Pooling Experiments for High Throughput Screening in Drug Discovery

Transcription

1 Pooling Experiments for High Throughput Screening in Drug Discovery Jacqueline M. Hughes-Oliver Department of Statistics North Carolina State University Spring Research Conference, June

2 Outline Motivation What is a Pooling Experiment? + synergism & blocking, saves money, time, materials logistics are difficult, needs careful design & analysis Analysis of Pooling Experiments Issues Current Work Spring Research Conference, June

3 High Throughput Screening 500,000+ molecules available for screening < 5% are active (high potencies) Must find m diverse leads leads toxicity Phase I clinical trials etc. Search for Structure-Activity-Relationships, SARs Relate activity to chemical structure Often, n= #responses << p= #descriptors Assay 1: n = 1000 p = 1873 Assay 2: n 500, 000 p>1mil Testing done by liquid-handling robotic systems Spring Research Conference, June

4 State of the Art Test all molecules in training set Recursive partitioning (RP) Nonlinear, fragmented relationships Use hypothesis testing to split nodes Excellent for n<<p Needs large n, since Pr(active) is small Make predictions for untested molecules, then do ordered testing Accumulation curves: # actives found vs. # tests performed Spring Research Conference, June

5 State of the Art Test all molecules in training set Recursive partitioning (RP) Nonlinear, fragmented relationships Use hypothesis testing to split nodes Excellent for n<<p Needs large n, since Pr(active) is small Predict for untested molecules, then do ordered testing Accumulation curves: # actives found vs. # tests performed Can We Increase efficiency? Discover combination therapies in vitro? Spring Research Conference, June

6 Pooling Experiment Test molecules in mixtures, not individually Spring Research Conference, June

7 Pooling Experiment Test molecules in mixtures, not individually HTS Plate Spring Research Conference, June

8 Pooling Experiment Test molecules in mixtures, not individually Individual Compounds Pools Figure 1: One-way Pooling experiment where pooling is by column. Spring Research Conference, June

9 Pooling Experiment: Dorfman Assumptions Test molecules in mixtures, not individually p =Pr(active) k = pool size n =#pools X =#active pools X bin(n, θ) θ =1 (1 p) k p same for all molecules No errors in interpreting pooled responses all molecules in pool are inactive inactive pool 1+ molecule active active pool Pooling does not alter behavior of individuals No degeneration of activity No enhancement of activity Spring Research Conference, June

10 Pooling Experiment: Dorfman Assumptions Violated Test molecules in mixtures, not individually p =Pr(active) k = pool size n =#pools X =#active pools X bin(n, θ) θ =1 (1 p) k p same for all molecules SAR No errors in interpreting pooled responses all molecules inactive inactive pool Specificity+ 1+ molecule active active pool Sensitivity+ Pooling does not alter behavior of individuals No degeneration of activity Dilution? Blocking? No enhancement of activity Additivity? Synergism? Spring Research Conference, June

11 Active Compound Inactive Compound Blocker Compound Individual Compounds Pools Synergism occurs active Pool Blocking occurs active Pool Figure 2: One-way Pooling experiment where pooling is by column. Pool 1 illustrates synergism and Pool 8 illustrates blocking. Pools 4 and 11 show regular activity. Spring Research Conference, June

12 Assay 1 y =%inhibition relative to reference molecule n = 100 pools each of size k =10 Pooling by dissimilarity according to Burden Numbers avoid additivity conc. for pool =10 conc. for individual avoid dilution Control over design Active is y 60 Active pools: 4 of 100 (4%) Active molecules: 40 of 1000 (4%) Spring Research Conference, June

13 [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] pools [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] [2,] [3,] [4,] * [5,] [6,] * [7,] *1 0 *1 [8,] [9,] [10,] pools Blocking Spring Research Conference, June

14 Pool along the rows, using activity thresholds 60 (individuals) and (pools) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] pools [1,] [2,] [3,] [4,] *1 [5,] [6,] [7,] [8,] [9,] [10,] Synergism Spring Research Conference, June

15 Pooling Experiment: Decoding Retesting? Dorfman: individually test all molecules in active pools Random: individually test some molecules in active pools and some molecules in inactive pools Can estimate synergism and blocking probabilities No retesting? Saves time and money Lose information Not a good idea Spring Research Conference, June

16 Analysis of Pooling Experiments Nonparametric Fully parametric Semiparametric Model as a missing data problem Yi et al. (2003, JSM) Chemical descriptors Atom pairs, BCUT numbers, Mol weight, etc. Spring Research Conference, June

17 Nonparametric: RP on Pools Pooled descriptors: binary Atom pair in pool? Need large number of pools for this to be effective Useful for determining preliminary covariate classes for (semi-) parametric models Excellent indicator of synergism Spring Research Conference, June

18 n= 140 u= 13 s= 29 ap= 7.28E-004 bp= 6.74E-001 N I NO x.1348 n= 52 u= 24 s= 38 ap= 3.16E-003 bp= 1.00E+000 N1 YES x.1348 n= 88 u= 7 s= 21 ap= 9.12E-005 bp= 7.43E-002 N2 I I NO x.1637 YES x.1637 NO x.1048 YES x.1048 n= 38 u= 14 s= 28 ap= 9.24E-004 bp= 2.45E-001 N11 n= 14 u= 49 s= 50 ap= 3.42E-004 bp= 6.46E-002 N12 n= 83 u= 4 s= 17 N21 n= 5 u= 40 s= 44 N22 I I I I NO x.106 YES x.106 NO x.1392 YES x.1392 n= 31 u= 8 s= 17 ap= 4.43E-003 bp= 7.85E-001 N111 n= 7 u= 44 s= 45 N112 n= 7 u= 88 s= 42 N121 n= 7 u= 9 s= 7 N122 I I I I NO x.583 n= 26 u= 4 s= 10 N1111 YES x.583 n= 5 u= 27 s= 34 N1112 I I min node size is 5; splits forced based on = 140 tests Spring Research Conference, June

19 Atom Pairs In Tree Individuals class active total the rest Synergism in class 2? Spring Research Conference, June

20 Number of Actives Found Random testing RP on pools, PT= Number of Tests RP on only 140 tests; need more data Testing order within a node? Spring Research Conference, June

21 Number of Actives Found Random testing RP on pools, PT=60 RP on pools, PT= Number of Tests RP on 390 tests when PT=13.14 Why PT=13.14? Spring Research Conference, June

22 Fully Parametric Model at the individual molecule level Trinomial (active, blocker, other), with class probabilities dependent on chemical features; see Zhu et al (2001) Binomial (active or not), conditioned on interactions in a pool Blocking probability same across all classes Synergism probability same across all classes Activity probabilities dependent on chemical features Scale-up to obtain model on pooled responses Predict activities of untested molecules Test molecules according to rank from predictions Spring Research Conference, June

23 Parametric: Conditional Binomial For i =1,...,n and l =1,...,L, s il = # molecules in pool i and covariate class l W il = # active molecules in pool i and class l Y i = I(pool i active) W il bin(s il,p l ), independent over i and l l s il = k b =Pr(Y i =0 l W il > 0), constant blocking g =Pr(Y i =1 l W il =0), constant synergism Can also model sensitivity and specificity in this manner Spring Research Conference, June

24 Dorfman: test all molecules in active pools. Then L(θ) = i φ y i i (1 ψ i) 1 y i, where ψ i =Pr(Y i =1)=(1 b)+(g + b 1) l (1 p l ) s il φ i = (1 b) l (s il w il p w il l )(1 p l f l ) s il w il l w il > 0 g l (1 p l) s il l w il =0 Spring Research Conference, June

25 Assay 1: Dorfman Experiment, PT=13.14 Class Observed Active Total Pr(active) Conditionally Binomial Pr(active) Pr(blocking).292 Pr(synergism).101 Spring Research Conference, June

26 Number of Actives Found Random testing RP on pools, PT=13.14 MLE, PT= Number of Tests Spring Research Conference, June

27 Issues Design of Pooling Experiments large Flawed designs are not as informative as small but carefully selected designs (additivity, dilution) Zhu et al. (2002), Remlinger et al. (2002) Dilution effect may be unavoidable. Model it. Can we truly disentangle Yi et al. (2002) (synergism,blocking), (additivity,dilution), (effect of activity threshold), (sensitivity,specificity)? Variable selection under parametric models Large dataset Spring Research Conference, June

28 Pooling experiments can be risky: pharmaceutical industry is cautious Pooling experiments can pay off in big ways: Reduce testing costs Shorten testing and development cycle Discover synergistic relationships Discover blocking relationships Spring Research Conference, June

29 Acknowledgements Katja Remlinger, NC State Bingming Yi, Merck Stan Young, NISS & CGStat Ke Zhang, NC State Lei Zhu, GlaxoSmithKline Spring Research Conference, June

30 Current Work Design Random retesting schemes Effect of pool threshold for activity Semi-parametric model, data missing at random Explore pairs/triplets of chemical descriptors, stochastic search Multiple trees Spring Research Conference, June