     19.56
Log likelihood  =   -289.41333                     Prob > chi2     =    0.0002

------------------------------------------------------------------------------
          _t |
          _d | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        age2 |   3.310047   1.492948     2.65   0.008     1.367453    8.012279
        age3 |   3.718392   1.706358     2.86   0.004     1.512661    9.140474
        age4 |    6.42631   3.015919     3.96   0.000      2.56145    16.12269
------------------------------------------------------------------------------
Table 4.4, page 125.
matrix list e(V)

symmetric e(V)[3,3]
           age2       age3       age4
age2  .20343276
age3  .16365896   .2105861
age4  .17047514  .16661653  .22025002
Table 4.7, page 127.
replace age2 = age2 - age1
replace age3 = age3 - age1
replace age4 = age4 - age1

stcox age2 age3 age4, nohr

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(3)      =     19.56
Log likelihood  =   -289.41333                     Prob > chi2     =    0.0002

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        age2 |   .1042989   .1920546     0.54   0.587    -.2721212     .480719
        age3 |   .2206278   .2058906     1.07   0.284    -.1829103     .624166
        age4 |   .7677369   .2093199     3.67   0.000     .3574775    1.177996
------------------------------------------------------------------------------

/* alternative method using xi3/ 
NOTE: You will need to download xi3, which can be installed by typing findit xi3 in the command line (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
xi3: stcox e.agegrp, nohr

d.agegrp          _Iagegrp_1-4        (naturally coded; _Iagegrp_1 omitted)

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(3)      =     19.56
Log likelihood  =   -289.41333                     Prob > chi2     =    0.0002

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  _Iagegrp_2 |   .1042989   .1920546     0.54   0.587    -.2721212     .480719
  _Iagegrp_3 |   .2206278   .2058906     1.07   0.284    -.1829103     .624166
  _Iagegrp_4 |   .7677369   .2093199     3.67   0.000     .3574775    1.177996
------------------------------------------------------------------------------
Table 4.8, page 129.
stcox age, nohr

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(1)      =     21.35
Log likelihood  =   -288.51804                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0814042   .0174352     4.67   0.000     .0472317    .1155766
------------------------------------------------------------------------------
Table 4.9 1.4, page 133.
use uis, clear
stset time, failure(censor)
generate drug = ivhx
recode drug 1=0 2/3=1

stcox drug if age~=., nohr

Cox regression -- Breslow method for ties

No. of subjects =          605                     Number of obs   =       605
No. of failures =          489
Time at risk    =       144822
                                                   LR chi2(1)      =     11.78
Log likelihood  =   -2825.9664                     Prob > chi2     =    0.0006

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drug |   .3210045   .0948107     3.39   0.001     .1351789    .5068301
------------------------------------------------------------------------------

stcox drug age, nohr

Cox regression -- Breslow method for ties

No. of subjects =          605                     Number of obs   =       605
No. of failures =          489
Time at risk    =       144822
                                                   LR chi2(2)      =     23.32
Log likelihood  =   -2820.1989                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drug |   .4394466   .1007151     4.36   0.000     .2420487    .6368445
         age |  -.0263792   .0078392    -3.37   0.001    -.0417438   -.0110147
------------------------------------------------------------------------------
Table 4.10, page 135.
stcox treat if age~=., nohr

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)      =      6.05
Log likelihood  =    -2930.087                     Prob > chi2     =    0.0139

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       treat |  -.2196282   .0893249    -2.46   0.014    -.3947018   -.0445546
------------------------------------------------------------------------------

stcox treat age, nohr

Cox regression -- Breslow method for ties

No. of subjects =          623                     Number of obs   =       623
No. of failures =          504
Time at risk    =       146816
                                                   LR chi2(2)      =      9.48
Log likelihood  =   -2928.3748                     Prob > chi2     =    0.0088

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       treat |  -.2229808   .0893303    -2.50   0.013    -.3980651   -.0478966
         age |   -.013268   .0072117    -1.84   0.066    -.0274027    .0008667
------------------------------------------------------------------------------

generate trtxage = treat*age
stcox treat age trtxage, nohr

Cox regression -- Breslow method for ties

No. of subjects =          623                     Number of obs   =       623
No. of failures =          504
Time at risk    =       146816
                                                   LR chi2(3)      =     12.04
Log likelihood  =   -2927.0915                     Prob > chi2     =    0.0072

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       treat |   .5227169   .4744893     1.10   0.271     -.407265    1.452699
         age |  -.0017705   .0101253    -0.17   0.861    -.0216156    .0180747
     trtxage |  -.0231941   .0145004    -1.60   0.110    -.0516144    .0052261
------------------------------------------------------------------------------
Figure 4.2, page 139.
use hmohiv, clear
stset time, failure(censor)
stcox drug, nohr bases(bs0)

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(1)      =     10.20
Log likelihood  =   -294.09639                     Prob > chi2     =    0.0014

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drug |   .7792305   .2422582     3.22   0.001     .3044132    1.254048
------------------------------------------------------------------------------

generate bs1 = bs0^exp(.7792305)
graph twoway scatter bs0 bs1 time, connect(J J) sort ylabel(0 1) xlabel(0(10)60)
Figure 4.3, page 141.
replace bs0=. if drug==1
replace bs1=. if drug==0

graph twoway scatter bs0 bs1 time, connect(J J) sort ylabel(0 1) xlabel(0(10)60)
Table 4.12, page 143.
generate age35 = age-35

stcox drug age35, nohr bases(bs0_35)

Cox regression -- Breslow method for ties

No. of subjects =          100                     Number of obs   =       100
No. of failures =           80
Time at risk    =         1136
                                                   LR chi2(2)      =     34.98
Log likelihood  =   -281.70404                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drug |   .9413856   .2555104     3.68   0.000     .4405943    1.442177
       age35 |   .0915319   .0184879     4.95   0.000     .0552963    .1277675
------------------------------------------------------------------------------
Fig. 4.4, page 144.
gen bs1_35 = bs0_35^exp(.9413856)

gen bs0_35a=bs0_35 if drug==0
gen bs1_35a=bs1_35 if drug==1

label variable bs0_35a "IV Drug Use Present"
label variable bs1_35a "IV Drug Use Absent"

graph twoway scatter bs0_35a bs1_35a time, connect(J J) sort ylabel(0(.25)1) xlabel(0(10)60)
Fig. 4.5a, page 146.
gen age30 = age - 30

quietly quietly stcox drug age30, nohr bases(bs0_30)

gen bs1_30 = bs0_30^exp(.9413856  )
label variable bs0_30 "IV Drug Use Present"
label variable bs1_30 "IV Drug Use Absent"

graph twoway scatter bs0_30 bs1_30 time, connect(J J) sort ylabel(0 1) xlabel(0(10)60)
Fig. 4.5b, page 146.
Note: We created the variables used in the graph in the code for table 4.12 and fig. 4.4.
label variable bs0_35 "IV Drug Use Present"
label variable bs1_35 "IV Drug Use Absent"

graph twoway scatter bs0_35 bs1_35 time, connect(J J) sort ylabel(0(.25)1) xlabel(0(10)60)
Fig. 4.5c, page 146.
gen age40 = age - 40

quietly stcox drug age40, nohr bases(bs0_40)

gen bs1_40 = bs0_40^exp(.9413856  )
label variable bs0_40 "IV Drug Use Present"
label variable bs1_40 "IV Drug Use Absent"

graph twoway scatter bs0_40 bs1_40 time, connect(J J) sort ylabel(0(.25)1) xlabel(0(10)60)
Fig. 4.5d, page 146.
gen age45 = age - 45

quietly stcox drug age45, nohr bases(bs0_45)

gen bs1_45 = bs0_45^exp(.9413856  )
label variable bs0_45 "IV Drug Use Present"
label variable bs1_45 "IV Drug Use Absent"

graph twoway scatter bs0_45 bs1_45 time, connect(J J) sort ylabel(0(.25)1) xlabel(0(10)60)
Table 4.13 and fig. 4.6, page 148.
use uis
stset time, failure(censor)
generate agec = age-30
generate ndrgtxc = ndrugtx-3
generate drug = ivhx
recode drug 1=0 2/3=1

stcox treat agec drug ndrgtxc, nohr bases(bs0)

Cox regression -- Breslow method for ties

No. of subjects =          593                     Number of obs   =       593
No. of failures =          481
Time at risk    =       141069
                                                   LR chi2(4)      =     41.09
Log likelihood  =   -2753.4247                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |
          _d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       treat |  -.2271044   .0915798    -2.48   0.013    -.4065975   -.0476113
        agec |  -.0307434   .0079358    -3.87   0.000    -.0462974   -.0151895
        drug |   .3425819   .1042631     3.29   0.001     .1382299    .5469339
     ndrgtxc |   .0309095   .0079891     3.87   0.000     .0152511    .0465679
------------------------------------------------------------------------------

gen bs1 = bs0^exp( -.2271044 )
label variable bs0 "Treat = 0"
label variable bs1 "Treat = 1"

graph twoway scatter bs0 bs1 time, msymbol(i i) connect(l l) sort ylabel(0(.25)1) xlabel(0(500)1500)
Fig. 4.8, page 155. We currently don't know how to do this example.

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