Life table estimation of relative survival with strs

We first load the colon cancer data (restricting to localised stage) and then use stset to declare the time at risk and event indicator.

. use colon if stage==1, clear
(Colon carcinoma, diagnosed 1975-94, follow-up to 1995)

. stset surv_mm, fail(status==1 2) id(id) scale(12)

                id:  id
     failure event:  status == 1 2
obs. time interval:  (surv_mm[_n-1], surv_mm]
 exit on or before:  failure
    t for analysis:  time/12

------------------------------------------------------------------------------
      6,274  total observations
          0  exclusions
------------------------------------------------------------------------------
      6,274  observations remaining, representing
      6,274  subjects
      3,291  failures in single-failure-per-subject data
  35,598.75  total analysis time at risk and under observation
                                                at risk from t =         0
                                     earliest observed entry t =         0
                                          last observed exit t =  20.95833

Survival times in completed months are stored in the variable surv_mm. The scale(12) option converts to years, as required by strs.

The variable status contains vital status, coded as follows:

We specify codes 1 and 2 as events (fail(status==1 2)) as we wish to estimate all-cause survival, which we will then divide by expected survival to get relative survival.

We now call strs to produce life tables for each sex. The mergeby() option specifies the variables upon which expected survival depends (i.e., the variables by which the popmort data is sorted). The by(sex) option specifies that we would like life tables for each sex. The breaks(0(1)10) option specifies the life table intervals; 0(1)10 is Stata shorthand for ‘from 0 to 10 by 1’.

. strs using popmort, breaks(0(1)10) mergeby(_year sex _age) by(sex) save(replace)

         failure _d:  status == 1 2
   analysis time _t:  surv_mm/12
                 id:  id

No late entry detected - p is estimated using the actuarial method

----------------------------------------------------------------------------------------------------------------
-> sex = Male

  +------------------------------------------------------------------------------------------------------------+
  | start   end      n     d     w        p   p_star        r       cp    cp_e2    cr_e2   lo_cr_e2   hi_cr_e2 |
  |------------------------------------------------------------------------------------------------------------|
  |     0     1   2620   328     0   0.8748   0.9470   0.9238   0.8748   0.9470   0.9238     0.9098     0.9366 |
  |     1     2   2292   229   166   0.8963   0.9483   0.9452   0.7841   0.8980   0.8732     0.8549     0.8904 |
  |     2     3   1897   180   139   0.9015   0.9470   0.9519   0.7069   0.8504   0.8312     0.8097     0.8518 |
  |     3     4   1578   140   119   0.9078   0.9449   0.9607   0.6417   0.8036   0.7986     0.7742     0.8221 |
  |     4     5   1319   113   104   0.9108   0.9428   0.9660   0.5845   0.7576   0.7715     0.7444     0.7977 |
  |------------------------------------------------------------------------------------------------------------|
  |     5     6   1102   102    81   0.9039   0.9414   0.9601   0.5283   0.7132   0.7407     0.7110     0.7698 |
  |     6     7    919    71    71   0.9196   0.9409   0.9774   0.4859   0.6711   0.7239     0.6916     0.7557 |
  |     7     8    777    59    72   0.9204   0.9391   0.9800   0.4472   0.6303   0.7095     0.6745     0.7441 |
  |     8     9    646    49    62   0.9203   0.9380   0.9811   0.4115   0.5912   0.6961     0.6582     0.7337 |
  |     9    10    535    33    58   0.9348   0.9365   0.9981   0.3847   0.5537   0.6948     0.6538     0.7357 |
  +------------------------------------------------------------------------------------------------------------+

----------------------------------------------------------------------------------------------------------------
-> sex = Female

  +------------------------------------------------------------------------------------------------------------+
  | start   end      n     d     w        p   p_star        r       cp    cp_e2    cr_e2   lo_cr_e2   hi_cr_e2 |
  |------------------------------------------------------------------------------------------------------------|
  |     0     1   3654   423     1   0.8842   0.9585   0.9225   0.8842   0.9585   0.9225     0.9113     0.9329 |
  |     1     2   3230   313   203   0.9000   0.9590   0.9384   0.7958   0.9192   0.8657     0.8510     0.8797 |
  |     2     3   2714   216   178   0.9177   0.9572   0.9587   0.7303   0.8799   0.8300     0.8129     0.8463 |
  |     3     4   2320   171   194   0.9231   0.9545   0.9671   0.6741   0.8398   0.8027     0.7835     0.8211 |
  |     4     5   1955   134   135   0.9290   0.9526   0.9752   0.6262   0.8000   0.7828     0.7617     0.8032 |
  |------------------------------------------------------------------------------------------------------------|
  |     5     6   1686   131   139   0.9190   0.9503   0.9670   0.5755   0.7603   0.7569     0.7338     0.7796 |
  |     6     7   1416   109   128   0.9194   0.9477   0.9701   0.5291   0.7205   0.7343     0.7090     0.7591 |
  |     7     8   1179    73   103   0.9353   0.9460   0.9886   0.4948   0.6816   0.7260     0.6986     0.7529 |
  |     8     9   1003    53   102   0.9443   0.9437   1.0007   0.4673   0.6432   0.7265     0.6969     0.7557 |
  |     9    10    848    56    82   0.9306   0.9399   0.9901   0.4349   0.6046   0.7193     0.6871     0.7512 |
  +------------------------------------------------------------------------------------------------------------+

The life table quantities are as follows:

n         Alive at start
d         Deaths during the interval
w         Withdrawals during the interval
p         Interval-specific observed survival
p_star    Interval-specific expected survival
r         Interval-specific relative survival
cp        Cumulative observed survival
cp_e2     Cumulative expected survival (Ederer II)
cr_e2     Cumulative relative survival (Ederer II)

We see that the five-year relative survival for males is 0.7715, while for females it is 0.7828.