Performance of INLA analysing bivariate meta-regression and age-period-cohort models Andrea Riebler Biostatistics Unit, Institute of Social and Preventive Medicine University of Zurich INLA workshop, May 2009 Joint work with Lucas Bachmann, Leonhard Held, Michaela Paul and H˚ avard Rue
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Performance of INLA analysingbivariate meta-regression and age-period-cohort
models
Andrea Riebler
Biostatistics Unit, Institute of Social and Preventive MedicineUniversity of Zurich
INLA workshop, May 2009
Joint work with Lucas Bachmann, Leonhard Held, Michaela Pauland Havard Rue
Introduction Bivariate meta-analysis Age-period-cohort model Summary
Outline
1. Introduction
2. Bivariate meta-analysis
3. Age-period-cohort model
4. Summary
Andrea Riebler 2/ 29
Introduction Bivariate meta-analysis Age-period-cohort model Summary
1. Introduction
Bivariate meta-analysis
Comparison of the performance of inla and the performanceobtained by the maximum likelihood procedure SAS PROCNLMIXED (Paul et al., 2009).
Age-period-cohort models
Comparison of the performance of inla and an MCMC algorithmimplemented in C using the GMRFLib library (Rue and Held, 2005,Appendix).
All analyses were run under Kubuntu 8.04 on a laptop withIntel(R) Core(TM) 2 Duo T7200 processor with 2.00 GHz.
Andrea Riebler 3/ 29
Introduction Bivariate meta-analysis Age-period-cohort model Summary
Bivariate meta-analysis
Meta-analyses are used to summarise the results of separatelyperformed studies, here diagnostic studies.
Diagnostic studies often report two-by-two tables
⇒ Sensitivity Se = TPTP + FN and specificity Sp = TN
TN + FP .
Bivariate meta-analysis:
Models the relationship between sensitivity and specificity (afterlogit transformation), including random effects for both andallowing for correlation between them.
Focus: Estimation of the expected sensitivity and specificity
Introduction Bivariate meta-analysis Age-period-cohort model Summary
Covariate effects
Time constant effect exp(β):
10%-quantile Median 90%-quantile
1.11 1.13 1.15
Time-varying effect exp(βj):
1975 1980 1985 1990 1995 2000 2005 2010
0.0
0.5
1.0
1.5
2.0
Periods
exp((
ββ j))
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Introduction Bivariate meta-analysis Age-period-cohort model Summary
Model assessment
PIT histogram for count data (Czado et al. 2009):APC (RW2)
PIT
Rel
ativ
e fr
eque
ncy
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Time−constant covariate effect
PIT0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Time−varying covariate effect
PIT0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Log-score:APC constant RW2
−log(CPO) 3.895? 3.887? 3.905?
?Two CPO values were removed as they were classified as unreliable.
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Introduction Bivariate meta-analysis Age-period-cohort model Summary
Prediction until 2010
1975 1980 1985 1990 1995 2000 2005 2010
3040
5060
7080
50−54Period
Num
ber
of c
ases
per
100
000
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Observations
APC (RW2)time−constant effect of covariatetime−varying effect of covariate
Median 80% region
1975 1980 1985 1990 1995 2000 2005 2010
6080
100
120
140
55−59Period
Num
ber
of c
ases
per
100
000
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Introduction Bivariate meta-analysis Age-period-cohort model Summary
Discussion
INLA facilitates the analysis of Bayesian APC models.
Prediction is straightforward.
Covariate information can be easily incorporated.
Model diagnostics available, but not completely robust.
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Introduction Bivariate meta-analysis Age-period-cohort model Summary
4. Summary
For both applications presented, INLA is an alternative to thestandard used inference approaches (ML, MCMC). It is:
User-friendly and easy to apply
Fast
Flexible
Issues for future work might be:
Improved model diagnostics,
Calculation of joint credibility intervals,
Calculation of predictive distribution for response.
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Introduction Bivariate meta-analysis Age-period-cohort model Summary
Thank you for your attention
Chu, H. and Cole, S.R. (2006).Bivariate meta-analysis of sensitivity and specificity with sparse data: a generalised linear mixed modelapproach. Journal of Clinical Epidemiology, 59, 1331–1333.
Czado, C., Gneiting, T. and Held, L. (2009).Predictive Model Assessment for Count Data. Biometrics, to appear.
Knorr-Held, L. and Rainer, E. (2001).Projections of lung cancer mortality in West Germany: a case study in Bayesian prediction. Biostatistics, 2,109–129.
Paul, M., Riebler, A., Bachmann, L., Rue, H. and Held, L. (2009). Bivariate meta-analysis with INLA: anapproximate Bayesian inference. Statistics in Medicine, submitted.
Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Volume 104 ofMonographs on Statistics and Applied Probability, Chapmann & Hall/CRC.
Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by usingintegrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society: Series B,71, 319–392.
Scheidler, J., Hricak, H., Yu, K. K., Subak, L. Segal, M. R. (1997). Radiological evaluation of lymph nodemetastases in patients with cervical cancer. Journal of the American Medical Association,278, 1096–1101.