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Estimating cancer survival in small areas: possible and useful Susanna Cramb, Kerrie Mengersen and Peter Baade susannacramb@cancerqld.org.au Survival The proportion who survive a given length of time after diagnosis Survival Key

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Estimating cancer survival in small areas: possible and useful

Susanna Cramb, Kerrie Mengersen and Peter Baade susannacramb@cancerqld.org.au

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Survival

  • The proportion who survive a

given length of time after diagnosis

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Survival

  • Key measure of cancer

patient care

  • Allows monitoring and

evaluation of health services

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Estimating Net Survival Cause-specific Relative

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Estimating Net Survival Cause-specific Relative

Based on death certificate

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Estimating Net Survival Cause-specific Relative

Based on death certificate Compares against population mortality

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Estimating Net Survival Cause-specific Relative

Based on death certificate Compares against population mortality

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Data sources

  • Cancer incidence data (contains death information)
  • Queensland Cancer Registry (population-based)
  • Unit record file mortality data by age group, sex, time and area
  • Australian Bureau of Statistics
  • Population data by age group, sex, time and area
  • Australian Bureau of Statistics
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Data preparation

1. Population mortality data

  • Create lifetables by SLA, sex and year

group (e.g. 2003-2007). 2. Cancer incidence data

  • Calculate the person-time at risk, and the

expected deaths using the lifetable data. 3. Neighbourhood adjacency matrix file

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Data preparation

1. Population mortality data

  • Create lifetables by SLA, sex and year

group (e.g. 2003-2007). 2. Cancer incidence data

  • Calculate the person-time at risk, and the

expected deaths using the lifetable data. 3. Neighbourhood adjacency matrix file

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Data preparation

1. Population mortality data

  • Create lifetables by SLA, sex and year

group (e.g. 2003-2007). 2. Cancer incidence data

  • Calculate the person-time at risk, and the

expected deaths using the lifetable data. 3. Neighbourhood adjacency matrix file

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Relative survival model

Dickman et al. (2004): dj ~ Poisson(μj) log(μj – d*j) = log(yj) + xβ

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Relative survival model

Dickman et al. (2004): dj ~ Poisson(μj) log(μj – d*j) = log(yj) + xβ

Excess deaths Person-time at risk

}

Covariate parameters Observed deaths

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Bayesian relative survival model

Based on Fairley et al (2008): dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + ui + vi

where k = broad age groups j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

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Bayesian relative survival model

Based on Fairley et al (2008): dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + ui + vi

where k = broad age groups j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

Intercept Unobserved and unstructured Unobserved with spatial structure

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The Bayesian difference

  • Parameters considered to arise from

underlying distribution (“stochastic”)

  • Use probability distributions (“priors”)
  • Simplifies inclusion of spatial

relationships

  • Posterior distributions for output

parameters

  • Posterior proportional to Likelihood x Prior
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Posterior distributions

Trace plot Density plot

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Bayesian relative survival model

Based on Fairley et al (2008): dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + ui + vi where k = broad age groups j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

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Bayesian relative survival model

Based on Fairley et al (2008): dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + ui + vi where k = broad age groups j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

e.g. ~Normal(0,1000)

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Bayesian relative survival model

Based on Fairley et al (2008): dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + ui + vi where k = broad age groups j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

e.g. ~Normal(0,1000) CAR prior

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The Conditional AutoRegressive (CAR) distribution

Area full conditional distributions:

𝑞 𝑣𝑗 𝑣𝑘, 𝑗 ≠ 𝑘, 𝜏2 ~𝑂 𝜈 𝑗, 𝜏2 𝑜𝜀𝑗 𝜈 𝑗 = 𝑣𝑘 𝑜𝜀𝑗

𝑘∈𝜀𝑗

𝑜𝜀𝑗 = number of neighbours 𝜏2 = variance

uj uj uj uj uj uj uj

ui

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Raw estimates

RER

Breast cancer survival (risk of death within 5 years)

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Raw estimates

RER

Problems

  • Many large areas have small

populations (and vice versa)

  • Excessive random variation –
  • bscures the true geographic

pattern

Breast cancer survival (risk of death within 5 years)

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Raw estimates Smoothed estimates

RER

Breast cancer survival (risk of death within 5 years)

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Results and Benefits

This model allows us to determine:

  • Robust small area estimates with uncertainty
  • Influence of important covariates
  • Probabilities (e.g. probability RER > 1)
  • Ranking
  • Number of deaths resulting from spatial inequalities
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Graphs

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Bayesian relative survival model

Breast and colorectal cancers

dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + vi + ui where k = broad age groups/SES/remoteness/stage/gender j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

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Bayesian relative survival model

Breast and colorectal cancers

dkji ~ Poisson(μkji) log(μkji – d*kji) = log(ykji)+ αj + xβk + vi + ui where k = broad age groups/SES/remoteness/stage/gender j = 1,2,…5 follow-up years i = 1,2,…478 SLAs

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Breast cancer survival (risk of death within 5 years) Adjusted for age

Adjusted for age & stage

RER

Spatial variation p-value=0.001 Spatial variation p-value=0.042

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Breast cancer survival (risk of death within 5 years)

Adjusted for age, stage & SES Adjusted for age , stage, SES & distance

RER

Spatial variation p-value=0.452 Spatial variation p-value=0.631

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How many deaths could be prevented if no spatial inequalities?

Number of deaths within 5 years from diagnosis due to non-diagnostic spatial inequalities (1997-2008):

Colorectal cancer: Breast cancer:

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How many deaths could be prevented if no spatial inequalities?

Number of deaths within 5 years from diagnosis due to non-diagnostic spatial inequalities (1997-2008):

Colorectal cancer: Breast cancer: 470 (7.8%) 170 (7.1%)

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  • Neighbourhood matrix created in GeoDa (https://geodacenter.asu.edu/)
  • Ran in WinBUGS (Bayesian inference Using Gibbs Sampling) interfaced

with Stata

  • Freely available at: www.mrc-bsu.cam.ac.uk/bugs
  • 250,000 iterations discarded, 100,000 iterations monitored

(kept every 10th)

  • Time taken: 3 hours 15 minutes+
  • On a dedicated server:
  • Dual CPU Quad Core Xeon E5520’s: 8 Cores and 16 Threads, large

8MB Cache

  • Quick Path Interconnect: fast memory access

Implementation

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Cramb SM, Mengersen KL, Baade PD. 2011. The Atlas of Cancer in Queensland: Geographical variation in incidence and survival, 1998-2007. Cancer Council Queensland: Brisbane.

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Cramb SM, Mengersen KL, Baade PD. 2011. The Atlas of Cancer in Queensland: Geographical variation in incidence and survival, 1998-2007. Cancer Council Queensland: Brisbane. Cramb SM, Mengersen KL, Baade PD. 2011. Developing the atlas of cancer in Queensland: methodological issues. Int J Health Geogr, 10:9

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Cramb SM, Mengersen KL, Baade PD. 2011. The Atlas of Cancer in Queensland: Geographical variation in incidence and survival, 1998-2007. Cancer Council Queensland: Brisbane. Cramb SM, Mengersen KL, Baade PD. 2011. Developing the atlas of cancer in Queensland: methodological issues. Int J Health Geogr, 10:9 Cramb SM, Mengersen KL, Turrell G, Baade PD. 2012. Spatial inequalities in colorectal and breast cancer survival: Premature deaths and associated factors. Health & Place;18:1412-21.

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Cramb SM, Mengersen KL, Baade PD. 2011. The Atlas of Cancer in Queensland: Geographical variation in incidence and survival, 1998-2007. Cancer Council Queensland: Brisbane. Cramb SM, Mengersen KL, Baade PD. 2011. Developing the atlas of cancer in Queensland: methodological issues. Int J Health Geogr, 10:9 Cramb SM, Mengersen KL, Turrell G, Baade PD. 2012. Spatial inequalities in colorectal and breast cancer survival: Premature deaths and associated factors. Health & Place;18:1412-21. Earnest A, Cramb SM, White NM. 2013. Disease mapping using Bayesian hierarchical models. In Alston CL, Mengersen KL, Pettitt AN (eds): Case Studies in Bayesian Statistical Modelling and Analysis, Wiley: Chichester.

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“By increasing our understanding of the small area inequalities in cancer outcomes, this type of innovative modelling provides us with a better platform to influence government policy, monitor changes, and allocate Cancer Council Queensland resources”

~ Professor Jeff Dunn, Cancer Council Queensland CEO