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 • • • • • • 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?