Session 19 Crude probability of death: estimation and ... · PDF fileSession 19 Crude...

Session 19

Crude probability of death:

estimation and application

Paul W Dickman1 and Paul C Lambert1,2

1Department of Medical Epidemiology and Biostatistics,Karolinska Institutet, Stockholm, Sweden

2Department of Health Sciences,University of Leicester, UK

Cancer survival: principles, methods and analysisLSHTM

June 2014

Overview

Introduction to competing risks.

Net survival versus crude survival; concepts and definitions.

Which measure (crude or net) is most relevant for my researchquestion?

Assumptions and estimation.

My presentation will focus on concepts; I have included slideswith details and examples that I won’t cover.

Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 2

Survival of patients with colon cancer in Finland

Coding of vital status

Freq. Numeric Label

4642 0 Alive

8369 1 Dead: colon cancer

2549 2 Dead: other

The event of interest is death due to (colon) cancer.

Other events are known as ‘competing events’ or‘competing risks’.

Based on the research question, we choose between one of twoquantities to estimate:

1 Eliminate the competing events (estimate net survival)2 Accommodate the competing events (estimate crude survival)


Many synonyms for the same concept

Net probabilityof death

due to cancer=

Probability of death in ahypothetical world where the

cancer under study is the onlypossible cause of death

Crude probabilityof death

due to cancer=

Probability of death in thereal world where you may die

of other causes before thecancer kills you

Net probability also known as the marginal probability.

Crude probability also known as the cause-specific cumulativeincidence function (Geskus) or the cumulative incidence function.


Net survival

In cancer patient survival we typically choose to eliminate thecompeting events.

That is, we aim to estimate net survival (using eithercause-specific survival or relative survival).

It is important to recognise that net survival is interpreted in ahypothetical world where competing risks are assumed to beeliminated. Requires conditional independence.

I will later show how ‘real world’ probabilities (i.e., crudeprobabilities) can be estimated by accommodating, rather thaneliminating, competing risks.


The choice between relative and cause-specific

survival for estimating net survival

Both methods involve assumptions specific to the approach:

Cause-specific Accurate classification of cause-of-deathRelative Appropriate estimation of expected survival

We choose the approach for which we have the strongest beliefin the underlying assumptions.

For population-based studies this is typically relative survival butevery study must be evaluated on its specific merits.


use colon if age > 70stset exit, origin(dx) failure(status==1) scale(365.25)sts graph

0.2

5.5

.75

1C

ause

-spe

cific

sur

viva

l

0 5 10 15Years since diagnosis

Cancer death (status=1) as the outcome


use colon if age > 70stset exit, origin(dx) failure(status==1) scale(365.25)sts graph, fail

0.2

5.5

.75

1N

et p

roba

bilit

y of

dea

th


Cancer death (status=1) as the outcome


use colon if age > 70stset exit, origin(dx) failure(status==2) scale(365.25)sts graph

0.2

5.5

.75

1C

ause

-spe

cific

sur

viva

l


Non-cancer death (status=2) as the outcome


use colon if age > 70stset exit, origin(dx) failure(status==2) scale(365.25)sts graph, fail

0.2

5.5

.75

1N

et p

roba

bilit

y of

dea

th


Non-cancer death (status=2) as the outcome


0.2

5.5

.75

1N

et p

roba

bilit

y of

dea

th


CancerNon-cancer

Net probabilities do not sum to the total probability of death!


Two estimates of the same quantity (net survival)

0.2

5.5

.75

1N

et s

urvi

val


Cause-specific survivalRelative survival

Two estimates of net survival (patients aged > 70 at Dx)


But they are very similar for ‘young’ patients

0.2

5.5

.75

1N

et s

urvi

val


Cause-specific survivalRelative survival

Two estimates of net survival (patients aged < 70 at dx)


Why the hypothetical world?

Net survival estimates survival in the hypothetical world whereyou cannot die of causes other than the cancer of interest.

Net survival is a theoretical construct. We can attempt toestimate it using either cause-specific survival or relative survival.

It is useful as a measure of cancer-patient survival that isindependent of background mortality so we can makecomparisons across time, across different age-groups in ourpopulation and across different countries.


Interpreting estimates of net survival

The cumulative relative survival ratio can be interpreted as theproportion of patients alive after i years of follow-up in thehypothetical situation where the cancer in question is the onlypossible cause of death.

1-RSR can be interpreted as the proportion of patients who willdie of cancer within i years of follow-up in the hypotheticalsituation where the cancer in question is the only possible causeof death.

We do not live in this hypothetical world (where we estimatewhat is called the net probability of death). Estimates of theproportion of patients who will die of cancer in the presence ofcompeting risks can also be made (crude probabilities of death).

Cronin and Feuer (2000) [1] extended the theory of competingrisks to relative survival; their method is implemented in ourStata command strs.


Net (left) and crude (right) probabilities of death in men with localized

prostate cancer aged 70+ at diagnosis (Cronin and Feuer [1])


What this means

Among these men, the probability of dying of prostate cancerwithin 15 of diagnosis is 40% in the hypothetical world where itis not possible to die of other causes. This is how the relativesurvival or cause-specific survival is interpreted.

However, in the real world where it is possible to die of othercauses the probability of dying of prostate cancer within 15 yearsof diagnosis is less than 20%.


Net (left) and crude (right) probabilities of death due to cancer in

women with regional breast cancer (Cronin and Feuer [1])


What this means

In the hypothetical world, where it is not possible to die ofcauses other than breast cancer, the probability of dying ofregional breast cancer is similar for all age groups.

However, in the real world the probability of dying of breastcancer is lower for elderly women because they are more likely todie of other causes.


http://www.cancerresearchuk.org/cancer-

info/cancerstats/survival/

Relative survival was estimated to be 50%.


Should we estimate crude or net survival?

Prostate Cancer

Association Between Use of b-Blockers and Prostate

Cancer–Specific Survival: A Cohort Study of 3561 Prostate

Cancer Patients with High-Risk or Metastatic Disease

Helene Hartvedt Grytli a, Morten Wang Fagerland b, Sophie D. Fossa c,d,Kristin Austlid Tasken a,d,*

a Department of Tumor Biology, Institute of Cancer Research, Oslo University Hospital, Oslo, Norway; b Unit of Biostatistics and Epidemiology, Oslo University

Hospital, Oslo, Norway; c Department of Oncology, Oslo University Hospital, Oslo, Norway; d Institute of Clinical Medicine, University of Oslo, Oslo, Norway

E U R O P E A N U R O L O G Y 6 5 ( 2 0 1 4 ) 6 3 5 – 6 4 1

ava i lable at www.sciencedirect .com

journal homepage: www.europeanurology.com

Article info

Article history:

Accepted January 6, 2013Published online ahead ofprint on January 14, 2013

Keywords:

ASA

b-Adrenergic receptor

antagonist

b-Blocker

Epidemiology

High-risk prostate cancer

Metastasis

Norway

Prostate cancer

Prostate cancer–specific

mortality

Statin

Abstract

Background: We recently reported reduced prostate cancer (PCa)–specific mortality forb-blocker users among patients receiving androgen-deprivation therapy in a healthsurvey cohort including 655 PCa patients. Information on clinical characteristics waslimited.Objective: To assess the association between b-blockers and PCa-specific mortality in acohort of 3561 prostate cancer patients with high-risk or metastatic disease, and toaddress potential confounding from the use of statins or acetylsalicylic acid (ASA).Design, setting, and participants: Clinical information from all men reported to theCancer Registry of Norway with a PCa diagnosis between 2004 and 2009 (n = 24 571)was coupled with information on filled prescriptions between 2004 and 2011 from theNorwegian Prescription Database. Exclusion criteria were low- or intermediate-riskdisease; planned radiotherapy or radical prostatectomy; initiation of b-blocker, ASA, orstatin use after diagnosis where applicable; missing information on baseline Gleasonscore, prostate-specific antigen level, T stage or performance status; and missingfollow-up.Outcome measurements and statistical analysis: Cox proportional hazards modellingand competing risk regression modelling were used to analyse the effects of b-blockeruse on all-cause and PCa-specific mortality, respectively. Differences between b-blockerusers and nonusers regarding baseline clinical characteristics were assessed by theWilcoxon-Mann-Whitney U test, Pearson chi-square test, and Student t test.Results and limitations: Median follow-up was 39 mo. b-Blocker use was associatedwith reduced PCa mortality (adjusted subhazard ratio: 0.79; 95% confidence interval[CI], 0.68–0.91; p value: 0.001). The observed reduction in PCa mortality was indepen-dent of the use of statins or ASA. We observed no association with all-cause mortality(adjusted hazard ratio: 0.92; 95% CI, 0.83–1.02). The main limitations of the study werethe observational study design and short follow-up.Conclusions: b-Blocker use was associated with reduced PCa-specific mortality inpatients with high-risk or metastatic disease at the time of diagnosis. Our findingsneed validation from further observational studies.

# 2013 European Association of Urology. Published by Elsevier B.V. All rights reserved.

* Corresponding author. Oslo University Hospital, Institute of Cancer Research, Department of TumorBiology, P.O. Box 4953 Nydalen, NO-0424 Oslo, Norway. Tel. +47 22781878; Fax: +47 22781795.E-mail address: [email protected] (K.A. Tasken).

0302-2838/$ – see back matter # 2013 European Association of Urology. Published by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.eururo.2013.01.007


Should we estimate crude or net survival?

We wish to compare PrCa-specific survival among two groups:1 Men with prostate cancer using beta-blockers2 Men with prostate cancer not using beta-blockers

The authors used a ‘competing risks analysis’ and concludedthat the men who used beta-blockers were less likely to die ofprostate cancer.

Bernard co-authored a commentary that very nicely explainedwhy such an analysis is incorrect [2] and that net probabilitiesare more appropriate than crude probabilities.


‘An Introduction to Competing Risks Analysis’ [3]

Focus on: Contemporary Methods in Biostatistics (II)

An Introduction to Competing Risks Analysis

Melania Pintilie*

Department of Biostatistics, Ontario Cancer Institute/Princess Margaret Hospital, University Health Network, Dalla Lana School of Public Health, University of Toronto, Canada

INTRODUCTION

Competing risks (CR) has been recognized as a special case oftime-to-event analysis since the 18th century. Occasionally work

in the statistical or mathematical area has been publishedincorporating new developments, including the monograph ofDavid and Moeschberger.1 As the data became more extensive,clear, and precise regarding the different types of outcomes, CRresurfaced as a crucial type of analysis within time-to-eventanalysis, necessary for a better understanding of a disease. Theconnection between the mathematical results and the applied fieldneeded to be made. Several authors have contributed to theunderstanding of CR situations.2,3 Other authors enhanced anddeveloped techniques and in some cases made available ready-to-use computer code for applied statistics.4–6

INTRODUCTION TO TIME-TO-EVENT ANALYSIS

In many studies the outcome is observed longitudinally. In thisway every subject in the cohort is observed for a period of time untilthe event occurs. For example the event of interest may be death,heart attack, or cancer recurrence. The goals of the study may be to

Rev Esp Cardiol. 2011;64(7):599–605

Article history:

Available online 31 May 2011

Keywords:

Survival analysis

Competing risks analysis

Fine and Gray model

A B S T R A C T

The need to develop treatments and/or programs specific to a disease requires the analysis of outcomes

to be specific to that disease. Such endpoints as heart failure, death due to a specific disease, or control of

local disease in cancer may become impossible to observe due to a prior occurrence of a different type

of event (such as death from another cause). The event which hinders or changes the possibility of

observing the event of interest is called a competing risk.

The usual techniques for time-to-event analysis applied in the presence of competing risks give

biased or uninterpretable results. The estimation of the probability of the event therefore needs to be

calculated using specific techniques such as the cumulative incidence function introduced by Kalbfleisch

and Prentice. The model introduced by Fine and Gray can be applied to test a covariate when competing

risks are present. Using specific techniques for the analysis of competing risks will ensure that the results

are unbiased and can be correctly interpreted.

� 2011 Sociedad Espanola de Cardiologıa. Published by Elsevier Espana, S.L. All rights reserved.

Analisis de riesgos competitivos

Palabras clave:

Analisis de supervivencia

Analisis de riesgos competitivos

Modelo de Fine y Gray

R E S U M E N

La necesidad de desarrollar tratamientos o programas especıficos para una enfermedad requiere un

analisis de los resultados que sea especıfico para dicha enfermedad. Criterios de valoracion como la

insuficiencia cardiaca, la muerte debida a una enfermedad especıfica o el control de la enfermedad local

en el cancer pueden ser imposibles de observar debido a la aparicion previa de un tipo de evento

diferente (como la muerte por otra causa). El evento que dificulta o modifica la posibilidad de observar el

evento de interes se denomina riesgo competitivo.

Las tecnicas habituales de analisis del tiempo hasta el evento aplicadas en presencia de riesgos

competitivos producen unos resultados sesgados o no interpretables. La estimacion de la probabilidad

del evento debe calcularse, pues, con el empleo de tecnicas especıficas como la funcion acumulativa de

incidencia introducida por Kalbfleisch y Prentice. El modelo introducido por Fine y Gray puede aplicarse

para evaluar una covariable cuando hay riesgos competitivos. Con el empleo de tecnicas especıficas para

el analisis de los riesgos competitivos se asegurara que los resultados no esten sesgados y puedan

interpretarse correctamente.

� 2011 Sociedad Espanola de Cardiologıa. Publicado por Elsevier Espana, S.L. Todos los derechos reservados.

Abbreviations

CIF: cumulative incidence function

Cox PH: Cox proportional hazards model

CR: competing risks

F&G: Fine and Gray model

KM: Kaplan-Meier

* Corresponding author: Biostatistics Department, Ontario Cancer Institute/UHN,

610 University Ave., Toronto, M5G 2M9, Canada.

E-mail address: [email protected]

1885-5857/$ – see front matter � 2011 Sociedad Espanola de Cardiologıa. Published by Elsevier Espana, S.L. All rights reserved.

doi:10.1016/j.rec.2011.03.016

Document downloaded from http://www.revespcardiol.org, day 17/06/2014. This copy is for personal use. Any transmission of this document by any media or format is strictly prohibited.


This article is misleading and causes confusion

‘When the CR are ignored and the CR observations are censoredthe analysis reduces to a ‘usual’ time-to-event scenario. Due tothe familiarity of this type of analysis and the availability ofsoftware, many researchers resort to this approach, as seen inthe earlier examples. However, it is unanimously agreed not onlyamong statisticians, that the estimation of the probability ofevent in this case overestimates the true probability.’


Net (left) and crude (right) probabilities of death in men with localized

prostate cancer aged 70+ at diagnosis (Cronin and Feuer [1])


Natural frequencies presented using infographics


Cancer Survival Query System (Rocky Feuer)


The independence assumption - crucial for the

interpretation of survival curves when competing

risks are present

Independence assumptionThe time to death from the cancer in question is conditionallyindependent of the time to death from other causes. i.e., thereshould be no factors that influence both cancer and non-cancermortality other than those factors that have been controlled for in theestimation.


If the independence assumption is not satisfied

Cause-specific survival curves provide biased estimates of netsurvival.

If it is not possible to adjust for the mechanism that introducesthe dependence then survival curves should be interpreted withcare.

However, the cause-specific hazard rates still have a usefulinterpretation as the rates that are observed when competingrisks are present.


If the independence assumption is satisfied

Cause-specific survival curves provide estimates of net survival(provided that the classification of cause-of death is accurate).

The survival curves are interpreted as the survival that we wouldobserve if it was possible to eliminate all competing causes ofdeath.

This is a strictly hypothetical (but useful!) construct.

The cause-specific hazard rates provide estimates of the ratesthat we would observe in the absence of competing causes ofdeath.

In the competing risks literature, net survival and hazard aretypically referred to as marginal survival and hazard, respectively.


How can we test if the independence assumption is

satisfied?

Simple answerYou can’t!

It is not possible to formally test if the independence assumptionis satisfied based on the observable data.

You have to make the decision of whether your estimates providean estimate of something useful based on your subject matterknowledge.


How do these concepts translate to relative

survival?

Cause-specific survival and relative survival aim to estimate thesame underlying quantity.

Even though we do not make use of explicit cause of deathinformation, the independence assumption applies also in arelative survival framework.

If satisfied, relative survival and excess mortality rates provideestimates of net survival (given that the patients areexchangeable to the population used to estimate expectedsurvival)

If not satisfied, relative survival curves are biased whereas theexcess mortality rates are interpretable as real-world rates (in thepresence of competing risks).


Estimating crude probabilities (life table, RS)

The contribution to the crude probability for each interval.

Interval crude probability of death due to cancer

gjc =

(j−1∏

i=1

pj

)(1− pj

p∗j

)(1− 1

2

(1− p∗j

))

Interval crude probability of death due to other causes

gjo =

(j−1∏

i=1

pj

)(1− p∗j

)(

1− 1

2

(1− pj

p∗j

))

First term: survival to start of interval.

Second term: probability of dying of cause in interval.

Third term: needed as dealing with grouped time.


Estimation II

Cumulative crude probabilities obtained by summing intervalestimates.

Crjc =

j∑

i=1

gjc

Crjo =

j∑

i=1

gjo

Crjc + Crjo gives the all-cause probability of death at the end ofinterval j

Also possible to obtain variance estimates.

Implemented in strs using cuminc option.

Also available in SEER*Stat.


Using strs

strs will perform the calculations described in Cronin and Feuer.

Adding the cuminc option will do this.

For example,

strs using popmort, br(0(1)10) mergeby( year sex age) by(agegrp) ///cuminc savgroup(cuminc grp,replace)


Colon cancer: crude probabilities

. use grouped, clear

. list start end agegrp cp F cr_e2 ci_dc ci_do if agegrp == 1, noobs

start end agegrp cp F cr_e2 ci_dc ci_do

0 1 45-59 0.7499 0.2501 0.7558 0.2432 0.00681 2 45-59 0.6317 0.3683 0.6419 0.3559 0.01242 3 45-59 0.5672 0.4328 0.5814 0.4151 0.01773 4 45-59 0.5273 0.4727 0.5457 0.4497 0.02294 5 45-59 0.4943 0.5057 0.5168 0.4775 0.0282

5 6 45-59 0.4710 0.5290 0.4981 0.4953 0.03366 7 45-59 0.4561 0.5439 0.4882 0.5046 0.03937 8 45-59 0.4398 0.5602 0.4770 0.5150 0.04518 9 45-59 0.4336 0.5664 0.4769 0.5151 0.05139 10 45-59 0.4248 0.5752 0.4744 0.5174 0.0578


Colon cancer: crude probabilities

. use grouped, clear

. list start end agegrp cp F cr_e2 ci_dc ci_do if agegrp == 3, noobs

start end agegrp cp F cr_e2 ci_dc ci_do

0 1 75+ 0.5424 0.4576 0.5994 0.3816 0.07601 2 75+ 0.4188 0.5812 0.5104 0.4584 0.12282 3 75+ 0.3531 0.6469 0.4772 0.4842 0.16263 4 75+ 0.2994 0.7006 0.4527 0.5015 0.19914 5 75+ 0.2585 0.7415 0.4413 0.5086 0.2329

5 6 75+ 0.2187 0.7813 0.4253 0.5173 0.26406 7 75+ 0.1860 0.8140 0.4162 0.5218 0.29237 8 75+ 0.1571 0.8429 0.4092 0.5246 0.31838 9 75+ 0.1302 0.8698 0.3997 0.5280 0.34189 10 75+ 0.1090 0.8910 0.4004 0.5278 0.3632


Limitation of life table approach

Only estimated at end of interval.

Large age groups: The crude probability of death for someoneaged 60 will be different to someone aged 70.

Limited to how many groups you can investigate (no borrowingof strength).

We will now move to model based estimates of crudeprobabilities.


Crude probabilities from models

We can obtain an estimate of relative survival from the variousmodels we have described (Poisson, flexible parametric, cure).

For individual level models this gives an individual basedprediction of the net probability of death due to cancer (1 -relative survival).

However, we use the ideas from competing risks theory to alsocalculate the crude probability of death due to cancer and due toother causes.


Brief mathematical details[4]h∗(t) - expected mortality rateλ(t) - excess mortality rateh(t) = h∗(t) + λ(t) - all-cause mortality rate

S∗(t) - expected survivalR(t) - relative survivalS(t) = S∗(t)R(t) - All cause survival

Net Prob of Death = 1− R(t) = 1− exp

(−∫ t

0λ(u)du

)

Crude Prob of Death (cancer) =

∫ t

0S∗(u)R(u)λ(u)du

Crude Prob of Death (other causes) =

∫ t

0S∗(u)R(u)h∗(u)du


Estimating the crude probabilities

We will use flexible parametric relative survival models.

For any particular covariate pattern, we can estimate the excessmortality rate, λi(t|xi).

The overall survival for individual i is S∗i (t)Ri(t).

We plug these into the equations in the previous slide toestimate the crude probabilities.

We have to do the integration numerically.


The stpm2cm command

The stpm2cm command is a post estimation command.

It assumes that you have already fitted a relative survival model.

The prediction is for a particular covariate pattern, specifiedusing the at() option.

You need to specify the values for variables in the life table thatthe prediction is for (age, sex, calendar year).

Note that even if you model age as groups then you still have tospecify an exact age, calender year etc, that the prediction is for.

For example,

stpm2 agegrp2-agegrp4, scale(hazard) bhazard(rate) df(5) ///tvc(agegrp2-agegrp4) dftvc(3)

stpm2cm using popmort, at(agegrp2 0 agegrp3 0 agegrp4 0) ///mergeby(_year sex _age) ///diagage(40) diagyear(1985) ///sex(1) stub(cm1) nobs(1000) ///tgen(cm1_t)


Crude probabilities (woman aged 75)

P(Dead − Breast Cancer)

P(Dead − Other Causes)

P(Alive)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babi

lity

of D

eath

0 2 4 6 8Years from diagnosis

Dead (Breast Cancer) Dead (Other Causes) Alive


Comparison with net probability

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babi

lity

of D

eath

0 2 4 6 8Years from diagnosis



Male Hodgkin lymphoma: trends in 5-year RSR

0

.2

.4

.6

.8

1

5-Y

ear

Rel

ativ

e S

urvi

val R

atio

1973

1978

1983

1988

1993

1998

2003

Year of Diagnosis

Age:19-35Age:36-50Age:51-65Age:66-80


Male Hodgkin lymphoma: trends in 10-year RSR

0

.2

.4

.6

.8

1

10-Y

ear

Rel

ativ

e S

urvi

val R

atio

1973

1978

1983

1988

1993

1998

2003

Year of Diagnosis

Age:19-35Age:36-50Age:51-65Age:66-80


Males aged 60 at diagnosis: real-world probabilities

0.0

0.2

0.4

0.6

0.8

1.0

20-y

ear

Pro

babi

lity

of D

eath

19731979

19851991

19972003

Year of Diagnosis

Excess HLOther Causes


Males aged 60 at Dx: partitioning HL mortality

0.0

0.2

0.4

0.6

0.8

1.0

20-y

ear

Pro

babi

lity

of D

eath

19731979

19851991

19972003

Year of Diagnosis

Excess DCSExcess HL (Non-DCS)Other Causes


Eloranta et al. BMC Medical Research Methodology 2012, 12:86http://www.biomedcentral.com/1471-2288/12/86

RESEARCH ARTICLE Open Access

Partitioning of excess mortality in population-based cancer patient survival studies usingflexible parametric survival modelsSandra Eloranta1*, Paul C Lambert1,2, Therese ML Andersson1, Kamila Czene1, Per Hall1, Magnus Bjorkholm3

and Paul W Dickman1

Abstract

Background: Relative survival is commonly used for studying survival of cancer patients as it captures both the directand indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to theexpected survival in a comparable cancer-free population. However, existing methods do not allow estimation of theimpact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose weextend flexible parametric survival models for relative survival, which use restricted cubic splines for the baselinecumulative excess hazard and for any time-dependent effects.

Methods: In the extended model we partition the excess mortality associated with a diagnosis of cancer throughestimating a separate baseline excess hazard function for the outcomes under investigation. This is done byincorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported inthe Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. Thisapproach thereby enables modeling of temporal trends in e.g., excess cardiovascular mortality and remaining cancerexcess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used toderive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence ofcompeting causes of death.

Results: The method is illustrated with examples where the total excess mortality experienced by patients diagnosedwith breast cancer is partitioned into excess cardiovascular mortality and remaining cancer excess mortality.

Conclusions: The proposed method can be used to simultaneously study disease patterns and temporal trends forvarious causes of cancer-consequent deaths. Such information should be of interest for patients and clinicians as oneway of improving prognosis after cancer is through adapting treatment strategies and follow-up of patients towardsreducing the excess mortality caused by side effects of the treatment.

Keywords: Survival analysis, Cancer, Relative survival, Regression models, Competing risks

BackgroundObservational studies of cancer patient survival oftenuse data recorded by population-based cancer registriesand are typically analyzed using relative survival. Rela-tive survival is defined as the observed (all-cause) survival,S(t), among the cancer patients divided by the expectedsurvival, S∗(t), in a comparable group (with respect to

*Correspondence: [email protected] of Medical Epidemiology and Biostatistics, Karolinska Institutet,Box 281, SE-177 77 Stockholm, SwedenFull list of author information is available at the end of the article

age, sex, calendar year and possibly other covariates)in the general population. On the hazard scale, rela-tive survival provides a measure of excess mortality thatcan be assumed to be entirely, directly or indirectly,attributable to the disease [1]. One reason for why mod-elling excess mortality has become the preferred methodfor population-based cancer patient survival analysis isthat it not only captures deaths that are directly due tothe cancer in question but also deaths that can be thoughtof as indirect or cancer-consequent, without relying onthe classification of cause of death. There are, however,

© 2012 Eloranta et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

Temporal Trends in Mortality From Diseases of theCirculatory System After Treatment for HodgkinLymphoma: A Population-Based Cohort Study in Sweden(1973 to 2006)Sandra Eloranta, Paul C. Lambert, Jan Sjoberg, Therese M.L. Andersson, Magnus Bjorkholm,and Paul W. Dickman

All authors: Karolinska Institutet; JanSjoberg and Magnus Bjorkholm, Karolin-ska University Hospital Solna, Stock-holm, Sweden; Paul C. Lambert,University of Leicester, Leicester,United Kingdom.

Published online ahead of print atwww.jco.org on February 25, 2013.

Supported by Grants No. CAN 2010/676 (P.W.D.), CAN 2009/1012 (P.C.L.),and CAN 2009/1203 (M.B.) from theSwedish Cancer Society and by theAdolf H. Lundin Charitable Foundation(M.B.).

Both M.B. and P.W.D. contributedequally to this study.

Presented in part at the 2012 NorthAmerican Association of Central CancerRegistries Annual Conference, June2-8, 2012, Portland, OR, and the 2011Annual Meeting of the Association ofNordic Cancer Registries, August31-September 2, 2011, Åland, Finland.

Authors’ disclosures of potential con-flicts of interest and author contribu-tions are found at the end of thisarticle.

Corresponding author: Sandra Eloranta,MSc, Department of Medical Epidemi-ology and Biostatistics, Karolinska Insti-tutet, Box 281, SE-171 77 Stockholm,Sweden; e-mail: [email protected].

© 2013 by American Society of ClinicalOncology

0732-183X/13/3199-1/$20.00

DOI: 10.1200/JCO.2012.45.2714

A B S T R A C T

PurposeHodgkin lymphoma (HL) survival in Sweden has improved dramatically over the last 40 years, butlittle is known about the extent to which efforts aimed at reducing long-term treatment-relatedmortality have contributed to the improved prognosis.

MethodsWe used population-based data from Sweden to estimate the contribution of treatment-relatedmortality caused by diseases of the circulatory system (DCS) to temporal trends in excess HLmortality among 5,462 patients diagnosed at ages 19 to 80 between 1973 and 2006. Flexibleparametric survival models were used to estimate excess mortality. In addition, we used recentadvances in statistical methodology to estimate excess mortality in the presence of competingcauses of death.

ResultsExcess DCS mortality within 20 years after diagnosis has decreased continually since themid-1980s and is expected to further decrease among patients diagnosed in the modern era. Ageat diagnosis and sex were important predictors for excess DCS mortality, with advanced age andmale sex being associated with higher excess DCS mortality. However, when accounting forcompeting causes of death, we found that excess DCS mortality constitutes a relatively smallproportion of the overall mortality among patients with HL in Sweden.

ConclusionExcess DCS mortality is no longer a common source of mortality among Swedish patients withHL. The main causes of death among long-term survivors today are causes other than HL,although other (non-DCS) excess mortality also persists for as long as 20 years after diagnosis,particularly among older patients.

J Clin Oncol 31. © 2013 by American Society of Clinical Oncology

INTRODUCTION

Survival after Hodgkin lymphoma (HL) has in-creased substantially over the last four decades,and for patients age younger than 65 years atdiagnosis, the disease is now highly curable.1 Theimproved prognosis is likely attributable to im-proved patient assessment and staging, the devel-opment of effective multiagent chemotherapy,introduction of combined-modality therapy withreductions in radiation field size and dose, andmore apt evaluation of treatment response. As aresult of improvements in patient survival, researchand clinical practice in recent decades have focusedon understanding and reducing long-termtreatment-related morbidity and mortality.2-7 In

this article, we focus on excess mortality caused bycerebrovascular and cardiovascular diseases, with aparticular focus on its absolute and relative contri-bution to the total excess mortality from HL.

Treatment-related mortality has typically beenquantified using cause-specific mortality or excessmortality (ie, the difference between the observedand expected mortality rate in patients comparedwith a disease-free population). Both measures aimto provide estimates of the net survival associatedwith the disease (ie, survival in a hypothetical worldwhere patients are assumed immune to death fromcauses other than the disease of interest).8 However,to accurately estimate the risk of, for example, deathfrom treatment-induced cardiovascular disease, weshould acknowledge that patients may also die from

JOURNAL OF CLINICAL ONCOLOGY O R I G I N A L R E P O R T

© 2013 by American Society of Clinical Oncology 1

http://jco.ascopubs.org/cgi/doi/10.1200/JCO.2012.45.2714The latest version is at Published Ahead of Print on February 25, 2013 as 10.1200/JCO.2012.45.2714

Copyright 2013 by American Society of Clinical OncologyBLACKWELL INC on February 26, 2013 from 130.229.54.93

Information downloaded from jco.ascopubs.org and provided by at Karolinska Institutet University Library / SWETSCopyright © 2013 American Society of Clinical Oncology. All rights reserved.

Temporal Trends in Mortality From Diseases of theCirculatory System After Treatment for HodgkinLymphoma: A Population-Based Cohort Study in Sweden(1973 to 2006)Sandra Eloranta, Paul C. Lambert, Jan Sjoberg, Therese M.L. Andersson, Magnus Bjorkholm,and Paul W. Dickman

All authors: Karolinska Institutet; JanSjoberg and Magnus Bjorkholm, Karolin-ska University Hospital Solna, Stock-holm, Sweden; Paul C. Lambert,University of Leicester, Leicester,United Kingdom.

Published online ahead of print atwww.jco.org on February 25, 2013.

Supported by Grants No. CAN 2010/676 (P.W.D.), CAN 2009/1012 (P.C.L.),and CAN 2009/1203 (M.B.) from theSwedish Cancer Society and by theAdolf H. Lundin Charitable Foundation(M.B.).

Both M.B. and P.W.D. contributedequally to this study.

Presented in part at the 2012 NorthAmerican Association of Central CancerRegistries Annual Conference, June2-8, 2012, Portland, OR, and the 2011Annual Meeting of the Association ofNordic Cancer Registries, August31-September 2, 2011, Åland, Finland.

Authors’ disclosures of potential con-flicts of interest and author contribu-tions are found at the end of thisarticle.

Corresponding author: Sandra Eloranta,MSc, Department of Medical Epidemi-ology and Biostatistics, Karolinska Insti-tutet, Box 281, SE-171 77 Stockholm,Sweden; e-mail: [email protected].

© 2013 by American Society of ClinicalOncology

0732-183X/13/3199-1/$20.00

DOI: 10.1200/JCO.2012.45.2714

A B S T R A C T

PurposeHodgkin lymphoma (HL) survival in Sweden has improved dramatically over the last 40 years, butlittle is known about the extent to which efforts aimed at reducing long-term treatment-relatedmortality have contributed to the improved prognosis.

MethodsWe used population-based data from Sweden to estimate the contribution of treatment-relatedmortality caused by diseases of the circulatory system (DCS) to temporal trends in excess HLmortality among 5,462 patients diagnosed at ages 19 to 80 between 1973 and 2006. Flexibleparametric survival models were used to estimate excess mortality. In addition, we used recentadvances in statistical methodology to estimate excess mortality in the presence of competingcauses of death.

ResultsExcess DCS mortality within 20 years after diagnosis has decreased continually since themid-1980s and is expected to further decrease among patients diagnosed in the modern era. Ageat diagnosis and sex were important predictors for excess DCS mortality, with advanced age andmale sex being associated with higher excess DCS mortality. However, when accounting forcompeting causes of death, we found that excess DCS mortality constitutes a relatively smallproportion of the overall mortality among patients with HL in Sweden.

ConclusionExcess DCS mortality is no longer a common source of mortality among Swedish patients withHL. The main causes of death among long-term survivors today are causes other than HL,although other (non-DCS) excess mortality also persists for as long as 20 years after diagnosis,particularly among older patients.

J Clin Oncol 31. © 2013 by American Society of Clinical Oncology

INTRODUCTION

Survival after Hodgkin lymphoma (HL) has in-creased substantially over the last four decades,and for patients age younger than 65 years atdiagnosis, the disease is now highly curable.1 Theimproved prognosis is likely attributable to im-proved patient assessment and staging, the devel-opment of effective multiagent chemotherapy,introduction of combined-modality therapy withreductions in radiation field size and dose, andmore apt evaluation of treatment response. As aresult of improvements in patient survival, researchand clinical practice in recent decades have focusedon understanding and reducing long-termtreatment-related morbidity and mortality.2-7 In

this article, we focus on excess mortality caused bycerebrovascular and cardiovascular diseases, with aparticular focus on its absolute and relative contri-bution to the total excess mortality from HL.

Treatment-related mortality has typically beenquantified using cause-specific mortality or excessmortality (ie, the difference between the observedand expected mortality rate in patients comparedwith a disease-free population). Both measures aimto provide estimates of the net survival associatedwith the disease (ie, survival in a hypothetical worldwhere patients are assumed immune to death fromcauses other than the disease of interest).8 However,to accurately estimate the risk of, for example, deathfrom treatment-induced cardiovascular disease, weshould acknowledge that patients may also die from

JOURNAL OF CLINICAL ONCOLOGY O R I G I N A L R E P O R T

© 2013 by American Society of Clinical Oncology 1

http://jco.ascopubs.org/cgi/doi/10.1200/JCO.2012.45.2714The latest version is at Published Ahead of Print on February 25, 2013 as 10.1200/JCO.2012.45.2714

Copyright 2013 by American Society of Clinical OncologyBLACKWELL INC on February 26, 2013 from 130.229.54.93

Information downloaded from jco.ascopubs.org and provided by at Karolinska Institutet University Library / SWETSCopyright © 2013 American Society of Clinical Oncology. All rights reserved.


Breast cancer survival comparison [5]

Data from England and Norway.

The data consists of

303,657 women from England.24,919 women from Norway.Year of Diagnosis was between 1996 and 2004.

Extension ofMøller, H., Sandin, F., Bray, F., Klint, A., Linklater, K. M., Purushotham,

A., Robinson, D. & Holmberg, L. Breast cancer survival in England, Norway

and Sweden: a population-based comparison International Journal of

Cancer 2010;127:2630-2638.


Quantifying differences in breast cancer survival between England and Norway

Paul C. Lambert a,b,*, Lars Holmberg c, Fredrik Sandin d, Freddie Bray e,f, Karen M. Linklater g,Arnie Purushotham h, David Robinson g, Henrik Møller g

Contents lists available at ScienceDirect

Cancer EpidemiologyThe International Journal of Cancer Epidemiology, Detection, and Prevention

jou r nal h o mep age: w ww.c an cer ep idem io log y.n et

A B S T R A C T

Background: Survival from breast cancer is lower in the UK than in some other European countries. We

compared survival in England and Norway by age and time from diagnosis. Methods: We included

303,648 English and 24,919 Norwegian cases of breast cancer diagnosed 1996–2004 using flexible

parametric relative survival models, enabling improved quantification of differences in survival. Crude

probabilities were estimated to partition the probability of death due to all causes into that due to cancer

and other causes and to estimate the number of ‘‘avoidable’’ deaths. Results: England had lower relative

survival for all ages with the difference increasing with age. Much of the difference was due to higher

excess mortality in England in the first few months after diagnosis. Older patients had a higher

proportion of deaths due to other causes. At 5 years post diagnosis, a woman aged 85 in England had

probabilities of 0.35 of dying of cancer and 0.32 of dying of other causes, whilst in Norway they were 0.26

and 0.35. By eight years the number of ‘‘avoidable’’ all-cause deaths in England was 1020 with the

number of ‘‘avoidable’’ breast cancer related deaths 1488. Conclusion: Lower breast cancer survival in

England is mainly due to higher mortality in the first year after diagnosis. Crude probabilities aid our

understanding of the impact of disease on individual patients and help assess different treatment

options.

ß

Flexible parametric models

H(t) = H∗ (t) + Λ(t)

Model ln [Λ(t)] scale which includes terms for

Baseline hazard (time) - Splines (6 parameters)Country - 1 dummy covariateAge - Splines (4 parameters)Age×Country - (4 parameters)Country×Time - Splines (3 parameters)Age×Time - 4×3 = 12 parameters

Results extremely robust to number and locations of the knots.


Relative survival

0.4

0.6

0.8

1.0

Rel

ativ

e S

urvi

val

0 2 4 6 8Years from Diagnosis

Age 35

0.4

0.6

0.8

1.0

Rel

ativ

e S

urvi

val


Age 45

0.4

0.6

0.8

1.0

Rel

ativ

e S

urvi

val


Age 55

0.4

0.6

0.8

1.0

Rel

ativ

e S

urvi

val


Age 65

0.4

0.6

0.8

1.0

Rel

ativ

e S

urvi

val


Age 75

0.4

0.6

0.8

1.0

Rel

ativ

e S

urvi

val


Age 85


Difference in relative survival

−0.15

−0.10

−0.05

0.00

0.05

0.10

Diff

eren

ce in

Rel

ativ

e S

urvi

val


Age 35

−0.15

−0.10

−0.05

0.00

0.05

0.10

Diff

eren

ce in

Rel

ativ

e S

urvi

val


Age 45

−0.15

−0.10

−0.05

0.00

0.05

0.10

Diff

eren

ce in

Rel

ativ

e S

urvi

val


Age 55

−0.15

−0.10

−0.05

0.00

0.05

0.10

Diff

eren

ce in

Rel

ativ

e S

urvi

val


Age 65

−0.15

−0.10

−0.05

0.00

0.05

0.10

Diff

eren

ce in

Rel

ativ

e S

urvi

val


Age 75

−0.15

−0.10

−0.05

0.00

0.05

0.10

Diff

eren

ce in

Rel

ativ

e S

urvi

val


Age 85


Excess mortality rates

10

25

50

100

200

400

Exc

ess

Mor

talit

y R

ate

(per

100

0 py

)


Age 35

10

25

50

100

200

400

Exc

ess

Mor

talit

y R

ate

(per

100

0 py

)


Age 45

10

25

50

100

200

400

Exc

ess

Mor

talit

y R

ate

(per

100

0 py

)


Age 55

10

25

50

100

200

400

Exc

ess

Mor

talit

y R

ate

(per

100

0 py

)


Age 65

10

25

50

100

200

400

Exc

ess

Mor

talit

y R

ate

(per

100

0 py

)


Age 75

10

25

50

100

200

400

Exc

ess

Mor

talit

y R

ate

(per

100

0 py

)


Age 85


Excess mortality rate ratios

1

2

3

0 2 4 6 8

Age 35

1

2

3

0 2 4 6 8

Age 45

1

2

3

0 2 4 6 8

Age 55

1

2

3

0 2 4 6 8

Age 65

1

2

3

0 2 4 6 8

Age 75

1

2

3

0 2 4 6 8

Age 85

Exc

ess

Mor

talit

y R

ate

Rat

io

Years from Diagnosis


Excess mortality rate differences

−10

0

10

20

30

40

50

0 2 4 6 8

Age 35

−10

0

10

20

30

40

50

0 2 4 6 8

Age 45

−10

0

10

20

30

40

50

0 2 4 6 8

Age 55

−10

0

10

20

30

40

50

0 2 4 6 8

Age 65

0

50

100

150

200

250

300

0 2 4 6 8

Age 75

0

50

100

150

200

250

300

0 2 4 6 8

Age 85

Diff

eren

ce in

Exc

ess

Mor

talit

y (1

000p

ys)

Years from Diagnosis

(b)


Breast cancer crude probabilities, England

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 35

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 45

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 55

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 65

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 75

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 85



Breast cancer crude probabilities, Norway

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 35

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 45

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 55

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 65

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 75

0.00.20.40.60.81.0

Pro

babi

lity

of D

eath


Age 85



Probabilities at 5 Years

Crude Probabilities Net ProbabilitiesAge Cancer Other Alive Dead Alive

England45 0.15 0.01 0.84 0.15 0.8555 0.13 0.02 0.85 0.13 0.8765 0.16 0.06 0.78 0.17 0.8375 0.25 0.14 0.61 0.27 0.7385 0.35 0.32 0.33 0.42 0.58

Norway45 0.13 0.01 0.86 0.13 0.8755 0.11 0.02 0.87 0.11 0.8965 0.13 0.05 0.82 0.13 0.8775 0.19 0.12 0.68 0.21 0.7985 0.26 0.35 0.39 0.31 0.69


References

[1] Cronin KA, Feuer EJ. Cumulative cause-specific mortality for cancer patients in thepresence of other causes: a crude analogue of relative survival. Statistics in Medicine 2000;19:1729–1740.

[2] Bhaskaran K, Rachet B, Evans S, Smeeth L. Re: Helene hartvedt grytli, morten wangfagerland, sophie d. fossa, kristin austlid tasken. association between use of β-blockers andprostate cancer-specific survival: a cohort study of 3561 prostate cancer patients withhigh-risk or metastatic disease. eur urol. in press.http://dx.doi.org/10.1016/j.eururo.2013.01.007.: beta-blockers and prostate cancersurvival–interpretation of competing risks models. Eur Urol 2013;64:e86–e87.

[3] Pintilie M. An introduction to competing risks analysis. Rev Esp Cardiol 2011;64:599–605.

[4] Lambert PC, Dickman PW, Nelson CP, Royston P. Estimating the crude probability ofdeath due to cancer and other causes using relative survival models. Stat Med 2010;29:885– 895.

[5] Lambert PC, Holmberg L, Sandin F, Bray F, Linklater KM, Purushotham A, et al..Quantifying differences in breast cancer survival between England and Norway. CancerEpidemiology 2011;35:526–533.


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