Non-parametric estimation of net survival with four approaches
Under construction: Stata code and output is shown below. I plan to add additional comments.
The code used in this tutorial, along with links to the data, is available here.
. use http://pauldickman.com/data/colon.dta if stage == 1, clear
(Colon carcinoma, diagnosed 1975-94, follow-up to 1995)
.
. stset exit, origin(dx) fail(status==1 2) id(id) scale(365.24)
id: id
failure event: status == 1 2
obs. time interval: (exit[_n-1], exit]
exit on or before: failure
t for analysis: (time-origin)/365.24
origin: time dx
------------------------------------------------------------------------------
6,274 total observations
0 exclusions
------------------------------------------------------------------------------
6,274 observations remaining, representing
6,274 subjects
3,291 failures in single-failure-per-subject data
35,607.707 total analysis time at risk and under observation
at risk from t = 0
earliest observed entry t = 0
last observed exit t = 20.96156
. gen long potfu = date("31/12/1995","DMY")
. strs using popmort, br(0(1)20) mergeby(_year sex _age) by(year8594) ///
> list(start end n d w cr_e1 cr_e2 cr_hak cns_pp) pohar ederer1 potfu(potfu)
failure _d: status == 1 2
analysis time _t: (exit-origin)/365.24
origin: time dx
id: id
No late entry detected - p is estimated using the actuarial method
------------------------------------------------------------------------------------------------------------
-> year8594 = Diagnosed 75-84
+--------------------------------------------------------------------+
| start end n d w cr_e1 cr_e2 cr_hak cns_pp |
|--------------------------------------------------------------------|
| 0 1 2557 339 1 0.9089 0.9089 0.9089 0.9064 |
| 1 2 2217 253 0 0.8449 0.8425 0.8449 0.8401 |
| 2 3 1964 176 1 0.8085 0.8039 0.8086 0.8032 |
| 3 4 1787 154 0 0.7780 0.7720 0.7781 0.7734 |
| 4 5 1633 129 0 0.7559 0.7489 0.7560 0.7527 |
|--------------------------------------------------------------------|
| 5 6 1504 129 1 0.7302 0.7229 0.7304 0.7259 |
| 6 7 1374 114 0 0.7089 0.7014 0.7091 0.7015 |
| 7 8 1260 86 0 0.7005 0.6921 0.7008 0.6947 |
| 8 9 1174 67 0 0.7017 0.6925 0.7021 0.7073 |
| 9 10 1107 75 0 0.6962 0.6868 0.6966 0.7065 |
|--------------------------------------------------------------------|
| 10 11 1032 67 0 0.6939 0.6844 0.6944 0.7112 |
| 11 12 965 58 106 0.6937 0.6839 0.6939 0.7027 |
| 12 13 801 51 87 0.6915 0.6814 0.6909 0.7018 |
| 13 14 663 29 131 0.7042 0.6922 0.7025 0.7226 |
| 14 15 503 27 97 0.7095 0.6966 0.7064 0.7431 |
|--------------------------------------------------------------------|
| 15 16 379 18 75 0.7208 0.7055 0.7157 0.7553 |
| 16 17 286 20 63 0.7128 0.6971 0.7055 0.7549 |
| 17 18 203 12 48 0.7146 0.7006 0.7045 0.7213 |
| 18 19 143 5 47 0.7366 0.7248 0.7220 0.7616 |
| 19 20 91 11 38 0.6719 0.6625 0.6544 0.7490 |
+--------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> year8594 = Diagnosed 85-94
+--------------------------------------------------------------------+
| start end n d w cr_e1 cr_e2 cr_hak cns_pp |
|--------------------------------------------------------------------|
| 0 1 3717 412 0 0.9328 0.9328 0.9328 0.9305 |
| 1 2 3305 289 369 0.8897 0.8874 0.8896 0.8845 |
| 2 3 2647 220 316 0.8540 0.8495 0.8541 0.8483 |
| 3 4 2111 157 313 0.8285 0.8226 0.8291 0.8221 |
| 4 5 1641 118 239 0.8075 0.8005 0.8086 0.8049 |
|--------------------------------------------------------------------|
| 5 6 1284 104 219 0.7791 0.7708 0.7804 0.7751 |
| 6 7 961 66 199 0.7628 0.7534 0.7644 0.7569 |
| 7 8 696 46 175 0.7493 0.7396 0.7513 0.7449 |
| 8 9 475 35 164 0.7268 0.7174 0.7299 0.7175 |
| 9 10 276 14 140 0.7226 0.7167 0.7297 0.7149 |
|--------------------------------------------------------------------|
| 10 11 122 8 114 0.6773 0.6800 0.6910 0.7175 |
+--------------------------------------------------------------------+
.
. /* Now with shorter intervals, don't show the tables as we will draw a graph */
. strs using popmort, br(0 0.01 0.25(0.25)10) mergeby(_year sex _age) by(year8594) ///
> list(start end n d w cr_e1 cr_e2 cr_hak cns_pp) pohar ederer1 potfu(potfu) save(replace) notables
failure _d: status == 1 2
analysis time _t: (exit-origin)/365.24
origin: time dx
id: id
No late entry detected - p is estimated using the actuarial method
.
. /* Now graph the estimates */
. use grouped if year8594==0, clear
(Collapsed (or grouped) survival data)
. twoway ///
> (connected cr_e1 end, sort lwidth(medthick) msymbol(none) lpattern(dot)) ///
> (connected cr_e2 end, sort lwidth(medthick) msymbol(none) lpattern(shortdash)) ///
> (connected cr_hak end, sort lwidth(medthick) msymbol(none) lpattern(longdash)) ///
> (connected cns_pp end, sort lwidth(medthick) msymbol(none) lpattern(solid)), ///
> yti("Relative/net survival") yscale(range(0.6 1)) ///
> ylabel(0.6(0.1)1, format(%3.1f)) title("Localised colon carcinoma diagnosed 1975-84") ///
> xtitle("Years from diagnosis") xlabel(0(1)10) ysize(8) xsize(11) ///
> legend(order(1 "Ederer I" 2 "Ederer II" 3 "Hakulinen" 4 "Pohar Perme") ring(0) pos(1) col(1))
Paul Dickman
Professor of Biostatistics
Biostatistician working with register-based cancer epidemiology.