Age-standardised net survival (non-parametric)
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.
This tutorial illustrates how to use strs to estimate age-standardised net survival with ICSS weights. Both the Ederer II and Pohar Perme estimators are used.
. use http://pauldickman.com/data/colon.dta if stage == 1, clear
(Colon carcinoma, diagnosed 1975-94, follow-up to 1995)
.
. // Reclassify age groups according to International Cancer Survival Standard
. drop agegrp
. label drop agegrp
. egen agegrp=cut(age), at(0 15 45 55 65 75 200) icodes
. label variable agegrp "Age group"
. label define agegrp 1 "15-44" 2 "45-54" 3 "55-64" 4 "65-74" 5 "75+"
. label values agegrp agegrp
.
. /* Specify weights for each agegroup */
. recode agegrp (1=0.07) (2=0.12) (3=0.23) (4=0.29) (5=0.29), gen(ICSSwt)
(6274 differences between agegrp and ICSSwt)
.
. 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
Now we call strs.
. strs using http://pauldickman.com/data/popmort [iw=ICSSwt], ///
> breaks(0(1)10) mergeby(_year sex _age) diagage(age) ///
> by(sex) standstrata(agegrp) pohar f(%7.5f)
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
------------------------------------------------------------------------------------------------------------
-> sex = Male, agegrp = 15-44
+-----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-----------------------------------------------------------------------------------------------------|
| 0 1 161 7 0 0.95652 0.99683 0.95957 0.95652 0.95958 0.91244 0.98159 |
| 1 2 154 15 7 0.90033 0.99663 0.90338 0.86119 0.86691 0.80159 0.91189 |
| 2 3 132 4 9 0.96863 0.99629 0.97223 0.83417 0.84281 0.77316 0.89255 |
| 3 4 119 5 10 0.95614 0.99607 0.95991 0.79758 0.80898 0.73387 0.86482 |
| 4 5 104 3 8 0.97000 0.99578 0.97411 0.77366 0.78820 0.70942 0.84789 |
|-----------------------------------------------------------------------------------------------------|
| 5 6 93 4 6 0.95556 0.99544 0.95994 0.73927 0.75652 0.67274 0.82168 |
| 6 7 83 1 4 0.98765 0.99516 0.99246 0.73014 0.75074 0.66513 0.81745 |
| 7 8 78 1 8 0.98649 0.99475 0.99169 0.72028 0.74438 0.65662 0.81288 |
| 8 9 69 2 3 0.97037 0.99445 0.97579 0.69894 0.72606 0.63427 0.79844 |
| 9 10 64 2 7 0.96694 0.99411 0.97267 0.67583 0.70629 0.61030 0.78281 |
+-----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Male, agegrp = 45-54
+-----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-----------------------------------------------------------------------------------------------------|
| 0 1 226 15 0 0.93363 0.99189 0.94126 0.93363 0.94124 0.89809 0.96646 |
| 1 2 211 6 12 0.97073 0.99147 0.97908 0.90630 0.92162 0.87224 0.95243 |
| 2 3 193 15 11 0.92000 0.99080 0.92855 0.83380 0.85568 0.79573 0.89915 |
| 3 4 167 6 14 0.96250 0.98995 0.97228 0.80253 0.83222 0.76764 0.88024 |
| 4 5 147 6 9 0.95789 0.98909 0.96846 0.76874 0.80623 0.73684 0.85906 |
|-----------------------------------------------------------------------------------------------------|
| 5 6 132 5 12 0.96032 0.98828 0.97171 0.73823 0.78317 0.70915 0.84046 |
| 6 7 115 3 10 0.97273 0.98754 0.98500 0.71810 0.77130 0.69349 0.83174 |
| 7 8 102 7 5 0.92965 0.98642 0.94245 0.66758 0.72666 0.64223 0.79434 |
| 8 9 90 2 12 0.97619 0.98514 0.99091 0.65169 0.71964 0.63153 0.79016 |
| 9 10 76 3 10 0.95775 0.98383 0.97349 0.62415 0.70125 0.60788 0.77646 |
+-----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Male, agegrp = 55-64
+-----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-----------------------------------------------------------------------------------------------------|
| 0 1 552 34 0 0.93841 0.98013 0.95743 0.93841 0.95735 0.93128 0.97366 |
| 1 2 518 33 34 0.93413 0.97885 0.95432 0.87659 0.91362 0.87969 0.93832 |
| 2 3 451 35 27 0.92000 0.97723 0.94144 0.80647 0.85991 0.81919 0.89206 |
| 3 4 389 23 29 0.93858 0.97564 0.96202 0.75694 0.82756 0.78216 0.86432 |
| 4 5 337 22 19 0.93282 0.97369 0.95803 0.70609 0.79241 0.74242 0.83379 |
|-----------------------------------------------------------------------------------------------------|
| 5 6 296 16 23 0.94376 0.97207 0.97088 0.66638 0.76948 0.71557 0.81452 |
| 6 7 257 13 24 0.94694 0.96958 0.97665 0.63102 0.75150 0.69352 0.80011 |
| 7 8 220 9 22 0.95694 0.96689 0.98971 0.60385 0.74424 0.68214 0.79604 |
| 8 9 189 7 20 0.96089 0.96476 0.99599 0.58023 0.74029 0.67332 0.79562 |
| 9 10 162 2 20 0.98684 0.96255 1.02523 0.57260 0.75941 0.68784 0.81676 |
+-----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Male, agegrp = 65-74
+-----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-----------------------------------------------------------------------------------------------------|
| 0 1 912 97 0 0.89364 0.95434 0.93640 0.89364 0.93626 0.91163 0.95420 |
| 1 2 815 83 67 0.89379 0.95128 0.93957 0.79873 0.87921 0.84671 0.90521 |
| 2 3 665 68 54 0.89342 0.94788 0.94254 0.71360 0.82903 0.79031 0.86123 |
| 3 4 543 48 42 0.90805 0.94334 0.96258 0.64798 0.79733 0.75317 0.83447 |
| 4 5 453 51 38 0.88249 0.93970 0.93912 0.57184 0.74831 0.69866 0.79103 |
|-----------------------------------------------------------------------------------------------------|
| 5 6 364 36 20 0.89831 0.93502 0.96073 0.51368 0.71800 0.66301 0.76562 |
| 6 7 308 27 25 0.90863 0.93031 0.97670 0.46675 0.70158 0.64108 0.75387 |
| 7 8 256 20 25 0.91786 0.92452 0.99280 0.42841 0.69904 0.63215 0.75614 |
| 8 9 211 20 22 0.90000 0.91821 0.98017 0.38557 0.68555 0.61083 0.74889 |
| 9 10 169 17 15 0.89474 0.91224 0.98082 0.34498 0.67103 0.58708 0.74168 |
+-----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Male, agegrp = 75+
+------------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|------------------------------------------------------------------------------------------------------|
| 0 1 769 175 0 0.77243 0.89076 0.86716 0.77243 0.86316 0.82589 0.89298 |
| 1 2 594 92 46 0.83888 0.88959 0.94299 0.64798 0.81437 0.76652 0.85336 |
| 2 3 456 58 38 0.86728 0.88314 0.98204 0.56198 0.79926 0.74068 0.84598 |
| 3 4 360 58 24 0.83333 0.87630 0.95097 0.46831 0.76949 0.70046 0.82460 |
| 4 5 278 31 30 0.88213 0.86623 1.01836 0.41311 0.78994 0.70455 0.85319 |
|------------------------------------------------------------------------------------------------------|
| 5 6 217 41 20 0.80193 0.85874 0.93385 0.33129 0.72051 0.61395 0.80232 |
| 6 7 156 27 8 0.82237 0.85158 0.96570 0.27244 0.68836 0.56464 0.78349 |
| 7 8 121 22 12 0.80870 0.84395 0.95823 0.22032 0.65488 0.51593 0.76281 |
| 8 9 87 18 5 0.78698 0.83458 0.94297 0.17339 0.63711 0.48122 0.75741 |
| 9 10 64 9 6 0.85246 0.82109 1.03820 0.14781 0.65766 0.46069 0.79724 |
+------------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Female, agegrp = 15-44
+----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|----------------------------------------------------------------------------------------------------|
| 0 1 136 5 0 0.96324 0.99883 0.96436 0.96324 0.96437 0.91424 0.98542 |
| 1 2 131 6 5 0.95331 0.99875 0.95450 0.91826 0.92047 0.85876 0.95590 |
| 2 3 120 8 3 0.93249 0.99867 0.93373 0.85627 0.85947 0.78642 0.90896 |
| 3 4 109 6 5 0.94366 0.99856 0.94502 0.80803 0.81229 0.73258 0.87032 |
| 4 5 98 5 5 0.94764 0.99841 0.94915 0.76572 0.77094 0.68622 0.83551 |
|----------------------------------------------------------------------------------------------------|
| 5 6 88 2 4 0.97674 0.99829 0.97841 0.74791 0.75424 0.66740 0.82142 |
| 6 7 82 1 10 0.98701 0.99818 0.98881 0.73820 0.74582 0.65755 0.81453 |
| 7 8 71 1 2 0.98571 0.99797 0.98772 0.72766 0.73665 0.64665 0.80711 |
| 8 9 68 1 7 0.98450 0.99780 0.98667 0.71637 0.72676 0.63477 0.79922 |
| 9 10 60 0 3 1.00000 0.99757 1.00244 0.71637 0.72853 0.63618 0.80106 |
+----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Female, agegrp = 45-54
+-----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-----------------------------------------------------------------------------------------------------|
| 0 1 294 11 1 0.96252 0.99703 0.96538 0.96252 0.96537 0.93531 0.98160 |
| 1 2 282 17 21 0.93738 0.99686 0.94033 0.90225 0.90776 0.86631 0.93683 |
| 2 3 244 16 27 0.93059 0.99660 0.93376 0.83962 0.84762 0.79745 0.88624 |
| 3 4 201 8 13 0.95887 0.99631 0.96242 0.80509 0.81578 0.76129 0.85899 |
| 4 5 180 7 12 0.95977 0.99610 0.96353 0.77270 0.78602 0.72773 0.83327 |
|-----------------------------------------------------------------------------------------------------|
| 5 6 161 9 14 0.94156 0.99578 0.94554 0.72754 0.74316 0.68010 0.79567 |
| 6 7 138 4 11 0.96981 0.99547 0.97423 0.70558 0.72403 0.65849 0.77912 |
| 7 8 123 3 11 0.97447 0.99506 0.97931 0.68756 0.70917 0.64139 0.76650 |
| 8 9 109 0 15 1.00000 0.99461 1.00542 0.68756 0.71303 0.64474 0.77055 |
| 9 10 94 0 8 1.00000 0.99412 1.00592 0.68756 0.71727 0.64841 0.77500 |
+-----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Female, agegrp = 55-64
+-----------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-----------------------------------------------------------------------------------------------------|
| 0 1 617 37 0 0.94003 0.99247 0.94716 0.94003 0.94712 0.92459 0.96305 |
| 1 2 580 31 30 0.94513 0.99195 0.95281 0.88846 0.90243 0.87368 0.92492 |
| 2 3 519 19 31 0.96226 0.99110 0.97091 0.85493 0.87623 0.84397 0.90222 |
| 3 4 469 18 32 0.96026 0.99016 0.96980 0.82096 0.84990 0.81434 0.87916 |
| 4 5 419 19 33 0.95280 0.98915 0.96325 0.78220 0.81885 0.77979 0.85164 |
|-----------------------------------------------------------------------------------------------------|
| 5 6 367 18 27 0.94908 0.98793 0.96067 0.74238 0.78645 0.74391 0.82277 |
| 6 7 322 10 28 0.96753 0.98670 0.98057 0.71827 0.77087 0.72584 0.80950 |
| 7 8 284 8 28 0.97037 0.98521 0.98494 0.69699 0.75941 0.71191 0.80020 |
| 8 9 248 3 25 0.98726 0.98346 1.00387 0.68811 0.76238 0.71299 0.80445 |
| 9 10 220 7 23 0.96643 0.98172 0.98443 0.66501 0.74988 0.69691 0.79498 |
+-----------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Female, agegrp = 65-74
+------------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|------------------------------------------------------------------------------------------------------|
| 0 1 1108 93 0 0.91606 0.97715 0.93749 0.91606 0.93744 0.91840 0.95215 |
| 1 2 1015 94 65 0.90433 0.97497 0.92754 0.82842 0.86917 0.84358 0.89085 |
| 2 3 856 59 50 0.92900 0.97237 0.95540 0.76960 0.83055 0.80109 0.85604 |
| 3 4 747 54 59 0.92474 0.96912 0.95421 0.71168 0.79294 0.75993 0.82195 |
| 4 5 634 36 32 0.94175 0.96553 0.97536 0.67023 0.77261 0.73650 0.80444 |
|------------------------------------------------------------------------------------------------------|
| 5 6 566 45 48 0.91697 0.96217 0.95303 0.61458 0.73727 0.69773 0.77250 |
| 6 7 473 30 42 0.93363 0.95755 0.97502 0.57379 0.71774 0.67466 0.75618 |
| 7 8 401 22 32 0.94286 0.95303 0.98933 0.54100 0.71149 0.66483 0.75290 |
| 8 9 347 22 35 0.93323 0.94687 0.98559 0.50488 0.70037 0.64908 0.74567 |
| 9 10 290 23 30 0.91636 0.94068 0.97415 0.46265 0.68444 0.62789 0.73425 |
+------------------------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Female, agegrp = 75+
+-------------------------------------------------------------------------------------------------------+
| start end n d w p p_star r cp cns_pp lo_cns~p hi_cns~p |
|-------------------------------------------------------------------------------------------------------|
| 0 1 1499 277 0 0.81521 0.91942 0.88666 0.81521 0.88360 0.86015 0.90334 |
| 1 2 1222 165 82 0.86029 0.91716 0.93799 0.70132 0.82797 0.79782 0.85403 |
| 2 3 975 114 67 0.87892 0.91096 0.96482 0.61640 0.80203 0.76615 0.83301 |
| 3 4 794 85 85 0.88689 0.90298 0.98218 0.54668 0.78767 0.74490 0.82414 |
| 4 5 624 67 53 0.88787 0.89525 0.99176 0.48538 0.78453 0.73363 0.82686 |
|-------------------------------------------------------------------------------------------------------|
| 5 6 504 57 46 0.88150 0.88673 0.99410 0.42786 0.78436 0.72396 0.83306 |
| 6 7 401 64 37 0.83268 0.87798 0.94841 0.35627 0.74935 0.67824 0.80698 |
| 7 8 300 39 30 0.86316 0.86708 0.99547 0.30752 0.75559 0.66948 0.82223 |
| 8 9 231 27 20 0.87783 0.85610 1.02538 0.26995 0.80054 0.68445 0.87763 |
| 9 10 184 26 18 0.85143 0.84233 1.01080 0.22984 0.80936 0.64265 0.90377 |
+-------------------------------------------------------------------------------------------------------+
Adjusted survival estimates weighting stratum-specific survival in each group of agegrp by ICSSwt weights.
------------------------------------------------------------------------------------------------------------
-> sex = Male
+---------------------------------------------------------------------------------------+
| start end cp cr_e2 lo_cr_e2 hi_cr_e2 cns_pp lo_cns~p hi_cns~p |
|---------------------------------------------------------------------------------------|
| 0 1 0.87799 0.92336 0.90910 0.93547 0.92214 0.90788 0.93428 |
| 1 2 0.79020 0.87370 0.85504 0.89012 0.87255 0.85384 0.88903 |
| 2 3 0.71385 0.83289 0.81042 0.85294 0.83166 0.80898 0.85190 |
| 3 4 0.64996 0.79975 0.77392 0.82297 0.80121 0.77508 0.82466 |
| 4 5 0.59444 0.77712 0.74763 0.80362 0.78027 0.74999 0.80736 |
|---------------------------------------------------------------------------------------|
| 5 6 0.53865 0.74341 0.71013 0.77349 0.74109 0.70486 0.77360 |
| 6 7 0.49678 0.72537 0.68799 0.75908 0.72103 0.67986 0.75788 |
| 7 8 0.45755 0.70787 0.66583 0.74565 0.70312 0.65708 0.74421 |
| 8 9 0.42268 0.69000 0.64278 0.73230 0.69102 0.63969 0.73657 |
| 9 10 0.39681 0.69383 0.63927 0.74183 0.69357 0.63227 0.74675 |
+---------------------------------------------------------------------------------------+
------------------------------------------------------------------------------------------------------------
-> sex = Female
+---------------------------------------------------------------------------------------+
| start end cp cr_e2 lo_cr_e2 hi_cr_e2 cns_pp lo_cns~p hi_cns~p |
|---------------------------------------------------------------------------------------|
| 0 1 0.90121 0.93020 0.91992 0.93921 0.92929 0.91899 0.93832 |
| 1 2 0.82052 0.87429 0.86049 0.88682 0.87309 0.85923 0.88569 |
| 2 3 0.75927 0.83703 0.82075 0.85198 0.83686 0.82046 0.85190 |
| 3 4 0.70692 0.80864 0.79020 0.82564 0.80861 0.78986 0.82587 |
| 4 5 0.66136 0.78745 0.76686 0.80646 0.78819 0.76702 0.80769 |
|---------------------------------------------------------------------------------------|
| 5 6 0.61271 0.76188 0.73891 0.78313 0.76413 0.74030 0.78610 |
| 6 7 0.57126 0.73851 0.71318 0.76199 0.74185 0.71510 0.76651 |
| 7 8 0.53982 0.73021 0.70213 0.75611 0.73679 0.70651 0.76447 |
| 8 9 0.51562 0.73308 0.70167 0.76177 0.74705 0.71117 0.77918 |
| 9 10 0.48643 0.72809 0.69236 0.76040 0.74274 0.69747 0.78232 |
+---------------------------------------------------------------------------------------+
Note: The cumulative relative/net survival exceeds 1 or is greater
than the estimate in the previous interval for at least one
level of agegrp. The CI is set to missing.
Paul Dickman
Professor of Biostatistics
Biostatistician working with register-based cancer epidemiology.