Download Session 19 Crude probability of death: estimation and application

Session 19
Crude probability of death:
estimation and application
Paul W Dickman1 and Paul C Lambert1,2
1 Department
of Medical Epidemiology and Biostatistics,
Karolinska Institutet, Stockholm, Sweden
2 Department of Health Sciences,
University of Leicester, UK
Cancer survival: principles, methods and analysis
LSHTM
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 research
question?
Assumptions and estimation.
My presentation will focus on concepts; I have included slides
with details and examples that I won’t cover.
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Survival of patients with colon cancer in Finland
Coding of vital status
Freq.
4642
8369
2549
Numeric
0
1
2
Label
Alive
Dead: colon cancer
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 two
quantities to estimate:
1
2
Eliminate the competing events (estimate net survival)
Accommodate the competing events (estimate crude survival)
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Many synonyms for the same concept
Probability of death in a
Net probability
hypothetical world where the
of death
=
cancer under study is the only
due to cancer
possible cause of death
Probability of death in the
Crude probability
real world where you may die
of death
=
of other causes before the
due to cancer
cancer kills you
Net probability also known as the marginal probability.
Crude probability also known as the cause-specific cumulative
incidence function (Geskus) or the cumulative incidence function.
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Net survival
In cancer patient survival we typically choose to eliminate the
competing events.
That is, we aim to estimate net survival (using either
cause-specific survival or relative survival).
It is important to recognise that net survival is interpreted in a
hypothetical world where competing risks are assumed to be
eliminated. Requires conditional independence.
I will later show how ‘real world’ probabilities (i.e., crude
probabilities) can be estimated by accommodating, rather than
eliminating, competing risks.
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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-death
Relative Appropriate estimation of expected survival
We choose the approach for which we have the strongest belief
in the underlying assumptions.
For population-based studies this is typically relative survival but
every study must be evaluated on its specific merits.
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1
Cancer death (status=1) as the outcome
0
Cause-specific survival
.25
.5
.75
use colon if age > 70
stset exit, origin(dx) failure(status==1) scale(365.25)
sts graph
0
5
10
15
Years since diagnosis
Dickman and Lambert
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1
Cancer death (status=1) as the outcome
0
Net probability of death
.25
.5
.75
use colon if age > 70
stset exit, origin(dx) failure(status==1) scale(365.25)
sts graph, fail
0
5
10
15
Years since diagnosis
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1
Non-cancer death (status=2) as the outcome
0
Cause-specific survival
.25
.5
.75
use colon if age > 70
stset exit, origin(dx) failure(status==2) scale(365.25)
sts graph
0
5
10
15
Years since diagnosis
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1
Non-cancer death (status=2) as the outcome
0
Net probability of death
.25
.5
.75
use colon if age > 70
stset exit, origin(dx) failure(status==2) scale(365.25)
sts graph, fail
0
5
10
15
Years since diagnosis
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Net probability of death
.25
.5
.75
1
Net probabilities do not sum to the total probability of death!
0
Cancer
Non-cancer
0
5
10
15
Years since diagnosis
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Two estimates of the same quantity (net survival)
.25
Net survival
.5
.75
1
Two estimates of net survival (patients aged > 70 at Dx)
0
Cause-specific survival
Relative survival
0
5
10
15
Years since diagnosis
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But they are very similar for ‘young’ patients
.25
Net survival
.5
.75
1
Two estimates of net survival (patients aged < 70 at dx)
0
Cause-specific survival
Relative survival
0
5
10
15
Years since diagnosis
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Why the hypothetical world?
Net survival estimates survival in the hypothetical world where
you cannot die of causes other than the cancer of interest.
Net survival is a theoretical construct. We can attempt to
estimate it using either cause-specific survival or relative survival.
It is useful as a measure of cancer-patient survival that is
independent of background mortality so we can make
comparisons across time, across different age-groups in our
population and across different countries.
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Interpreting estimates of net survival
The cumulative relative survival ratio can be interpreted as the
proportion of patients alive after i years of follow-up in the
hypothetical situation where the cancer in question is the only
possible cause of death.
1-RSR can be interpreted as the proportion of patients who will
die of cancer within i years of follow-up in the hypothetical
situation where the cancer in question is the only possible cause
of death.
We do not live in this hypothetical world (where we estimate
what is called the net probability of death). Estimates of the
proportion of patients who will die of cancer in the presence of
competing risks can also be made (crude probabilities of death).
Cronin and Feuer (2000) [1] extended the theory of competing
risks to relative survival; their method is implemented in our
Stata command strs.
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Net (left) and crude (right) probabilities of death in men with localized
prostate cancer aged 70+ at diagnosis (Cronin and Feuer [1])
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What this means
Among these men, the probability of dying of prostate cancer
within 15 of diagnosis is 40% in the hypothetical world where it
is not possible to die of other causes. This is how the relative
survival or cause-specific survival is interpreted.
However, in the real world where it is possible to die of other
causes the probability of dying of prostate cancer within 15 years
of diagnosis is less than 20%.
Dickman and Lambert
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LSHTM, June 2014
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Net (left) and crude (right) probabilities of death due to cancer in
women with regional breast cancer (Cronin and Feuer [1])
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What this means
In the hypothetical world, where it is not possible to die of
causes other than breast cancer, the probability of dying of
regional breast cancer is similar for all age groups.
However, in the real world the probability of dying of breast
cancer is lower for elderly women because they are more likely to
die of other causes.
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EUROPEAN UROLOGY 65 (2014) 635–641
http://www.cancerresearchuk.org/cancera v a i l a b l e a t w w w . s c i e n c e d i r e c t . cinfo/cancerstats/survival/
om
journal homepage: www.europeanurology.com
Relative survival was estimated to be 50%.
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. Fosså c,d,
Kristin Austlid Taskén a,d,*
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a
16
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
Article info
Article history:
Accepted January 6, 2013
Published online ahead of
print 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
Should we estimate crude or net survival?
Abstract
Background: We recently reported reduced prostate cancer (PCa)–specific mortality for
b-blocker users among patients receiving androgen-deprivation therapy in a health
survey cohort including 655 PCa patients. Information on clinical characteristics was
limited.
Objective: To assess the association between b-blockers and PCa-specific mortality in a
cohort of 3561 prostate cancer patients with high-risk or metastatic disease, and to
address potential confounding from the use of statins or acetylsalicylic acid (ASA).
Design, setting, and participants: Clinical information from all men reported to the
Cancer 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 the
Norwegian Prescription Database. Exclusion criteria were low- or intermediate-risk
disease; planned radiotherapy or radical prostatectomy; initiation of b-blocker, ASA, or
statin use after diagnosis where applicable; missing information on baseline Gleason
score, prostate-specific antigen level, T stage or performance status; and missing
follow-up.
Outcome measurements and statistical analysis: Cox proportional hazards modelling
and competing risk regression modelling were used to analyse the effects of b-blocker
use on all-cause and PCa-specific mortality, respectively. Differences between b-blocker
users and nonusers regarding baseline clinical characteristics were assessed by the
Wilcoxon-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 associated
with 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 indepenDickman and Lambert
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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 were
the observational study design and short follow-up.
Conclusions: b-Blocker use was associated with reduced PCa-specific mortality in
patients with high-risk or metastatic disease at the time of diagnosis. Our findings
need validation from further observational studies.
# 2013 European Association of Urology. Published by Elsevier B.V. All rights reserved.
Should we estimate crude or net survival?
* Corresponding author. Oslo University Hospital, Institute of Cancer Research, Department of Tumor
Biology, P.O. Box 4953 Nydalen, NO-0424 Oslo, Norway. Tel. +47 22781878; Fax: +47 22781795.
E-mail address: [email protected] (K.A. Taskén).
We wish to compare PrCa-specific survival among two groups:
1
2
Men with prostate cancer using beta-blockers
Men with prostate cancer not using beta-blockers
The authors used a ‘competing risks analysis’ and concluded
that the men who used beta-blockers were less likely to die of
prostate cancer.
Bernard co-authored a commentary that very nicely explained
why such an analysis is incorrect [2] and that net probabilities
are more appropriate than crude probabilities.
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
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Focus on: Contemporary Methods in Biostatistics (II)
An Introduction to Competing
Risks Analysis
‘An Introduction
to
Competing Risks Analysis’ [3]
Melania Pintilie*
Department of Biostatistics, Ontario Cancer Institute/Princess Margaret Hospital, University Health Network, Dalla Lana School of Public Health, University of Toronto, Canada
Article history:
Available online 31 May 2011
Keywords:
Survival analysis
Competing risks analysis
Fine and Gray model
ABSTRACT
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.
ß 2011 Sociedad Española de Cardiologı́a. Published by Elsevier España, S.L. All rights reserved.
Análisis de riesgos competitivos
RESUMEN
Palabras clave:
Análisis de supervivencia
Análisis de riesgos competitivos
Modelo de Fine y Gray
La necesidad de desarrollar tratamientos o programas especı́ficos para una enfermedad requiere un
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análisis de los resultados que sea especı́fico para dicha enfermedad. Criterios de valoración como la
insuficiencia cardiaca, la muerte debida a una enfermedad especı́fica o el control de la enfermedad local
en el cáncer pueden ser imposibles de observar debido a la aparición 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 interés se denomina riesgo competitivo.
Las técnicas habituales de análisis del tiempo hasta el evento aplicadas en presencia de riesgos
competitivos producen unos resultados sesgados o no interpretables. La estimación de la probabilidad
del evento debe calcularse, pues, con el empleo de técnicas especı́ficas como la función 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 técnicas especı́ficas para
el análisis de los riesgos competitivos se asegurará que los resultados no estén sesgados y puedan
interpretarse correctamente.
ß 2011 Sociedad Española de Cardiologı́a. Publicado por Elsevier España, S.L. Todos los derechos reservados.
This article is misleading and causes confusion
Abbreviations
CIF: cumulative incidence function
Cox PH: Cox proportional hazards model
CR: competing risks
F&G: Fine and Gray model
KM: Kaplan-Meier
‘When the CR are ignored and the CR observations are censored
the analysis reduces to a ‘usual’ time-to-event scenario. Due to
the familiarity of this type of analysis and the availability of
the statistical or mathematical area has been published
software, many in
researchers
resort to this approach, as seen in
incorporating new developments, including the monograph of
David and
Moeschberger.
As the data became
more not
extensive,
the earlier examples.
However,
it is1 unanimously
agreed
only
clear, and precise regarding the different types of outcomes, CR
among statisticians,
that
the
estimation
of
the
probability
of
resurfaced as a crucial type of analysis within time-to-event
event in this case
overestimates
trueunderstanding
probability.’
analysis,
necessary forthe
a better
of a disease. The
connection between the mathematical results and the applied field
needed to be made. Several authors have contributed to the
understanding of CR situations.2,3 Other authors enhanced and
developed techniques and in some cases made available ready-touse computer code for applied statistics.4–6
INTRODUCTION
Competing risks (CR) has been recognized Dickman
as a special
case of
and Lambert
time-to-event analysis since the 18th century. Occasionally work
* Corresponding author: Biostatistics Department, Ontario Cancer Institute/UHN,
610 University Ave., Toronto, M5G 2M9, Canada.
E-mail address: [email protected]
INTRODUCTION TO TIME-TO-EVENT ANALYSIS
Population-Based Cancer Survival
Net (left) and crude
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In many studies the outcome is observed longitudinally. In this
way every subject in the cohort is observed for a period of time until
the event occurs. For example the event of interest may be death,
(right)
probabilities
of death
in men
heart attack,
or cancer recurrence.
The goals
of thewith
study localized
may be to
prostate cancer aged 70+ at diagnosis (Cronin and Feuer [1])
1885-5857/$ – see front matter ß 2011 Sociedad Española de Cardiologı́a. Published by Elsevier España, S.L. All rights reserved.
doi:10.1016/j.rec.2011.03.016
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Natural frequencies presented using infographics
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Cancer Survival Query System (Rocky Feuer)
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The independence assumption - crucial for the
interpretation of survival curves when competing
risks are present
Independence assumption
The time to death from the cancer in question is conditionally
independent of the time to death from other causes. i.e., there
should be no factors that influence both cancer and non-cancer
mortality other than those factors that have been controlled for in the
estimation.
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If the independence assumption is not satisfied
Cause-specific survival curves provide biased estimates of net
survival.
If it is not possible to adjust for the mechanism that introduces
the dependence then survival curves should be interpreted with
care.
However, the cause-specific hazard rates still have a useful
interpretation as the rates that are observed when competing
risks are present.
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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 would
observe if it was possible to eliminate all competing causes of
death.
This is a strictly hypothetical (but useful!) construct.
The cause-specific hazard rates provide estimates of the rates
that we would observe in the absence of competing causes of
death.
In the competing risks literature, net survival and hazard are
typically referred to as marginal survival and hazard, respectively.
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How can we test if the independence assumption is
satisfied?
Simple answer
You can’t!
It is not possible to formally test if the independence assumption
is satisfied based on the observable data.
You have to make the decision of whether your estimates provide
an estimate of something useful based on your subject matter
knowledge.
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How do these concepts translate to relative
survival?
Cause-specific survival and relative survival aim to estimate the
same underlying quantity.
Even though we do not make use of explicit cause of death
information, the independence assumption applies also in a
relative survival framework.
If satisfied, relative survival and excess mortality rates provide
estimates of net survival (given that the patients are
exchangeable to the population used to estimate expected
survival)
If not satisfied, relative survival curves are biased whereas the
excess mortality rates are interpretable as real-world rates (in the
presence of competing risks).
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Estimating crude probabilities (life table, RS)
The contribution to the crude probability for each interval.
Interval crude probability of death due to cancer
ĝjc =
j−1
Y
p̂j
i=1
!
p̂j
1− ∗
pj
!
1
1−
1 − pj∗
2
Interval crude probability of death due to other causes
ĝjo =
j−1
Y
i=1
p̂j
!
∗
1 − pj
1
1−
2
p̂j
1− ∗
pj
!!
First term: survival to start of interval.
Second term: probability of dying of cause in interval.
Third term: needed as dealing with grouped time.
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Estimation II
Cumulative crude probabilities obtained by summing interval
estimates.
j
X
Crjc =
ĝjc
i=1
Crjo =
j
X
ĝjo
i=1
Crjc + Crjo gives the all-cause probability of death at the end of
interval j
Also possible to obtain variance estimates.
Implemented in strs using cuminc option.
Also available in SEER*Stat.
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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)
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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
2
3
4
1
2
3
4
5
45-59
45-59
45-59
45-59
45-59
0.7499
0.6317
0.5672
0.5273
0.4943
0.2501
0.3683
0.4328
0.4727
0.5057
0.7558
0.6419
0.5814
0.5457
0.5168
0.2432
0.3559
0.4151
0.4497
0.4775
0.0068
0.0124
0.0177
0.0229
0.0282
5
6
7
8
9
6
7
8
9
10
45-59
45-59
45-59
45-59
45-59
0.4710
0.4561
0.4398
0.4336
0.4248
0.5290
0.5439
0.5602
0.5664
0.5752
0.4981
0.4882
0.4770
0.4769
0.4744
0.4953
0.5046
0.5150
0.5151
0.5174
0.0336
0.0393
0.0451
0.0513
0.0578
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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
2
3
4
1
2
3
4
5
75+
75+
75+
75+
75+
0.5424
0.4188
0.3531
0.2994
0.2585
0.4576
0.5812
0.6469
0.7006
0.7415
0.5994
0.5104
0.4772
0.4527
0.4413
0.3816
0.4584
0.4842
0.5015
0.5086
0.0760
0.1228
0.1626
0.1991
0.2329
5
6
7
8
9
6
7
8
9
10
75+
75+
75+
75+
75+
0.2187
0.1860
0.1571
0.1302
0.1090
0.7813
0.8140
0.8429
0.8698
0.8910
0.4253
0.4162
0.4092
0.3997
0.4004
0.5173
0.5218
0.5246
0.5280
0.5278
0.2640
0.2923
0.3183
0.3418
0.3632
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Limitation of life table approach
Only estimated at end of interval.
Large age groups: The crude probability of death for someone
aged 60 will be different to someone aged 70.
Limited to how many groups you can investigate (no borrowing
of strength).
We will now move to model based estimates of crude
probabilities.
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Crude probabilities from models
We can obtain an estimate of relative survival from the various
models we have described (Poisson, flexible parametric, cure).
For individual level models this gives an individual based
prediction of the net probability of death due to cancer (1 relative survival).
However, we use the ideas from competing risks theory to also
calculate the crude probability of death due to cancer and due to
other causes.
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Brief mathematical details[4]
h∗ (t)
λ(t)
h(t) = h∗ (t) + λ(t)
-
expected mortality rate
excess mortality rate
all-cause mortality rate
S ∗ (t)
R(t)
S(t) = S ∗ (t)R(t)
-
expected survival
relative survival
All cause survival
Z t
Net Prob of Death = 1 − R(t) = 1 − exp −
λ(u)du
0
Crude Prob of Death (cancer) =
Z
t
S ∗ (u)R(u)λ(u)du
0
Crude Prob of Death (other causes) =
Z
t
S ∗ (u)R(u)h∗ (u)du
0
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Estimating the crude probabilities
We will use flexible parametric relative survival models.
For any particular covariate pattern, we can estimate the excess
mortality rate, λ̂i (t|xi ).
The overall survival for individual i is Si∗ (t)R̂i (t).
We plug these into the equations in the previous slide to
estimate the crude probabilities.
We have to do the integration numerically.
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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, specified
using the at() option.
You need to specify the values for variables in the life table that
the prediction is for (age, sex, calendar year).
Note that even if you model age as groups then you still have to
specify 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)
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LSHTM, June 2014
36
Crude probabilities (woman aged 75)
Probability of Death
1.0
0.8
P(Alive)
0.6
0.4
P(Dead − Other Causes)
0.2
P(Dead − Breast Cancer)
0.0
0
2
4
6
8
Years from diagnosis
Dead (Breast Cancer)
Dickman and Lambert
Population-Based Cancer Survival
Dead (Other Causes)
LSHTM, June 2014
Alive
37
Comparison with net probability
Probability of Death
1.0
0.8
0.6
0.4
0.2
0.0
0
2
4
6
8
Years from diagnosis
Dead (Breast Cancer)
Dickman and Lambert
Dead (Other Causes)
Population-Based Cancer Survival
Alive
LSHTM, June 2014
38
Male Hodgkin lymphoma: trends in 5-year RSR
.8
.6
.4
19
98
19
93
88
19
83
19
78
19
19
73
0
3
Age:19-35
Age:36-50
Age:51-65
Age:66-80
.2
20
0
5-Year Relative Survival Ratio
1
Year of Diagnosis
Dickman and Lambert
Population-Based Cancer Survival
LSHTM, June 2014
39
Male Hodgkin lymphoma: trends in 10-year RSR
.8
.6
.4
98
19
93
19
88
19
83
19
78
19
19
73
0
03
Age:19-35
Age:36-50
Age:51-65
Age:66-80
.2
20
10-Year Relative Survival Ratio
1
Year of Diagnosis
Dickman and Lambert
Population-Based Cancer Survival
LSHTM, June 2014
40
Males aged 60 at diagnosis: real-world probabilities
20-year Probability of Death
1.0
Excess HL
Other Causes
0.8
0.6
0.4
0.2
0.0
73
19
79
19
Dickman and Lambert
91
85
19
19
Year of Diagnosis
Population-Based Cancer Survival
19
97
03
20
LSHTM, June 2014
41
Males aged 60 at Dx: partitioning HL mortality
20-year Probability of Death
1.0
Excess DCS
Excess HL (Non-DCS)
Other Causes
0.8
0.6
0.4
0.2
0.0
73
19
79
19
Dickman and Lambert
85
91
19
19
Year of Diagnosis
Population-Based Cancer Survival
19
97
03
20
LSHTM, June 2014
42
Eloranta et al. BMC Medical Research Methodology 2012, 12:86
http://www.biomedcentral.com/1471-2288/12/86
RESEARCH ARTICLE
Open Access
Partitioning of excess mortality in populationbased cancer patient survival studies using
Published Ahead of Print on February 25, 2013 as 10.1200/JCO.2012.45.2714
The latest version
is at http://jco.ascopubs.org/cgi/doi/10.1200/JCO.2012.45.2714
flexible
parametric survival models
Sandra Eloranta1* , Paul C Lambert1,2 , Therese ML Andersson1 , Kamila Czene1 , Per Hall1 , Magnus Björkholm3
1
and Paul W Dickman
JOURNAL OF CLINICAL
ONCOLOGY
O R I G I N A L
R E P O R T
Published Ahead of Print on February 25, 2013 as 10.1200/JCO.2012.45.2714
AbstractThe latest version is at http://jco.ascopubs.org/cgi/doi/10.1200/JCO.2012.45.2714
Background: Relative survival is commonly used for studying survival of cancer patients as it captures both the direct
and indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to the
R I G
I N AdoLnotR
E P
O R T of the
JOURNAL
CLINICALcancer-free
ONCOLOGY
expected
survival OF
in a comparable
population. However,O
existing
methods
allow
estimation
impact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose we
extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline
cumulative excess hazard and for any time-dependent effects.
Methods: In the extended model we partition the excess mortality associated with a diagnosis of cancer through
estimating a separate baseline
excess hazardTrends
function for
outcomes under
investigation.
This isof
done
Temporal
intheMortality
From
Diseases
theby
incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in
Circulatory
System
After
Treatment
for
Hodgkin
the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. This
approach thereby enables modeling
of temporal
in e.g., excess cardiovascular
mortality
and remaining
cancer
Lymphoma:
Atrends
Population-Based
Cohort
Study
in Sweden
excess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used to
toJan
Sandra
Eloranta,
Paul C.of(1973
Lambert,
Sjöberg,
Therese
M.L.
Andersson,estimated
Magnus in
Björkholm,
derive crude
probabilities
death due
to2006)
the
component
parts,
i.e., probabilities
the presence of
and
Paul W.causes
Dickman
competing
of death.Sandra Eloranta, Paul C. Lambert, Jan Sjöberg, Therese M.L. Andersson, Magnus Björkholm,
and Paul W. Dickman
Results: The method is illustrated with examples where the total excess mortality experienced by patients diagnosed
All authors: Karolinska Institutet; Jan
All authors: Karolinska Institutet; Jan
A cardiovascular
B S Tmortality
A T remaining
CR AT Ccancer
A BR S and
T
with
cancer Karolinis partitioned into excess
excess mortality.
Sjöberg and Magnus Björkholm, KarolinSjöberg
andbreast
Magnus Björkholm,
ska University Hospital Solna, Stockska University Hospital Solna, StockConclusions:
The proposed
method can be used to simultaneously study disease patterns and temporal trends for
Purpose
holm,
Sweden;
Paul
C.
Lambert,
Purpose
holm, Sweden; Paul C. Lambert,
Hodgkin lymphoma
(HL) information
survival in Sweden
improved
last 40 as
years,
various
causes
of cancer-consequent
deaths. Such
shouldhas
be of
interestdramatically
for patientsover
andthe
clinicians
one but
University
of Leicester,
Leicester,
Hodgkin
lymphoma
(HL)
survival
Sweden
has
improved
dramatically
last
40 years, but 43
Dickman
and
Lambert
Population-Based
Cancer
Survival
LSHTM,
2014over
little
iscancer
knownisin
about
the adapting
extent
to treatment
which
efforts
aimedJune
at
reducing
long-term
treatment-related
University of Leicester, Leicester,
United
Kingdom.
way
of improving
prognosis
after
through
strategies
and
follow-up
ofthe
patients
towards
mortality
have to
contributed
to
the improved
prognosis.
little
is
known
about
the
extent
which
efforts
aimed
at
reducing
long-term
treatment-related
United Kingdom.
Published
online
ahead
of
print
at
reducing the excess mortality caused by side effects of the treatment.
Temporal Trends in Mortality From Diseases of the
Circulatory System After Treatment for Hodgkin
Lymphoma: A Population-Based Cohort Study in Sweden
(1973 to 2006)
Methods
mortality have contributed
to the improved prognosis.
www.jco.org on February 25, 2013.
Published online ahead of print at
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 of
Møller, 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
Contents lists available at ScienceDirect
Cancer Epidemiology
The International Journal of Cancer Epidemiology, Detection, and Prevention
journal homepage: www.cancerepidemiology.net
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
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 covariate
Age
- 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
Age 35
Age 45
0.6
1.0
Relative Survival
0.8
0.4
0.8
0.6
0.4
0
2
4
6
Years from Diagnosis
8
2
4
6
Years from Diagnosis
8
0
0.6
0.4
0.8
0.6
0.4
8
8
1.0
Relative Survival
Relative Survival
0.8
Dickman and Lambert
2
4
6
Years from Diagnosis
Age 85
1.0
2
4
6
Years from Diagnosis
0.6
Age 75
1.0
0
0.8
0.4
0
Age 65
Relative Survival
Age 55
1.0
Relative Survival
Relative Survival
1.0
0.8
0.6
0.4
0
2
4
6
Years from Diagnosis
Population-Based Cancer Survival
8
0
2
4
6
Years from Diagnosis
8
LSHTM, June 2014
47
Difference in relative survival
Age 35
Age 45
0.00
−0.05
−0.10
−0.15
2
4
6
Years from Diagnosis
0.10
Difference in Relative Survival
0.05
0
0.05
0.00
−0.05
−0.10
−0.15
8
0
Age 65
2
4
6
Years from Diagnosis
−0.05
−0.10
−0.15
Dickman and Lambert
−0.10
−0.15
0
2
4
6
Years from Diagnosis
8
Age 85
0.10
Difference in Relative Survival
Difference in Relative Survival
0.00
2
4
6
Years from Diagnosis
0.00
−0.05
8
0.10
0.05
0
0.05
Age 75
0.10
Difference in Relative Survival
Age 55
0.10
Difference in Relative Survival
Difference in Relative Survival
0.10
0.05
0.00
−0.05
−0.10
−0.15
8
0
2
4
6
Years from Diagnosis
Population-Based Cancer Survival
0.05
0.00
−0.05
−0.10
−0.15
8
0
2
4
6
Years from Diagnosis
8
LSHTM, June 2014
48
50
25
10
2
4
6
Years from Diagnosis
400
200
100
50
25
10
0
2
4
6
Years from Diagnosis
Dickman and Lambert
200
100
50
25
10
8
Age 65
8
Excess Mortality Rate (per 1000 py)
100
Age 45
400
0
2
4
6
Years from Diagnosis
Age 75
400
200
100
50
25
10
0
2
4
6
Years from Diagnosis
Population-Based Cancer Survival
8
Age 55
400
200
100
50
25
10
8
0
Excess Mortality Rate (per 1000 py)
200
0
Excess Mortality Rate (per 1000 py)
Excess Mortality Rate (per 1000 py)
Age 35
400
Excess Mortality Rate (per 1000 py)
Excess Mortality Rate (per 1000 py)
Excess mortality rates
2
4
6
Years from Diagnosis
8
Age 85
400
200
100
50
25
10
0
2
4
6
Years from Diagnosis
LSHTM, June 2014
8
49
Excess mortality rate ratios
Age 35
3
2
Excess Mortality Rate Ratio
Age 45
3
2
1
2
1
0
2
4
6
1
8
Age 65
3
0
2
4
6
8
Age 75
3
2
2
4
6
2
4
6
8
6
8
Age 85
2
1
0
0
3
2
1
Age 55
3
1
8
0
2
4
6
8
0
2
4
Years from Diagnosis
Dickman and Lambert
Population-Based Cancer Survival
LSHTM, June 2014
50
Excess mortality rate differences
(b)
Age 35
Difference in Excess Mortality (1000pys)
50
Age 45
50
40
40
30
30
30
20
20
20
10
10
10
0
0
0
−10
−10
−10
0
2
4
6
8
Age 65
50
0
2
4
6
8
Age 75
300
Age 55
50
40
0
40
250
250
30
200
200
20
150
150
10
100
100
0
50
50
−10
0
0
2
4
6
8
2
4
6
8
6
8
Age 85
300
0
0
2
4
6
8
0
2
4
Years from Diagnosis
Dickman and Lambert
Population-Based Cancer Survival
LSHTM, June 2014
51
0 2 4 6 8
Years from Diagnosis
1.0
0.8
0.6
0.4
0.2
0.0
Age 45
0 2 4 6 8
Years from Diagnosis
Age 75
0 2 4 6 8
Years from Diagnosis
Dead (Breast Cancer)
Dickman and Lambert
Population-Based Cancer Survival
Probability of Death
Age 65
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
Probability of Death
0 2 4 6 8
Years from Diagnosis
Probability of Death
1.0
0.8
0.6
0.4
0.2
0.0
Age 35
Probability of Death
Probability of Death
1.0
0.8
0.6
0.4
0.2
0.0
Probability of Death
Breast cancer crude probabilities, England
1.0
0.8
0.6
0.4
0.2
0.0
Age 55
0 2 4 6 8
Years from Diagnosis
Age 85
0 2 4 6 8
Years from Diagnosis
Dead (Other Causes)
LSHTM, June 2014
Alive
52
0 2 4 6 8
Years from Diagnosis
1.0
0.8
0.6
0.4
0.2
0.0
Age 45
0 2 4 6 8
Years from Diagnosis
Age 75
0 2 4 6 8
Years from Diagnosis
Dead (Breast Cancer)
Dickman and Lambert
Probability of Death
Age 65
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
Probability of Death
0 2 4 6 8
Years from Diagnosis
Probability of Death
1.0
0.8
0.6
0.4
0.2
0.0
Age 35
Probability of Death
Probability of Death
1.0
0.8
0.6
0.4
0.2
0.0
Probability of Death
Breast cancer crude probabilities, Norway
1.0
0.8
0.6
0.4
0.2
0.0
0 2 4 6 8
Years from Diagnosis
Age 85
0 2 4 6 8
Years from Diagnosis
Dead (Other Causes)
Population-Based Cancer Survival
Age 55
Alive
LSHTM, June 2014
53
Probabilities at 5 Years
Age
England
45
55
65
75
85
Norway
45
55
65
75
85
Crude Probabilities
Cancer Other Alive
Net Probabilities
Dead
Alive
0.15
0.13
0.16
0.25
0.35
0.01
0.02
0.06
0.14
0.32
0.84
0.85
0.78
0.61
0.33
0.15
0.13
0.17
0.27
0.42
0.85
0.87
0.83
0.73
0.58
0.13
0.11
0.13
0.19
0.26
0.01
0.02
0.05
0.12
0.35
0.86
0.87
0.82
0.68
0.39
0.13
0.11
0.13
0.21
0.31
0.87
0.89
0.87
0.79
0.69
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