Patrick Graham - Bayes, Data Mining and Pharmacovigilance

Report
Bayes, Data Mining and
Pharmacovigilance
Patrick Graham
University of Otago, Christchurch
Acknowledgements
• Funders: MedSafe and HRC
• Collaborators: Ruth Savage, Janelle Ashton, Michael
Tatley from New Zealand Pharmacovigilance Centre,
University of Otago
Background (1)
• Pharmacovigilance – post-marketing surveillance of
medicines.
• Seeks early detection of adverse drug reactions,
• Traditionally, clinical review of spontaneous reports
• Late 1990s? “Data mining” of databases of spontaneous
reports – “signal detection”
• Two Bayesian methods prominent:
-WHO –Independent 2 x 2 tables, Multinomial – Dirichlet
-FDA (DuMouchel) - Analyse all drugs by all reactions table
using a hierarchical Poisson – mixture of Gammas model
Background (2)
• Interest is now turning to the potential of longitudinal health
care databases, record-linkage, electronic prescribing and
other technologies
• MedSafe / HRC formed the “product-vigilance partnership”
2007 to advance product-vigilance research in NZ.
• Feasibility studies in 2008
• Collaborative group funded late 2009 led by Dr. Michael Tatley
of the NZ Pharmacovigilance Centre.
• Wider project includes work on: risk communication; ethics,
acceptability and methods for accessing general practice data;
epidemiological studies; signal detection in longitudinal
databases.
• Signal detection work includes Bayesian methods (me) as well
as investigation of machine-learning approaches, text mining
and natural language processing.
Features of health care databases
• More representative than spontaneous
reports
• Usually longitudinal
• Lots of time-stamped information
• Large size (makes analysis at the level of
individual patients difficult)
Signal detection in health care databases
•
•
•
•
Aim is exploratory analysis of:
Multiple drugs
Multiple outcomes, some of which will be rare
Large datasets, potentially large number of
comparisons, so computational efficiency will often
be an issue.
One approach: Noren et al (2010)
Published in Data Mining and Knowledge Discovery ,
2010, 20, 361-387.
• Simple Poisson-Gamma model for each combination of outcome,
drug, and time period.
• Exact posterior immediately available
• no smoothing, no pooling, just shrinkage towards a prior mean
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•
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Applied to a UK General Practice database, > 20 million scripts
Analysed 2,445 drugs x 5,753 outcomes x 72 time periods
Took ~8 hours on a server with 2 dual core, 2.4GHz processors
Nice graphs of temporal trends
Software system developed but not publicly available
A data mining approach?
Noren et al - Details
Y o d t  # o cu rren ces o f o u tco m e o , am o n g p eo p le ex p o sed to d , an d at risk
in p erio d t
N d t  p erso n -tim e at risk d u rin g p erio d t am o n g p eo p le ex p o sed to d
e o d t  (  a Yo a t /

a
N at )  N dt
indep
Y odt | e dt ,  odt ~ P oisson (  odt e odt )
 odt ~ G am m a (0.5, 0.5)
indep
so  odt | Y odt , e dt ~ G am m a (0.5  Y odt , 0.5  e odt )
and  (  odt | Y odt , e odt )  (0.5  Y odt ) / (0.5  e odt )
 (1  w dt )(Y odt / e dt )  w dt 1
w dt  0.5 / ( E dt  0.5)
Why did we not use Noren et al’s approach?
(i) A statistical modeller’s perspective
• Many similar parameters to be estimated
• Should we not be trying to learn from similar estimations
when estimating each particular parameter?
• Old idea for both Bayesians and frequentists.
(ii) Our paradigm is on a smaller scale, e.g.
• Compare a new drug with drugs currently used for
treating the same condition.
• 20-30 outcomes with thought a priori likely to be
associated with ADRs, e.g. (Trefiro et al 2009)
Hierarchical Bayesian Model
(similar notation to previously but specifically reference patient sub-groups by subscript g)
indep
Y godt | N gdt ,  godt ~ P oisson ( N gdt  godt )
indep
 godt |  o ,  o ~ G am m a ( o ,  0 /  godt )
log(  godt )  X gdt  0
[prior m odel]
zo
2


p (  o ,  o )   N (  0 i | 0, s i )
i

 ( z   )2
o
o
(Separate model for each outcome, o)
Focus is on sum m aries of the  godt e.g.  odt  (  N gdt  godt ) /
std
g

g
N gdt
for w hich inference follow s from p ( λ | Y , N ) -joint posterior for the  godt
Hierarchical Bayesian Model (cont’d)
Prior model permits full flexibility of statistical modelling, e.g.
- jump in event rate just after first prescription
-smooth but nonlinear changes elsewhere
-drug by time interactions
-drug by covariate interactions
-etc
But hierarchical model structure provides some protection against
model-misspecification.
E (  godt | Y , N ,  o , o )  (1  w godt )(Y godt / N gdt )  w godt  godt
w here w godt 
o
 o   godt N gdt
; log(  godt )  X gdt  o
Of course we don’t actually condition on  o ,  o
But integrate over the posterior to obtain p ( λ | Y , N )
Hierarchical Bayesian Model - Computation
p (λ o | Y , N ) 

p ( λ o |  o , o , Y , N ) p (  o , o | Y , N ) d  o d  o
 o , o
First part of the integrand is product of independent Gammas,
second part is the posterior for parameters of a negative binomial
model, suggesting Monte Carlo computation via
(i) M C M C to obtain a sam ple from p (  o ,  o | Y , N )
(ii) For each sam pled value of (  o ,  0 ) draw λ o from

gdt
G am m a (  godt |  0  Y godt , ( o /  godt )  N godt )
w here  godt  exp( X gdt  o )
Should be faster than Gibbs sampler
Hierarchical Bayes model computation
performance
• Burn-in of 4000 for MCMC seems adequate
• Example 1: Cohort of 4531, prescribed one of 4
atypical antipsychotics, 23 outcomes, adjusting
for age and sex, took 17 minutes
• Example 2: Cohort of 10,308 children receiving
one of 3 vaccines, 12 outcomes, adjusting for age,
sex and season, took 27.5 minutes
• Using 64 bit R on a laptop, 4 GB RAM, quad core
2.2 GHz, but with R not optimised for multi-core
Results: Atypical antipsychotics
Ischaemic Heart Disease (IHD)
Posterior probabilities for standardised IHD rates
exceeding baseline rates, by drug and period
Drug
Period 1
Period 2
Period 3
Period 4
Clozapine
0.08
0.01
0.00
0.00
Olanzapine
0.05
0.03
0.03
0.03
Quetiapine
0.93
0.89
0.81
0.74
Risperidone
0.00
0.00
0.00
0.00
Posterior probability that each drug has the
largest standard IHD rate, by period
Drug
Period 0
Period 1
Period 2
Period 3
Clozapine
0.16
0.03
<0.01
<0.01
Olanzapine
0.31
0.02
0.03
0.03
Quetiapine
0.02
0.89
0.83
0.94
Risperidone
0.51
0.06
0.14
0.03
Results. IVMP – local reactions
Summary
• Signal detection in Pharmacovigilance is an important and
interesting area
• “Data mining” approach emphasises large scale computation,
simple statistical model, independent analyses, no learning
across groups, outcomes, drugs or time-periods.
• “Statistical modelling” approach emphasises a more complex
statistical model which permits, for each outcome, learning
across groups, drugs, time-periods, (while still permitting
departures from the model) but is designed for smaller scale
computations
• Can each approach learn from the other?

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