# The scale option has changed

In stpm2 the choice of options when using the scale() option included hazard and odds. These really meant log cumulative hazard and log odds respectively.

In stpm3 you need to refer to these models as scale(lncumhazard) or scale(lnodds). This is because stpm3 allows models to be fitted on the log hazard scale (scale(lnhazard)) and thus there is a need to distinguish between models on the log cumulative hazard and log hazard scales.

We first load the example Rotterdam 2 breast cancer data and then use stset to declare the survival time and event indicator.

. use https://www.pclambert.net/data/rott2b, clear
(Rotterdam breast cancer data (augmented with cause of death))

. stset os, f(osi==1) scale(12) exit(time 120)

Survival-time data settings

Failure event: osi==1
Observed time interval: (0, os]
Exit on or before: time 120
Time for analysis: time/12

--------------------------------------------------------------------------
2,982  total observations
0  exclusions
--------------------------------------------------------------------------
2,982  observations remaining, representing
1,171  failures in single-record/single-failure data
20,002.424  total analysis time at risk and under observation
At risk from t =         0
Earliest observed entry t =         0
Last observed exit t =        10



The scale(12) option converts the times recorded in months to years.

To fit an stpm2 model we would use,

. stpm2 hormon, scale(hazard) df(5)

Iteration 0:   log likelihood = -2929.2995
Iteration 1:   log likelihood = -2928.2998
Iteration 2:   log likelihood = -2928.2966
Iteration 3:   log likelihood = -2928.2966

Log likelihood = -2928.2966                              Number of obs = 2,982

------------------------------------------------------------------------------
| Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
xb           |
hormon |   .4321954   .0861189     5.02   0.000     .2634054    .6009854
_rcs1 |    .914158   .0273548    33.42   0.000     .8605436    .9677725
_rcs2 |   .1672938   .0273886     6.11   0.000     .1136131    .2209746
_rcs3 |   .0360402   .0154393     2.33   0.020     .0057797    .0663006
_rcs4 |  -.0113638    .007644    -1.49   0.137    -.0263459    .0036182
_rcs5 |   .0058281   .0049328     1.18   0.237    -.0038401    .0154963
_cons |  -1.225443   .0332548   -36.85   0.000    -1.290622   -1.160265
------------------------------------------------------------------------------



The equivalent model in stpm3 is,

. stpm3 hormon, scale(lncumhazard) df(5)

Iteration 0:   log likelihood = -2929.2941
Iteration 1:   log likelihood = -2928.2998
Iteration 2:   log likelihood = -2928.2966
Iteration 3:   log likelihood = -2928.2966

Number of obs =  2,982
Wald chi2(1)  =  25.19
Log likelihood = -2928.2966                             Prob > chi2   = 0.0000

------------------------------------------------------------------------------
| Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
xb           |
hormon |   .4321954   .0861189     5.02   0.000     .2634054    .6009854
-------------+----------------------------------------------------------------
time         |
_ns1 |   -23.9834    1.92113   -12.48   0.000    -27.74874   -20.21805
_ns2 |   6.695765   1.027919     6.51   0.000     4.681082    8.710449
_ns3 |  -1.214676   .0497438   -24.42   0.000    -1.312172    -1.11718
_ns4 |  -.8095755   .0387379   -20.90   0.000    -.8855004   -.7336505
_ns5 |  -.4994385   .0418591   -11.93   0.000    -.5814808   -.4173963
_cons |  -.5713643   .0332128   -17.20   0.000    -.6364603   -.5062684
------------------------------------------------------------------------------
Warning: This is a test version of stpm3



Note the log-likelihoods are identical as are the coefficients/standard errors for hormon. Note that different basis functions are used, so the coefficients for the spline terms are different. However, predicted values for the same covariate pattern will not differ.

To fit a model on the log hazard scale use scale(lnhazard),

. stpm3 hormon, scale(lnhazard) df(5)

Iteration 0:   log likelihood = -14911.675
Iteration 1:   log likelihood = -3026.8801
Iteration 2:   log likelihood = -2948.3778
Iteration 3:   log likelihood =  -2932.594
Iteration 4:   log likelihood = -2930.2148
Iteration 5:   log likelihood = -2930.1543
Iteration 6:   log likelihood = -2930.1543

Number of obs =  2,982
Wald chi2(1)  =  25.25
Log likelihood = -2930.1543                             Prob > chi2   = 0.0000

------------------------------------------------------------------------------
| Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
xb           |
hormon |   .4327572   .0861241     5.02   0.000      .263957    .6015574
-------------+----------------------------------------------------------------
time         |
_ns1 |  -8.932832   1.582843    -5.64   0.000    -12.03515   -5.830516
_ns2 |   4.310232   .9613182     4.48   0.000     2.426083    6.194381
_ns3 |   .3888339   .1855177     2.10   0.036     .0252258    .7524419
_ns4 |   .1035977   .1619785     0.64   0.522    -.2138744    .4210698
_ns5 |   .0857984   .3383806     0.25   0.800    -.5774153    .7490121
_cons |  -2.911815    .146526   -19.87   0.000       -3.199   -2.624629
------------------------------------------------------------------------------
Quadrature method: Gauss-Legendre with 30 nodes
Warning: This is a test version of stpm3