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)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 2
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 3
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 4
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 5
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 5
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
0 5 10 15Years since diagnosis
Cancer death (status=1) as the outcome
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 6
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
0 5 10 15Years since diagnosis
Non-cancer death (status=2) as the outcome
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 7
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
0 5 10 15Years since diagnosis
Non-cancer death (status=2) as the outcome
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 8
0.2
5.5
.75
1N
et p
roba
bilit
y of
dea
th
0 5 10 15Years since diagnosis
CancerNon-cancer
Net probabilities do not sum to the total probability of death!
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 9
Two estimates of the same quantity (net survival)
0.2
5.5
.75
1N
et s
urvi
val
0 5 10 15Years since diagnosis
Cause-specific survivalRelative survival
Two estimates of net survival (patients aged > 70 at Dx)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 10
But they are very similar for ‘young’ patients
0.2
5.5
.75
1N
et s
urvi
val
0 5 10 15Years since diagnosis
Cause-specific survivalRelative survival
Two estimates of net survival (patients aged < 70 at dx)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 11
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 10
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 11
Net (left) and crude (right) probabilities of death in men with localized
prostate cancer aged 70+ at diagnosis (Cronin and Feuer [1])
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 12
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%.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 13
Net (left) and crude (right) probabilities of death due to cancer in
women with regional breast cancer (Cronin and Feuer [1])
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 14
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 15
http://www.cancerresearchuk.org/cancer-
info/cancerstats/survival/
Relative survival was estimated to be 50%.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 16
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 17
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 18
‘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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 19
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.’
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 20
Net (left) and crude (right) probabilities of death in men with localized
prostate cancer aged 70+ at diagnosis (Cronin and Feuer [1])
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 21
Natural frequencies presented using infographics
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 22
Cancer Survival Query System (Rocky Feuer)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 23
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 22
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 23
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 24
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 25
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).
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 26
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 27
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 28
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)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 29
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 30
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 31
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 32
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 33
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 34
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 35
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)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 36
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 37
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
Dead (Breast Cancer) Dead (Other Causes) Alive
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 38
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 39
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 40
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 41
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 42
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 43
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 44
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.
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 46
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
0 2 4 6 8Years from Diagnosis
Age 45
0.4
0.6
0.8
1.0
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 55
0.4
0.6
0.8
1.0
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 65
0.4
0.6
0.8
1.0
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 75
0.4
0.6
0.8
1.0
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 85
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 47
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
0 2 4 6 8Years from Diagnosis
Age 35
−0.15
−0.10
−0.05
0.00
0.05
0.10
Diff
eren
ce in
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 45
−0.15
−0.10
−0.05
0.00
0.05
0.10
Diff
eren
ce in
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 55
−0.15
−0.10
−0.05
0.00
0.05
0.10
Diff
eren
ce in
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 65
−0.15
−0.10
−0.05
0.00
0.05
0.10
Diff
eren
ce in
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 75
−0.15
−0.10
−0.05
0.00
0.05
0.10
Diff
eren
ce in
Rel
ativ
e S
urvi
val
0 2 4 6 8Years from Diagnosis
Age 85
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 48
Excess mortality rates
10
25
50
100
200
400
Exc
ess
Mor
talit
y R
ate
(per
100
0 py
)
0 2 4 6 8Years from Diagnosis
Age 35
10
25
50
100
200
400
Exc
ess
Mor
talit
y R
ate
(per
100
0 py
)
0 2 4 6 8Years from Diagnosis
Age 45
10
25
50
100
200
400
Exc
ess
Mor
talit
y R
ate
(per
100
0 py
)
0 2 4 6 8Years from Diagnosis
Age 55
10
25
50
100
200
400
Exc
ess
Mor
talit
y R
ate
(per
100
0 py
)
0 2 4 6 8Years from Diagnosis
Age 65
10
25
50
100
200
400
Exc
ess
Mor
talit
y R
ate
(per
100
0 py
)
0 2 4 6 8Years from Diagnosis
Age 75
10
25
50
100
200
400
Exc
ess
Mor
talit
y R
ate
(per
100
0 py
)
0 2 4 6 8Years from Diagnosis
Age 85
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 49
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 50
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)
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 51
Breast cancer crude probabilities, England
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 35
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 45
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 55
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 65
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 75
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 85
Dead (Breast Cancer) Dead (Other Causes) Alive
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 52
Breast cancer crude probabilities, Norway
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 35
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 45
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 55
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 65
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 75
0.00.20.40.60.81.0
Pro
babi
lity
of D
eath
0 2 4 6 8Years from Diagnosis
Age 85
Dead (Breast Cancer) Dead (Other Causes) Alive
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 53
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
Dickman and Lambert Population-Based Cancer Survival LSHTM, June 2014 54
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[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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