Estimation of Relative Survival Based on Cancer Registry Data

Transcription

1 Revew of Bonformatcs and Bometrcs (RBB) Volume 2 Issue 4, December Estmaton of Relatve Based on Cancer Regstry Data Olaf Schoffer *, Ante Nedostate 2, Stefane J. Klug,2 Cancer Epdemology, Unversty Cancer Center, TU Dresden, Fetscherstrasse 74, 0307 Dresden, Germany 2 Regonal Clncal Cancer Regstry Dresden, Fetscherstrasse 74, 0307 Dresden, Germany * olaf.schoffer@unlnum-dresden.de; ²ante.nedostate@unlnum-dresden.de;,2 stefane.lug@unlnum-dresden.de Abstract Relatve survval rates are sutable for the comparson of survval nformaton between patent groups wth dfferent age structures. They are well establshed as a common method for analyss of cancer regstry data. In the followng, the method for the estmaton of the relatve survval and the central components of the mplementaton of ths method wth SAS are presented. Examples of results of the descrbed program are presented and the program s compared wth a selecton of other techncal solutons. Keywords Relatve ; Cancer Regstry; Natural Mortalty; Kaplan- Meer Estmate; Nelson-Aalen Estmate; Ederer II; Pohar Perme Method Introducton The estmaton of the survval functon s an essental focus of epdemologcal research and frequently used n analyses of cancer regstry data. Besdes the partcular dsease, age of the observed patent group extensvely nfluences survval tme. Relatve survval rates are used to decompose the observed mortalty nto a populaton-based hazard and an excess hazard caused by the partcular dsease (net survval). Thus, the nfluence of the age structure s elmnated. Methods The most establshed method for the estmaton of survval functons s the Kaplan-Meer estmaton. Here, the survval functon for events at tme t < t2 < < t s estmated to Sˆ( = = =, d n d n,, t = 0 t t < t t t + t whereas n ndcates the number of ndvduals under rs at tme t and d the number of events at ths pont n tme (Allson 200). An ndvdual s under rs at a specfc pont n tme f the person has not experenced an event (death) or was not censored (lost-to-followup). The selecton of the populaton occurs mostly by provdng data for a certan tme perod where an ndvdual s part of the populaton (e.g. date of dagnoss n the years 2000 to 2009). Ths procedure s called cohort approach. Brenner and Gefeller (996) ntroduced the perod approach. In comparson to the cohort approach, the perod approach only uses events and censorng, whch occur n a predefned tme nterval. The populaton under rs s only defned for ths specfc tme nterval. The Lfe Table estmaton (Cutler and Ederer 958) s also commonly used, but dffers from the Kaplan- Meer estmaton. On one hand, the tme ponts t do not depct the events tme ponts but the borders of a pror chosen (equdstan ntervals. On the other hand, n s replaced by n (c/2) n the above mentoned equaton, n whch c ndcates the number of censorng wthn the nterval [t ; t ). Snce the ntervals are often selected wder than the possble tme nterval (for example years versus exact day), an mprecseness has to be accepted here. Another method s the Nelson-Aalen estmator for the cumulatve hazard functon. Ths s defned as, t = 0 ~ d H( =, t t < t + t = n d, t t = n whereas t, d and n are defned accordng to the 77

2 Revew of Bonformatcs and Bometrcs (RBB) Volume 2 Issue 4, December 203 Kaplan-Meer estmator. The contnuous verson of the Nelson-Aalen estmator s ~ H( = t dd( u) N( u 0 ) nn wth DD(t = = DD (t where DD (t s a countng nn process and wth NN(t = = NN (t where NN (t s the at-rs process for an ndvdual ( =,, n) as defned n Pohar Perme, Stare, and Estève (202). Hence, the Breslow estmator for the survval rate s ~ H ~ ( t ) S( = e wth an estmated standard error (Greenwood formula (Kalbflesch and Prentce 980)) ˆ σ ( ~ ) ~ d S( t ) = S( t ). = n ( n d ) A sutable confdence nterval wth boundares wthn the gven nterval [0;] can be estmated usng a transformaton of SS (t accordng to Borgan and Lestol (990). The Breslow estmator s asymptotcally equvalent to the Kaplan-Meer estmator and can be derved by the Martngale theory va countng process (Aalen 978). The approxmaton mproves wth ncrease of populaton under rs n relaton to the number of events per ponts n tme. The advantages and dsadvantages of both methods are dscussed n Colosmo and colleaques (2002). No advantages of one method compared to the other can be found. However, dstnct dfferences appear wthn small samples. However, for a number of applcatons, ncludng the analyss of cancer regstry data, the estmaton of observed survval should be extended as follows. Informaton on mortalty ndependent from age and sex structures of the observed populaton s necessary to allow for comparsons of mortalty rates between countres. For ths, the concept of relatve survval should be used. The basc dea of ths concept s to dvde the total mortalty nto natural mortalty and excess mortalty (Koch 200). The natural mortalty at tme t descrbes the proportonal mortalty of the standard populaton whch s dentcal regardng sex and age to the observed populaton under rs. Then the mortalty of the standard populaton can be derved from sex and age specfc mortalty tables of the offcal statstcs, for example the perod mortalty tables of the German Federal Statstcal Offce (Statstsches Bundesamt 20). The remanng excess mortalty after elmnaton of the natural mortalty from the total mortalty descrbes the addtonal mortalty due to a specfc dsease of the observed populaton. The Ederer II procedure (Ederer and Hese 959) s used for the estmaton of natural mortalty. The dervaton of the relatve survval s descrbed n the followng.. Replcaton of nformaton of the populaton for each event tme pont (.e. Cartesan product of n0 ndvduals und event s tme ponts). 2. Restrcton of the retreved data bass for each event tme pont on the respectve populaton under rs. 3. Determnaton of the age of each ndvdual at each event tme pont. 4. Assgnment of the natural mortalty (year, age and sex specfc) for each ndvdual at each event tme pont. 5. Per event tme pont: estmaton of the mean over the ndvdual natural mortaltes of all ndvduals under rs at the respectve event tme pont. 6. Weghng of the mean mortalty at tme pont t. As weght, the tme past the prevous event tme pont (t t ) s used. 7. Accumulaton of the weghted natural mortalty over all tme ponts t to: H * ( (t t < t+). The contnuous verson of the natural mortalty s n = t N( u) dh P ( u) * = H ( N( u) 0 whereas HH PP (t represents the natural mortalty for an ndvdual at tme t. Analogous to the dervaton of the Breslow estmator from the Nelson-Aalen estmator, the expected survval rate from the natural mortalty s estmated as follows * H ( ) ( ) * t S t = e. Thereby, the relatve survval rate s estmated as ~ S( S rel ( =. * S ( Snce the natural mortalty s estmated from the total standard populaton and, therefore, should not nclude error of estmaton, the estmated standard error s, accordng to the addtve hazard model, as follows 78

3 Revew of Bonformatcs and Bometrcs (RBB) Volume 2 Issue 4, December ~ ( ( ) ˆ σ ( S( ). ˆ σ = S rel A very promsng alternatve to the Ederer II method s the Pohar Perme method (Pohar Perme, Stare, and Estève 202), whch provdes an unbased estmaton of the net survval. In ths method, the terms DD (t and NN (t n the contnuous notatons of the Nelson-Aalen estmator and the natural mortalty are replaced by ther weghted counterparts DD ww (t = DD (t/ss PP (t and NN ww (t = NN (t/ss PP (t, whereas SS PP (t s the expected survval rate for an ndvdual at tme t. Hence, relatve survval rate s n w t N ( u) dh P ( u) t w PPM = dd ( u) Srel ( = exp w w N ( u) N ( u) 0 0. The relatve survval rate descrbes the proporton of survvors based on the part of the populaton that would have survved even n the age and sex dentcal standard populaton. For example, f the Breslow estmator calculates a fveyear total survval of 60%, whereas the reference populaton n the same tme frame ndcates an expected survval of 90%, the relatve survval s 66.7% (=60% / 0.9). If the total survval of the observed populaton s larger than the expected survval n the standard reference populaton, the relatve survval can be above 00%. Presentaton of Results The descrbed methods are mplemented n a SAS program that s brefly descrbed n the appendx. It produces graphcs and tabular overvews for the estmated total, expected and relatve survval. Ths wll n part be presented based on an example of data from clncal cancer regstres (CCR). In the frame of an ntatve of the Worng Group of German Clncal Cancer Regstres (ADT), 22 populaton-based and 4 nsttuton-based CCR provded, for an evaluaton of data of malgnant melanoma (ICD-0: C43 and D03), more than prmary cases notfed wthn the tme perod Among them, more than cases were part of the performed survval analyss (Breslow estmator wth Ederer II method and cohort approach). Only populaton-based regstres wth sound nformaton on the vtal status of the cancer patents were ncluded n the survval analyss. Case data that were based on multple notfcatons of the same patent were excluded from the analyss. Due to the large amount of data connected wth the above mentoned asymptotc equvalence, the Breslow estmator s a close approxmaton to the Kaplan Meer estmator. Fgure shows the total, the expected and the relatve 5-year survval. For the relatve survval, the 95% confdence nterval s presented...0 (B) 0.9 (C) (A) (A) (C) Relatve survval Tme (years) (B) Expected survval FIG. 5-YEAR SURVIVAL (TOTAL, EXPECTED, RELATIVE) OF MALIGNANT MELANOMA The 5-year relatve survval rate usng Ederer II method and cohort approach s 86.8%. Usng the Pohar Perme method, the 5-year relatve survval rate s 86.3%, whch s wthn the confdence bound of the relatve survval usng Ederer II. Hence, the bas of the Ederer II method s margnal. Usng perod approach wth a perod range coverng the years 2006 to 2009, the 5-year relatve survval rate s 85.5%. Relatve survval Tme (years) UICC stage 0 I II III IV X FIG. 2 5-YEAR RELATIVE SURVIVAL OF MALIGNANT MELANOMA STRATIFIED BY UICC STAGE Fgure 2 shows the relatve survval wth the 95% confdence ntervals stratfed by UICC stages 0 I II X III IV 79

4 Revew of Bonformatcs and Bometrcs (RBB) Volume 2 Issue 4, December 203 (Wttend and Internatonal Unon Aganst Cancer (UICC) 2003). For the stages 0 and the relatve survval s approxmately 00%. For hgher stages, a decrease n survval compared to the standard populaton can be seen. The severty of dsease has consderable consequences for the survval of the patents, even though the nformaton of the patents age structure was removed. Table quantfes the relaton between relatve, expected and total survval shown n Fgure. Comparng the total survval between both sexes 5 years after dagnoss, women have a consderably better perspectve wth a survval rate of 8.5% than men wth a survval rate of 74.2%. However, a group of the standard populaton dentcal to the age of the observed populaton would also have a better survval for women (expected survval rate: 9.4%) than for men (expected survval rate: 87.9%). It can be questoned whether the better survval of women versus men wth a malgnant melanoma s solely attrbutable to the already lower lfe expectancy of men or whether one can stll see ths dfference between both sexes after the removal of ths effect. After the removal of expected survval, an advantage of (relatve) survval n women remans. TABLE SURVIVAL (TOTAL, EXPECTED, RELATIVE) AFTER DIAGNOSIS MALIGNANT MELANOMA STRATIFIED BY SEX Sex Men Women Year (after dagnoss) Expected Relatve Relatve 95%-LCL Relatve 95%-UCL 94.6% 97.5% 97.0% 96.6% 97.4% % 95.% 93.4% 92.8% 94.0% % 92.7% 89.9% 89.0% 90.6% % 90.3% 86.8% 85.8% 87.7% % 87.9% 84.4% 83.3% 85.4% 96.% 98.3% 97.8% 97.4% 98.% 2 92.% 96.5% 95.4% 94.8% 95.9% % 94.8% 93.2% 92.5% 93.8% % 93.% 9.3% 90.5% 92.% 5 8.5% 9.4% 89.2% 88.2% 90.% Comparson wth other Solutons Table 2 compares the descrbed mplementaton (Koch 200) wth a selecton of other establshed solutons n regard to the used software and avalable methods. An analyss wth the program SURVSOFT (Gess, Meyer, Radespel-Troger, and Gefeller 2009) analogous to table reveals almost dentcal results for the percentage and the confdence ntervals of the relatve survval. Devaton from the 5-year survval occurs only n the second decmal place of the percentage values. Other solutons result n slghtly larger devatons, due to dfferent date accurateness or method. The conclusons reman, however, comparable. Besdes the descrbed dfferences and the smlartes of the dfferent solutons, dstnct dfferences partly reman n regard to the presentaton of results and the handlng, whch can, however, not be descrbed n more detal here. TABLE 2 OVERVIEW OF EXAMPLE SOLUTIONS TO ESTIMATE THE RELATIVE SURVIVAL Soluton Extenson of RSURV (Koch 200) SURVSOFT (Gess et al. 2009) Programs of P. Dcman (Dcman 2004) perod(r/h) (Brenner, Gefeller, and Haulnen 2004) Software SAS Own Development SAS / Stata SAS / R Lfe Table, Kaplan- Meer & Breslow Lfe Table & Kaplan- Meer Lfe Table Lfe Table Method Expected Pohar Perme* Haulnen (Haulnen 982) Pohar Perme Haulnen Relatve Cohort & Perod Approach* Cohort & Perod Approach Cohort & Perod Approach Perod** Approach *The smultaneous use of the Pohar Perme method wth the perod approach s not yet mplemented **Cohort estmaton can be performed by choosng a perod range that spans the entre range of data Conclusons Wth the presented program, a flexble and comparable soluton n regard to the results of establshed programs for the estmaton of relatve survval rates s avalable. Small dfferences n the results occur due to the dfferent methods n regard to, for example, the expected and the total survval, the selecton of the observed populaton, the accurateness of the tme axs and the lfe table used. Due to the reduced complexty of syntax and macro functonalty, the program can be adapted more flexbly and offers the whole spectrum of methods whch are avalable wth the procedure LIFETEST Snce SAS The produced results can be reported n dfferent fle formats va ODS and SAS/GRAPH. Durng programmng of the syntax, an optmal program flow was consdered. Specal focus was set 80

5 Revew of Bonformatcs and Bometrcs (RBB) Volume 2 Issue 4, December on the reducton of the data base already durng the establshment of the Cartesan product and the consequent explotaton of mprovements untl SAS 9.22 (LIFETEST; ODS; SQL). Appendx Implementaton n SAS The followng mplementaton n SAS s an advancement of the program RSURV (Koch 200). However, only a few essental steps and not the complete program are presented here. The combnaton of the avalable programmng elements wth the am to estmate the relatve survval has, to our nowledge, not been descrbed elsewhere. Macro-Functonalty The presented estmaton was embedded nto a macro that s defned by eyword parameters: %macro rsurv_s(ds=, strat=, methd=, net=, approach=, nzus=, tt2=); The macro varables for the names of the base data set (&ds), the stratfyng varable (&stra, the used method for estmatng observed survval (&methd), the used method for calculatng net survval (&ne, and the chosen cohort or perod approach (&approach) wll be needed n the followng. The method for estmatng observed survval can be chosen accordng to the avalable optons n PROC LIFETEST. For the base data set, a data set wth the followng varables s expected: patd (unque patent ID), ddate (date of dagnoss), bdate (date of brth), tme (number of days between date of dagnoss and date of event or censorng), status (0 =ˆ censored observaton, =ˆ observaton wth even, sex ( =ˆ male, 2 =ˆ female). Further parameters could be a text for the subttle n the output (&tt2) and a data name add on (&nzus). Besdes those, predefned macro varables are used wthn the macro. Those refer to the output format (&channel), for example PDF or RTF, the maxmal depcted observaton tme (&maxtme) as well as the ndcaton of the path for data output (&path). A further descrpton of the used macro functonalty can be found elsewhere (Krämer, Schoffer, and Tschersch 2008) and (SAS Insttute Inc. 2009). PROC LIFETEST wth ODS A central component of the estmaton of relatve survval rates s the estmaton of the total survval (by Lfe Table, Kaplan Meer or Breslow estmator). Ths has been mplemented for the cohort approach wth the procedure LIFETEST (SAS Insttute Inc. 200) n SAS snce verson For the perod approach and the Pohar Perme method, the total survval has to be estmated wthout the procedure LIFETEST. The procedure request used n the program and some optons are brefly descrbed. PROC LIFETEST DATA=&ds METHOD=BRESLOW NELSON ATRISK INTERVALS=(0 TO &maxtme BY ) CONFTYPE=LOGLOG OUTSURV=&ds._cl; TIME tme*status(0); STRATA &strat; RUN; In SAS versons 9.2 and 9.22, the followng optons for the LIFETEST procedure are newly ntroduced or extended. The ATRISK opton s used to output the number of ndvduals under rs. Wth CONFTYPE= the transformaton to estmate the confdence ntervals s ndcated. The METHOD= opton now allows the selecton of the Breslow estmator to estmate the total survval n addton to the earler avalable methods Kaplan-Meer and Lfe Table. The NELSON opton s used to output the Nelson-Aalen estmator. The result output n the program s operated by ODS. The ndcaton for the output channel s gven by the macro varable &channel, whch s defned at the begn of the program. In addton to the text and graphc output, ODS s also used to retreve estmaton results as SAS data set. Ths data set s the bass for the subsequent estmaton of the relatve survval and s later lned to the data set whch ncludes the confdence estmaton for the total survval. For ths, PROC LIFETEST s enclosed by the followng ODS OUTPUT statements. ODS OUTPUT BRESLOWESTIMATES=&ds._breslow; PROC LIFETEST < > ODS OUTPUT CLOSE; Cartesan Product wth PROC SQL As descrbed, for the estmaton of an age and sex dentcal reference populaton to the populaton under rs for all event tme ponts, the Cartesan product of all ndvduals (patd) and event tme ponts s to be estmated and the created amount of data restrcted to 8

6 Revew of Bonformatcs and Bometrcs (RBB) Volume 2 Issue 4, December 203 the populaton at rs at the approprate pont n tme. In the followng PROC SQL program step, both requrements wll be mplemented: the restrcton occurs n the WHERE condton, the rest of the SQL syntax s used for the creaton of the Cartesan product. A prerequste s, besdes the output data set, another data set whch ncludes only the event tme pont per strata wthout repettons. Ths s acheved wth the PROC FREQ. PROC FREQ DATA=&ds; TABLES tme*&strat /NOPRINT OUT=&ds._ereg(KEEP=tme &strat RENAME=(tme=globtme &strat=globstra); WHERE status=; RUN; PROC SQL NOPRINT; CREATE TABLE art AS SELECT a.patd, a.tme, a.&strat, b.globtme, b.globstrat FROM &ds a, &ds._ereg b WHERE (a.tme>=b.globtme AND a.&strat=b.globstra ORDER BY a.patd, b.globtme; QUIT; ACKNOWLEDGMENT The authors than Anne Neumann for Englsh translaton and formattng of the manuscrpt. REFERENCES Aalen OO Nonparametrc nference for a famly of countng processes. The Annals of Statstcs 6 (4): Allson P analyss usng SAS - a practcal gude (2nd ed.). Cary, NC: SAS Publshng. Borgan O, and Lestol K A Note on Confdence Interval and Bands for the data: theory, emprcal evaluaton, computatonal realzaton and applcatons. Scand J Statstcs 8: Brenner H, and Gefeller O An alternatve approach to montorng cancer patent survval. Cancer 78 (9): Brenner H, Gefeller O, and Haulnen T Perod analyss for 'up-to-date' cancer survval data: theory, emprcal evaluaton, computatonal realsaton and applcatons. Eur. J Cancer 40 (3): Colosmo EA, Ferrera FF, Olvera MD, and Sousa CB Emprcal comparsons between Kaplan-Meer and Nelson-AAlen survval functon estmators. J Stat Comput Smul 72 (4): Cutler SJ, and Ederer F Maxmum utlzaton of the lfe table method n analyzng survval. J Chronc. Ds. 8 (6): Dcman P Estmatng and modellng relatve survval usng SAS, manual. Ederer F, and Hese H Instructons to IBM 650 programmers n processng survval computatons - methodologcal note No. 0 - end results secton. Bethesda, MD: Natonal Cancer Insttute. Gess K, Meyer M, Radespel-Troger M, and Gefeller O SURVSOFT-Software for nonparametrc survval analyss. Comput Methods Programs Bomed. 96 (): Haulnen T Cancer survval corrected for heterogenety n patent wthdrawal. Bometrcs 38 (4): Kalbflesch JD, and Prentce RL Statstcal analyss of falure tme data. New Yor: Wley. Koch R Analyse von Überlebensdauervertelungen unter Berücschtgung der Altersstrutur der Patenten n Klnschen Krebsregstern. In Jahresbercht 200 des Tumorzentrums Dresden e.v., Krämer W, Schoffer O, and Tschersch L Datenanalyse mt SAS. Hedelberg: Sprnger. Pohar Perme M, Stare J, and Estève J On Estmaton n Relatve. Bometrcs 68: SAS Insttute Inc SAS 9.2 Macro Language - Reference. Cary, NC: SAS Publshng. SAS Insttute Inc SAS/STAT 9.22 User's Gude. Cary, NC: SAS Publshng. Statstsches Bundesamt. 20. Perodensterbetafeln für Deutschland 87/88 bs 2007/2009. Wesbaden: Statstsches Bundesamt. Wttend C, and Internatonal Unon Aganst Cancer (UICC) TNM-Klassfaton malgner Tumoren. Berln ; Hedelberg [u.a.]: Sprnger. 82