Modeling Relative Survival/Excess Mortality using Poisson Regression (Part 1)

Miguel Angel Luque-Fernandez

Statistical methods for population-based cancer survival analysis (CIBERSP & VICA), Spain

Note: Adapted with permission from Paul Dickman and Paul Lambert short course in Trevisso, Italy

1. Calling Stata software from Jupyter Notebook

import os
os.chdir('/Applications/stata/utilities/')
from pystata import config
config.init('mp')

  ___  ____  ____  ____  ____ ®
 /__    /   ____/   /   ____/      17.0
___/   /   /___/   /   /___/       MP—Parallel Edition

 Statistics and Data Science       Copyright 1985-2021 StataCorp LLC
                                   StataCorp
                                   4905 Lakeway Drive
                                   College Station, Texas 77845 USA
                                   800-STATA-PC        https://www.stata.com
                                   979-696-4600        stata@stata.com

Stata license: Single-user 4-core  perpetual
Serial number: 501706307451
  Licensed to: MALF
               IBS.GRANADA

Notes:
      1. Unicode is supported; see help unicode_advice.
      2. More than 2 billion observations are allowed; see help obs_advice.
      3. Maximum number of variables is set to 5,000; see help set_maxvar.

2. Getting the data

%%stata
use http://www.pauldickman.com/survival/colon

(Colon carcinoma, diagnosed 1975-94, follow-up to 1995)

3. Describing the data and generating failure indicator

%%stata
gen fail = (status == 1)
describe

. gen fail = (status == 1)

. describe

Contains data from http://www.pauldickman.com/survival/colon.dta
 Observations:        15,564                  Colon carcinoma, diagnosed
                                                1975-94, follow-up to 1995
    Variables:            15                  5 May 2015 12:58
-------------------------------------------------------------------------------
Variable      Storage   Display    Value
    name         type    format    label      Variable label
-------------------------------------------------------------------------------
sex             byte    %8.0g      sex        Sex
age             byte    %9.0g                 Age at diagnosis
stage           byte    %9.0g      stage      Clinical stage at diagnosis
mmdx            byte    %9.0g                 Month of diagnosis
yydx            int     %9.0g                 Year of diagnosis
surv_mm         float   %9.0g               * Survival time in months
surv_yy         float   %9.0g               * Survival time in years
status          byte    %17.0g     status     Vital status at exit
subsite         byte    %22.0g     colonsub   Anatomical subsite of tumour
year8594        byte    %15.0g     year8594   Indicator for diagnosed during
                                                1985-94
agegrp          byte    %9.0g      agegrp     Age in 4 categories
dx              int     %d                  * Date of diagnosis
exit            int     %d                  * Date of exit
id              int     %9.0g               * Unique patient ID
fail            float   %9.0g                 
                                            * indicated variables have notes
-------------------------------------------------------------------------------
Sorted by: 
     Note: Dataset has changed since last saved.

. 

4. Setting time

%%stata
 stset surv_yy, fail(status==1) id(id)

Survival-time data settings

           ID variable: id
         Failure event: status==1
Observed time interval: (surv_yy[_n-1], surv_yy]
     Exit on or before: failure

--------------------------------------------------------------------------
     15,564  total observations
          0  exclusions
--------------------------------------------------------------------------
     15,564  observations remaining, representing
     15,564  subjects
      8,369  failures in single-failure-per-subject data
     59,483  total analysis time at risk and under observation
                                                At risk from t =         0
                                     Earliest observed entry t =         0
                                          Last observed exit t =      20.5

5. Describing time

%%stata 
stdes

        Failure _d: status==1
  Analysis time _t: surv_yy
       ID variable: id

                                   |-------------- Per subject --------------|
Category                   Total        Mean         Min     Median        Max
------------------------------------------------------------------------------
Number of subjects         15564   
Number of records          15564           1           1          1          1

Entry time (first)                         0           0          0          0
Exit time (final)                   3.821832          .5        1.5       20.5

Subjects with gap              0   
Time on gap                    0           .           .          .          .
Time at risk               59483    3.821832          .5        1.5       20.5

Failures                    8369    .5377152           0          1          1
------------------------------------------------------------------------------

6. Relative survial using STRS: getting expected number of deaths

%%stata
cd /Users/MALF/Dropbox/CANSURV-slides-course/Granada/

/Users/MALF/Dropbox/CANSURV-slides-course/Granada

%%stata
strs using popmort, br(0(1)10) mergeby(_year sex _age) by(agegr sex stage) ///
list(start end n d d_star y) save(replace)

. strs using popmort, br(0(1)10) mergeby(_year sex _age) by(agegr sex stage) //
> /
> list(start end n d d_star y) save(replace)

        Failure _d: status==1
  Analysis time _t: surv_yy
       ID variable: id

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

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Male, stage = Unknown

  +--------------------------------------+
  | start   end    n   d   d_star      y |
  |--------------------------------------|
  |     0     1   37   4      0.1   35.0 |
  |     1     2   33   4      0.1   29.5 |
  |     2     3   26   3      0.1   23.0 |
  |     3     4   20   0      0.1   19.5 |
  |     4     5   19   0      0.1   18.5 |
  |--------------------------------------|
  |     5     6   18   0      0.1   17.0 |
  |     6     7   16   0      0.1   15.5 |
  |     7     8   15   0      0.1   13.0 |
  |     8     9   11   0      0.1   10.0 |
  |     9    10    9   0      0.1    8.5 |
  +--------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Male, stage = Localised

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   161    6      0.5   157.5 |
  |     1     2   154   14      0.5   143.0 |
  |     2     3   132    4      0.5   125.5 |
  |     3     4   119    4      0.4   111.5 |
  |     4     5   104    3      0.4    98.5 |
  |-----------------------------------------|
  |     5     6    93    4      0.4    88.0 |
  |     6     7    83    1      0.4    80.5 |
  |     7     8    78    1      0.4    73.5 |
  |     8     9    69    1      0.4    66.5 |
  |     9    10    64    2      0.4    59.5 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Male, stage = Regional

  +--------------------------------------+
  | start   end    n   d   d_star      y |
  |--------------------------------------|
  |     0     1   57   7      0.2   53.5 |
  |     1     2   50   6      0.1   45.5 |
  |     2     3   41   2      0.1   38.5 |
  |     3     4   36   1      0.1   34.0 |
  |     4     5   32   2      0.1   30.5 |
  |--------------------------------------|
  |     5     6   29   0      0.1   27.5 |
  |     6     7   26   0      0.1   25.0 |
  |     7     8   24   1      0.1   22.5 |
  |     8     9   21   0      0.1   20.0 |
  |     9    10   19   0      0.1   19.0 |
  +--------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Male, stage = Distant

  +----------------------------------------+
  | start   end     n    d   d_star      y |
  |----------------------------------------|
  |     0     1   129   72      0.3   92.5 |
  |     1     2    56   24      0.1   43.5 |
  |     2     3    31   10      0.1   24.5 |
  |     3     4    18    2      0.1   16.0 |
  |     4     5    14    3      0.0   12.5 |
  |----------------------------------------|
  |     5     6    11    1      0.0   10.5 |
  |     6     7    10    1      0.0    8.5 |
  |     7     8     7    0      0.0    6.5 |
  |     8     9     6    0      0.0    6.0 |
  |     9    10     6    0      0.0    6.0 |
  +----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Female, stage = Unknown

  +--------------------------------------+
  | start   end    n   d   d_star      y |
  |--------------------------------------|
  |     0     1   46   3      0.0   44.5 |
  |     1     2   43   2      0.0   41.5 |
  |     2     3   40   1      0.0   38.0 |
  |     3     4   36   1      0.1   35.0 |
  |     4     5   34   1      0.0   32.0 |
  |--------------------------------------|
  |     5     6   30   1      0.0   29.0 |
  |     6     7   28   1      0.0   26.0 |
  |     7     8   24   0      0.0   23.0 |
  |     8     9   22   0      0.0   22.0 |
  |     9    10   22   0      0.0   22.0 |
  +--------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Female, stage = Localised

  +----------------------------------------+
  | start   end     n   d   d_star       y |
  |----------------------------------------|
  |     0     1   136   5      0.2   133.5 |
  |     1     2   131   6      0.2   125.5 |
  |     2     3   120   8      0.2   114.5 |
  |     3     4   109   4      0.2   103.5 |
  |     4     5    98   4      0.1    93.0 |
  |----------------------------------------|
  |     5     6    88   0      0.1    85.0 |
  |     6     7    82   0      0.1    76.5 |
  |     7     8    71   1      0.1    69.5 |
  |     8     9    68   1      0.1    64.0 |
  |     9    10    60   0      0.1    58.5 |
  +----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Female, stage = Regional

  +---------------------------------------+
  | start   end    n    d   d_star      y |
  |---------------------------------------|
  |     0     1   57   11      0.1   51.5 |
  |     1     2   46    4      0.0   42.5 |
  |     2     3   39    6      0.0   33.5 |
  |     3     4   28    0      0.0   27.0 |
  |     4     5   26    0      0.0   23.5 |
  |---------------------------------------|
  |     5     6   21    1      0.0   20.5 |
  |     6     7   20    0      0.0   19.5 |
  |     7     8   19    0      0.0   18.5 |
  |     8     9   18    0      0.0   17.0 |
  |     9    10   16    1      0.0   14.5 |
  +---------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 0-44, sex = Female, stage = Distant

  +----------------------------------------+
  | start   end     n    d   d_star      y |
  |----------------------------------------|
  |     0     1   112   54      0.1   84.5 |
  |     1     2    57   27      0.1   43.0 |
  |     2     3    29    8      0.0   24.5 |
  |     3     4    20    2      0.0   18.5 |
  |     4     5    17    0      0.0   16.5 |
  |----------------------------------------|
  |     5     6    16    2      0.0   14.5 |
  |     6     7    13    2      0.0   11.0 |
  |     7     8     9    0      0.0    8.5 |
  |     8     9     8    0      0.0    7.0 |
  |     9    10     6    0      0.0    5.5 |
  +----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Male, stage = Unknown

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   128   23      1.3   116.5 |
  |     1     2   105    8      1.1    92.5 |
  |     2     3    80    2      1.0    77.0 |
  |     3     4    74    2      1.0    69.0 |
  |     4     5    64    2      0.9    60.0 |
  |-----------------------------------------|
  |     5     6    56    0      0.9    54.5 |
  |     6     7    53    0      0.9    51.0 |
  |     7     8    49    1      0.9    46.5 |
  |     8     9    44    1      0.8    42.5 |
  |     9    10    41    0      0.8    38.0 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Male, stage = Localised

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   462   18      5.3   449.5 |
  |     1     2   437   15      5.3   416.0 |
  |     2     3   395   23      5.1   370.0 |
  |     3     4   345   10      4.8   323.0 |
  |     4     5   301   12      4.6   287.5 |
  |-----------------------------------------|
  |     5     6   274    7      4.4   256.5 |
  |     6     7   239    4      4.2   224.0 |
  |     7     8   209    2      4.0   197.0 |
  |     8     9   185    0      3.8   172.5 |
  |     9    10   160    0      3.5   148.5 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Male, stage = Regional

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   165   21      1.7   154.5 |
  |     1     2   144   25      1.4   126.0 |
  |     2     3   108   12      1.1    94.5 |
  |     3     4    81    6      0.9    75.0 |
  |     4     5    69    7      0.9    62.5 |
  |-----------------------------------------|
  |     5     6    56    2      0.8    51.5 |
  |     6     7    47    4      0.7    43.0 |
  |     7     8    39    0      0.6    34.5 |
  |     8     9    30    0      0.5    28.0 |
  |     9    10    26    0      0.4    21.5 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Male, stage = Distant

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   421   248      3.4   294.5 |
  |     1     2   168    73      1.5   127.0 |
  |     2     3    86    22      0.9    72.5 |
  |     3     4    59     6      0.7    53.5 |
  |     4     5    48     9      0.6    40.5 |
  |------------------------------------------|
  |     5     6    33     1      0.5    30.5 |
  |     6     7    28     1      0.4    25.5 |
  |     7     8    23     0      0.4    22.0 |
  |     8     9    21     1      0.4    19.5 |
  |     9    10    18     0      0.3    16.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Female, stage = Unknown

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   134   20      0.5   123.0 |
  |     1     2   112   14      0.4    98.5 |
  |     2     3    85    6      0.4    77.0 |
  |     3     4    69    6      0.3    62.5 |
  |     4     5    56    3      0.3    51.0 |
  |-----------------------------------------|
  |     5     6    46    1      0.3    44.0 |
  |     6     7    42    3      0.3    38.5 |
  |     7     8    35    0      0.2    33.5 |
  |     8     9    32    0      0.2    30.5 |
  |     9    10    29    0      0.2    27.0 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Female, stage = Localised

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   531   19      2.1   519.0 |
  |     1     2   507   25      2.0   475.0 |
  |     2     3   443   22      2.0   413.0 |
  |     3     4   383   16      1.9   362.5 |
  |     4     5   342   10      1.8   323.0 |
  |-----------------------------------------|
  |     5     6   304    9      1.8   283.0 |
  |     6     7   262    5      1.7   251.0 |
  |     7     8   240    3      1.7   227.5 |
  |     8     9   215    0      1.7   203.0 |
  |     9    10   191    0      1.7   183.5 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Female, stage = Regional

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   164   25      0.6   151.5 |
  |     1     2   139   22      0.5   123.5 |
  |     2     3   108   13      0.5    98.0 |
  |     3     4    88   10      0.4    79.5 |
  |     4     5    71    2      0.4    68.0 |
  |-----------------------------------------|
  |     5     6    65    3      0.4    60.5 |
  |     6     7    56    0      0.3    53.5 |
  |     7     8    51    0      0.3    50.0 |
  |     8     9    49    1      0.3    44.5 |
  |     9    10    40    0      0.3    37.0 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 45-59, sex = Female, stage = Distant

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   363   198      1.1   263.0 |
  |     1     2   163    77      0.5   119.0 |
  |     2     3    75    22      0.3    62.5 |
  |     3     4    50     9      0.2    44.0 |
  |     4     5    38     5      0.2    35.0 |
  |------------------------------------------|
  |     5     6    32     2      0.2    29.5 |
  |     6     7    27     1      0.2    26.5 |
  |     7     8    26     0      0.2    23.5 |
  |     8     9    21     0      0.2    20.0 |
  |     9    10    19     1      0.1    17.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Male, stage = Unknown

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   371   70     12.9   326.5 |
  |     1     2   282   30     10.3   251.5 |
  |     2     3   221   17      8.6   196.5 |
  |     3     4   172   11      7.6   157.0 |
  |     4     5   142    7      6.9   130.0 |
  |-----------------------------------------|
  |     5     6   118    3      6.0   107.0 |
  |     6     7    96    1      5.3    88.0 |
  |     7     8    80    4      4.9    75.0 |
  |     8     9    70    0      4.7    66.5 |
  |     9    10    63    3      4.5    59.0 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Male, stage = Localised

  +-------------------------------------------+
  | start   end      n    d   d_star        y |
  |-------------------------------------------|
  |     0     1   1228   71     47.4   1167.5 |
  |     1     2   1107   74     43.8   1010.5 |
  |     2     3    914   56     38.9    834.0 |
  |     3     4    754   35     34.9    695.0 |
  |     4     5    636   30     30.9    577.0 |
  |-------------------------------------------|
  |     5     6    518   16     27.5    479.5 |
  |     6     7    441   13     25.0    405.0 |
  |     7     8    369    4     22.7    337.0 |
  |     8     9    305    2     20.0    276.0 |
  |     9    10    247    5     17.4    225.0 |
  +-------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Male, stage = Regional

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   307   45     10.6   278.5 |
  |     1     2   250   39      8.8   219.5 |
  |     2     3   189   26      7.2   165.5 |
  |     3     4   142   18      6.1   129.5 |
  |     4     5   117   10      5.2   104.5 |
  |-----------------------------------------|
  |     5     6    92    4      4.5    82.0 |
  |     6     7    72    3      3.8    63.0 |
  |     7     8    54    0      3.1    48.0 |
  |     8     9    42    0      2.6    37.5 |
  |     9    10    33    3      2.2    29.5 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Male, stage = Distant

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   993   616     27.1   675.0 |
  |     1     2   357   162     10.9   261.0 |
  |     2     3   165    42      6.2   136.5 |
  |     3     4   108    20      4.6    93.5 |
  |     4     5    79    16      3.5    68.5 |
  |------------------------------------------|
  |     5     6    58     5      2.9    52.5 |
  |     6     7    47     3      2.6    42.5 |
  |     7     8    38     2      2.3    35.5 |
  |     8     9    33     1      2.0    29.0 |
  |     9    10    25     1      1.7    22.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Female, stage = Unknown

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   487   109      8.9   425.0 |
  |     1     2   363    31      7.6   333.5 |
  |     2     3   304    18      7.1   283.5 |
  |     3     4   263    12      6.9   247.0 |
  |     4     5   231     6      6.8   216.5 |
  |------------------------------------------|
  |     5     6   202     4      6.8   192.5 |
  |     6     7   183     2      6.8   171.5 |
  |     7     8   160     1      6.5   149.5 |
  |     8     9   139     1      6.3   132.0 |
  |     9    10   125     0      6.2   115.5 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Female, stage = Localised

  +-------------------------------------------+
  | start   end      n    d   d_star        y |
  |-------------------------------------------|
  |     0     1   1488   97     27.8   1429.0 |
  |     1     2   1370   89     26.9   1273.0 |
  |     2     3   1176   53     25.8   1105.0 |
  |     3     4   1034   43     25.0    962.5 |
  |     4     5    891   28     24.1    840.5 |
  |-------------------------------------------|
  |     5     6    790   26     23.3    730.5 |
  |     6     7    671   11     21.9    619.5 |
  |     7     8    568    5     21.0    528.5 |
  |     8     9    489    7     20.2    451.0 |
  |     9    10    413    3     18.8    375.0 |
  +-------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Female, stage = Regional

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   465   86      7.8   419.5 |
  |     1     2   374   88      6.3   312.0 |
  |     2     3   250   26      5.0   224.5 |
  |     3     4   199   18      4.4   179.5 |
  |     4     5   160    7      4.1   147.5 |
  |-----------------------------------------|
  |     5     6   135    7      3.7   121.0 |
  |     6     7   107    5      3.4    99.0 |
  |     7     8    91    3      3.2    84.5 |
  |     8     9    78    1      3.0    70.0 |
  |     9    10    62    2      2.7    55.5 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 60-74, sex = Female, stage = Distant

  +-------------------------------------------+
  | start   end      n     d   d_star       y |
  |-------------------------------------------|
  |     0     1   1254   784     16.8   856.0 |
  |     1     2    458   213      6.9   338.0 |
  |     2     3    218    58      4.2   184.5 |
  |     3     4    151    30      3.3   129.0 |
  |     4     5    107    17      2.9    95.5 |
  |-------------------------------------------|
  |     5     6     84     5      2.7    77.5 |
  |     6     7     71     3      2.6    67.5 |
  |     7     8     64     3      2.4    58.0 |
  |     8     9     52     1      2.3    50.0 |
  |     9    10     48     3      2.3    42.5 |
  +-------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Male, stage = Unknown

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   349   164     34.0   251.0 |
  |     1     2   153    17     17.6   130.5 |
  |     2     3   108     9     13.3    97.0 |
  |     3     4    86     7     10.9    75.0 |
  |     4     5    64     5      8.2    52.5 |
  |------------------------------------------|
  |     5     6    41     1      5.7    35.5 |
  |     6     7    30     0      4.1    25.5 |
  |     7     8    21     1      3.1    18.0 |
  |     8     9    15     1      2.5    13.0 |
  |     9    10    11     0      1.9     9.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Male, stage = Localised

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   769   121     77.5   681.5 |
  |     1     2   594    60     61.5   525.0 |
  |     2     3   456    29     50.7   408.0 |
  |     3     4   360    22     42.6   319.0 |
  |     4     5   278    12     35.6   247.5 |
  |------------------------------------------|
  |     5     6   217     9     28.4   186.5 |
  |     6     7   156     1     22.2   138.5 |
  |     7     8   121     2     17.6   104.0 |
  |     8     9    87     2     13.8    75.5 |
  |     9    10    64     1     11.2    56.5 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Male, stage = Regional

  +-----------------------------------------+
  | start   end     n    d   d_star       y |
  |-----------------------------------------|
  |     0     1   186   43     17.7   161.5 |
  |     1     2   137   36     12.7   112.0 |
  |     2     3    87   12      9.0    74.0 |
  |     3     4    61    7      6.8    52.0 |
  |     4     5    43    5      5.0    36.5 |
  |-----------------------------------------|
  |     5     6    30    2      3.8    26.0 |
  |     6     7    22    0      2.9    18.5 |
  |     7     8    15    0      1.9    12.0 |
  |     8     9     9    0      1.2     7.5 |
  |     9    10     6    0      1.0     5.0 |
  +-----------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Male, stage = Distant

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   577   430     43.0   354.5 |
  |     1     2   132    63     10.8    94.5 |
  |     2     3    57    11      5.9    47.5 |
  |     3     4    38     4      4.3    31.0 |
  |     4     5    24     5      2.9    19.5 |
  |------------------------------------------|
  |     5     6    15     2      1.8    12.0 |
  |     6     7     9     0      1.2     8.0 |
  |     7     8     7     0      1.1     6.5 |
  |     8     9     6     0      0.9     4.5 |
  |     9    10     3     0      0.7     3.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Female, stage = Unknown

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   804   401     61.1   578.0 |
  |     1     2   352    67     29.7   298.0 |
  |     2     3   244    25     22.4   216.0 |
  |     3     4   188    15     18.1   163.0 |
  |     4     5   138     7     15.0   124.5 |
  |------------------------------------------|
  |     5     6   111     6     13.0    97.0 |
  |     6     7    83     0     11.0    74.0 |
  |     7     8    65     0      9.3    57.0 |
  |     8     9    49     0      7.5    44.0 |
  |     9    10    39     1      5.9    33.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Female, stage = Localised

  +--------------------------------------------+
  | start   end      n     d   d_star        y |
  |--------------------------------------------|
  |     0     1   1499   213    112.3   1360.5 |
  |     1     2   1222   109     94.8   1098.5 |
  |     2     3    975    58     82.9    884.5 |
  |     3     4    794    41     72.5    709.0 |
  |     4     5    624    24     62.6    564.0 |
  |--------------------------------------------|
  |     5     6    504    18     54.4    452.5 |
  |     6     7    401    18     45.9    350.5 |
  |     7     8    300     5     38.0    265.5 |
  |     8     9    231     3     32.7    207.5 |
  |     9    10    184     2     27.7    162.0 |
  +--------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Female, stage = Regional

  +------------------------------------------+
  | start   end     n     d   d_star       y |
  |------------------------------------------|
  |     0     1   386   106     24.6   325.5 |
  |     1     2   265    47     17.6   223.0 |
  |     2     3   181    24     13.6   158.5 |
  |     3     4   136    21     10.8   115.0 |
  |     4     5    94     5      8.8    85.0 |
  |------------------------------------------|
  |     5     6    76     1      7.3    63.0 |
  |     6     7    50     1      5.5    42.5 |
  |     7     8    35     1      4.2    30.0 |
  |     8     9    25     1      3.2    21.5 |
  |     9    10    18     1      2.5    15.0 |
  +------------------------------------------+

-------------------------------------------------------------------------------
-> agegrp = 75+, sex = Female, stage = Distant

  +-------------------------------------------+
  | start   end      n     d   d_star       y |
  |-------------------------------------------|
  |     0     1   1298   927     71.6   813.0 |
  |     1     2    328   146     20.9   240.5 |
  |     2     3    153    50     11.2   123.0 |
  |     3     4     93    13      8.2    80.0 |
  |     4     5     67    11      6.5    57.0 |
  |-------------------------------------------|
  |     5     6     47     3      5.4    43.5 |
  |     6     7     40     1      4.9    36.0 |
  |     7     8     32     0      4.4    29.0 |
  |     8     9     26     0      3.7    22.0 |
  |     9    10     18     1      2.9    15.5 |
  +-------------------------------------------+


. 

7. Relative survial using STRS: using grouped data for modeling

%%stata 
use grouped, clear

(Collapsed (or grouped) survival data)

8. Browse and list the data

%%stata
list start end n d d_star y ///
if agegrp == 1 & sex == 1 & stage == 1

. list start end n d d_star y ///
> if agegrp == 1 & sex == 1 & stage == 1

     +-----------------------------------------+
     | start   end     n    d   d_star       y |
     |-----------------------------------------|
 91. |     0     1   462   18      5.3   449.5 |
 92. |     1     2   437   15      5.3   416.0 |
 93. |     2     3   395   23      5.1   370.0 |
 94. |     3     4   345   10      4.8   323.0 |
 95. |     4     5   301   12      4.6   287.5 |
     |-----------------------------------------|
 96. |     5     6   274    7      4.4   256.5 |
 97. |     6     7   239    4      4.2   224.0 |
 98. |     7     8   209    2      4.0   197.0 |
 99. |     8     9   185    0      3.8   172.5 |
100. |     9    10   160    0      3.5   148.5 |
     +-----------------------------------------+

. 

9. Modeling Excess Mortality adjusted for age, sex, stage and year

%%stata
preserve
keep if end <= 5
tab stage
replace stage = . if stage == 1
glm d ib5.end i.sex ib1.agegrp i.stage, fam(pois) l(rs d_star) lnoffset(y) eform nocons
restore

. preserve

. keep if end <= 5
(160 observations deleted)

. tab stage

   Clinical |
   stage at |
  diagnosis |      Freq.     Percent        Cum.
------------+-----------------------------------
    Unknown |         40       25.00       25.00
  Localised |         40       25.00       50.00
   Regional |         40       25.00       75.00
    Distant |         40       25.00      100.00
------------+-----------------------------------
      Total |        160      100.00

. replace stage = . if stage == 1
(40 real changes made, 40 to missing)

. glm d ib5.end i.sex ib1.agegrp i.stage, fam(pois) l(rs d_star) lnoffset(y) ef
> orm nocons

Iteration 0:   log likelihood = -1740.3042  
Iteration 1:   log likelihood = -1445.3819  
Iteration 2:   log likelihood = -1438.1762  
Iteration 3:   log likelihood =  -1438.102  
Iteration 4:   log likelihood =  -1438.102  

Generalized linear models                         Number of obs   =        120
Optimization     : ML                             Residual df     =        110
                                                  Scale parameter =          1
Deviance         =  2344.448143                   (1/df) Deviance =   21.31316
Pearson          =  1834.886508                   (1/df) Pearson  =   16.68079

Variance function: V(u) = u                       [Poisson]
Link function    : g(u) = log(u-d*)               [Relative survival]

                                                  AIC             =   24.13503
Log likelihood   = -1438.102021                   BIC             =   1817.824

------------------------------------------------------------------------------
             |                 OIM
           d |     exp(b)   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         end |
          1  |   .7575144    .023741    -8.86   0.000     .7123832    .8055047
          2  |   .4299128    .017386   -20.87   0.000     .3971523    .4653757
          3  |   .2024888   .0135139   -23.93   0.000     .1776612    .2307859
          4  |   .1094397    .011901   -20.34   0.000     .0884325    .1354373
             |
         sex |
     Female  |   .7814694   .0198743    -9.70   0.000     .7434715    .8214094
             |
      agegrp |
       0-44  |   .4452351   .0293206   -12.29   0.000     .3913218     .506576
      60-74  |   .5463409   .0162633   -20.31   0.000     .5153775    .5791645
        75+  |   .7183094   .0233108   -10.20   0.000     .6740438     .765482
             |
       stage |
   Regional  |    .405009   .0202618   -18.07   0.000     .3671814    .4467337
    Distant  |   1.934658   .0550058    23.21   0.000     1.829797    2.045528
       ln(y) |          1  (exposure)
------------------------------------------------------------------------------

. restore

. 

GRACIAS