Modeling & Simulation in pharmacogenetics/personalised medicine

Transcription

1 Modeling & Simulation in pharmacogenetics/personalised medicine Julie Bertrand MRC research fellow UCL Genetics Institute 07 September, 2012 WCOP 07/09/12 1 / 20

2 Pharmacogenetics Study of the genetic variation in relation to interindividual variability in drug response Genetic variation single nucleotide polymorphism (SNP) biallelic (alleles C/T): 3 genotypes (CC, CT, TT) common and abundant (1 per 100 to 1000 bp) 90% of genetic differences linkage disequilibrium local correlation between markers close on the genome Drug response pharmacokinetics (PK) jbertrand@uclacuk WCOP 07/09/12 2 / 20

3 Personalised medicine WCOP 07/09/12 3 / 20

4 Pharmacogenetic studies Genetic studies in pharmacology explore many SNPs, but simple response PK studies use nonlinear mixed effect models (NLMEM), but few SNPs Large SNP panels rarely combined with PK models modified stepwise procedure 1 naive pooling of data per genotype 2 penalised regression methods 3 give better performance to select set of SNPs tagging most causal variants established in animal and plant genetics 1 Lehr et al Pharmacogenetics and Genomics, Wu et al Drug Discovery Today, Cordell et al Genetic Epidemiology, 2010 jbertrand@uclacuk WCOP 07/09/12 4 / 20

5 Stepwise procedure Commonly used strategy for covariate model building Iterative procedure screening on the individual PK parameters/random effects forward inclusion in the model final backward selection (often more stringent) Extension for HTS platform proposed by Lehr et al 4 correction for correlation in significant SNPs biological confirmation 4 Lehr et al Pharmacogenetics and Genomics, 2010 jbertrand@uclacuk WCOP 07/09/12 5 / 20

6 Penalized regression All SNPs considered simultaneously Bayesian perspective: specific priors on effect coefficients Ridge regression Gaussian prior penalty set automatically 5 approximate Wald test Lasso 6 Double Exponential (DE) prior penalty set by permutations for a targeted FWER HyperLasso 7 Normal exponential gamma (NEG) shape (λ) and scale (γ) parameters set by permutations 5 Cule et al ArXiv e-prints, Tibshirani R JRSS B, Hoggart et al PloS Genetics, 2008 jbertrand@uclacuk WCOP 07/09/12 6 / 20

7 HyperLasso λ small sharp peak at zero = sparse solutions heavy tails = variables minimally shrunk once included Double exponential recovered with large λ jbertrand@uclacuk WCOP 07/09/12 7 / 20

8 Explore penalized regression methods to incorporate SNP data into PK studies using NLMEM WCOP 07/09/12 8 / 20

9 Pharmacokinetic settings Structural and statistical model inspired from real study 8 Phase II-like study design 300 individuals with t= 05, 125, 2, 4, 9, 24 Pharmacokinetic modelling performed with SAEM in MONOLIX 31 8 Kappelhoff et al Clinical pharmacokinetics, 2005 jbertrand@uclacuk WCOP 07/09/12 9 / 20

10 Genetic settings Generation of genotypes using HAPGEN 9 HAPMAP caucasian reference haplotypes 1227 snps on 171 genes from the DMET Chip 10 6 [1-56] snps per gene Alternative hypothesis H simulated data sets 6 unobserved causal variants with allelic frequency, p>005 linear decrease in log(cl/f) global genetic component of variability of 30% R G = β2 l 2p(1 p) = (1, 2, 3, 5, 7, 12) βl 2 2p(1 p)+ω 2 9 Su et al Bioinformatics, Daly et al Clinical Chemistry, 2007 jbertrand@uclacuk WCOP 07/09/12 10 / 20

11 A typical simulated dataset WCOP 07/09/12 11 / 20

12 Computing times Method H 0 H 1 Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure jbertrand@uclacuk WCOP 07/09/12 12 / 20

13 Computing times Method H 0 H 1 Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure jbertrand@uclacuk WCOP 07/09/12 12 / 20

14 Family Wise Error Rate (FWER) and true positive count (TP) Method FWER (%) TP (%) Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure % prediction interval around 20 based on 3 tested parameters in each of 200 simulated data sets is [ ] jbertrand@uclacuk WCOP 07/09/12 13 / 20

15 Family Wise Error Rate (FWER) and true positive count (TP) Method FWER (%) TP (%) Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure % prediction interval around 20 based on 3 tested parameters in each of 200 simulated data sets is [ ] jbertrand@uclacuk WCOP 07/09/12 13 / 20

16 Family Wise Error Rate (FWER) and true positive count (TP) Method FWER (%) TP (%) Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure % prediction interval around 20 based on 3 tested parameters in each of 200 simulated data sets is [ ] jbertrand@uclacuk WCOP 07/09/12 13 / 20

17 Family Wise Error Rate (FWER) and true positive count (TP) Method FWER (%) TP (%) Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure % prediction interval around 20 based on 3 tested parameters in each of 200 simulated data sets is [ ] jbertrand@uclacuk WCOP 07/09/12 13 / 20

18 Power versus R G jbertrand@uclacuk WCOP 07/09/12 14 / 20

19 Power to detect x causal variants jbertrand@uclacuk WCOP 07/09/12 15 / 20

20 Power versus Genetic effect size WCOP 07/09/12 16 / 20

21 Power versus causal variant allelic frequency WCOP 07/09/12 17 / 20

22 False positive counts Method FP CL/F FP Vc/F FP Q/F Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure jbertrand@uclacuk WCOP 07/09/12 18 / 20

23 False positive counts Method FP CL/F FP Vc/F FP Q/F Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure jbertrand@uclacuk WCOP 07/09/12 18 / 20

24 False positive counts Method FP CL/F FP Vc/F FP Q/F Ridge Lasso HyperLasso (λ=1) HyperLasso (λ=005) Stepwise procedure jbertrand@uclacuk WCOP 07/09/12 18 / 20

25 False/True positive trade-off WCOP 07/09/12 19 / 20

26 Realistic simulation study large SNPs set in PG analyses using NLMEM Similar performances to detect marginal association ridge and stepwise proc associated to effect size lasso-based approach more sensible to allelic frequency score versus Wald/LR test? Advantages of Lasso-based regression shorter computing times higher (not significantly) FP counts better behaviour with decreasing γ Perspectives integration of HyperLasso in NLMEM estimation step faster computing time incentive for multiple imputations WCOP 07/09/12 20 / 20