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1 In-Vitro Screening for Combination Drug Discovery John J. Peterson GlaxoSmithKline Pharmaceuticals, R&D 2009 Midwest Biopharmaceutical Statistics Workshop

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2 Outline of Talk Experimental design used What is “excess over highest single agent” (EOHSA)? Simultaneous testing for EOHSA across all combinations Some examples An Introduction to “nonlinear blending” synergy.

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3 Experimental design for screening pairs of compounds A k x k factorial. Here k = 9. C = “combination” S = “single compound” V = “vehicle (control)”

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4 Excess over highest single agent (EOHSA) For a k x k factorial design let be the mean response for the combination of compound A at dose level i and compound B at dose level j. Let be the dose of compound A alone at dose level i. Let be the dose of compound B alone at dose level j. The compound combination at dose levels (i, j) exhibits EOHSA if EOHSA provides an easy-to-understand, low-level criterion for combination drug screening. - It is also an FDA criterion for (21 CRF 300.50) for combination drug approval. - Used by CombinatoRx Inc. for combination compound screening (Borisy et al, (2003) Proceedings of the National Academy of Science, 100, 7977–7982)

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5 Simultaneous testing for EOHSA across compound combinations Testing for EOHSA for one (i, j) compound combination can be accomplished by use of the “min test” to test the null and alternative hypotheses below. The above hypothesis can he tested by doing two one-sided tests of the form each at level for an overall false-positive error rate of (if both nulls are rejected) However since there are combinations, we need to adjust for multiple comparisons to control the family-wise error rate across all combinations. Hung (2000) and Westfall, Ho, and Prillaman (2001) have suggested procedures for conducting simultaneous min tests.

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6 Simultaneous testing for EOHSA across compound combinations Since there are combinations, we need to adjust for multiple comparisons to control the family-wise error rate across all combinations. Hung (2000) and Westfall, Ho, and Prillaman (2001) suggested procedures for conducting simultaneous min tests. However since the k x k design involves increasing doses of both compounds, we can expect dose-response trends along each row and column of the design. These dose-response trends can be exploited to gain additional power to test for EOHSA across the various compound combinations.

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7 Simultaneous testing for EOHSA across compound combinations C = “combination” S = “single compound” V = “vehicle (control)” Suppose there is a trend for compound A (for dose levels 0 to 5) at dose level 4 of compound B. Suppose also there is a trend for compound B (for dose levels 0 to 4) at dose level 5 of compound A. It follows then that the compound combination (5,4) has EOHSA.

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8 Simultaneous testing for EOHSA across compound combinations C = “combination” S = “single compound” V = “vehicle (control)” So intersecting trends can be used test for EOHSA. Since there are k dose levels of each compound there are 2(k-1) simultaneous trend tests involving exactly l dose levels. At each dose level, l, we can do 2(k-1) Bonferroni-adjusted trend tests. The Tukey step-down trend test can be used as we step from level l=(k-1) to l=1. The Tukey step-down test requires no adjustment of the (Bonferroni-adjusted) -level.

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9 Simultaneous testing for EOHSA across compound combinations C = “combination” S = “single compound” V = “vehicle (control)” PROPOSED TESTING PROCEDURE 1. At each dose level, l, do 2(k-1) Bonferroni-adjusted trend tests. 2. Use the Tukey step-down trend test as you step from level l=(k-1) to l=1. Note: The Tukey step-down test requires no adjustment of the (Bonferroni-adjusted) -level. It can be proven that this procedure controls the FWER strongly at level . The proposed procedure is more efficient than doing (k-1) 2 multiple comparisons, even with correlation adjusted p-values.

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10 Example Compound B Dose Level Numbers 8731015831586872 70323423566668 652-2518546368 5-4-3-7-3220566368 4-7-63217536365 3-9-6-4-214516668 2-10-9-10-2123546366 1-2-11 -5220526064 00-50-214526469 012345678 5’FU (Compound A) Dose Level Numbers Mean percent reduction in living cancer cells for 9 x 9 factorial experiment (n = 2) replications per treatment group) for compound A and compound B (A549 cell line). Means with boldface-italic font (in the highlighted cells) are associated with combinations having statistically significant EOHSA.

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11 Simultaneous testing for EOHSA across compound combinations Proposed Bonferroni testing procedure: 1. At each dose level, l, do 2(k-1)Bonferroni-adjusted trend tests. 2. Use the Tukey step-down trend test as you step down from level l=(k-1) to l=1. Proposed Modified Adjusted p-value testing procedure. In step 1 above replace the Bonferroni adjustment with a more efficient bootstrap adjusted p-value. - This modification can be easily executed using SAS ® PROC MULTTEST. - Simulations indicate that this procedure is more powerful than the Bonferroni adjusted version while still keeping the FWER to at most .

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12 It is possible to have many trends but no combinations with EOHSA So the null space of this testing procedure is complex. 6 If the 5 above were replaced by the (circled) 6 then the combination highlighted in yellow would have EOHSA.

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13 Simulations to assess overall Type I error rate Consider the following three null hypothesis situations: 1,000 (normally distributed) data sets were simulated under each of the three null hypotheses (with n=2 per cell and = 1). Nominal = 0.05. The false-positive error rates were: Compound B only has a strong trend

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14 Comparisons with some other testing procedures MATBOOT=“multiplicity adjusted Tukey step-down trend test (Bootstrap)” MATBON=“multiplicity adjusted Tukey step-down trend test (Bonferroni)” SHUIIUT=Simes-Hommel Union-Intersection-Intersection-Union Trend SHUIIU=Simes-Hommel Union-Intersection-Intersection-Union MAPC=“multiplicity adjusted (bootstrap) p-values for (pairwise) contrasts. Four drug combinations were tested in each of four cell lines resulting in 16 experiments MATBOOTMATBONSHUIIUTSHUIIUMAPC Average no. of cells with EOHSA reported 5.252.941.811.060.69 Median no. of cells with EOHSA reported 531.500

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15 Summary for Screening for EOHSA Using the Bonferroni procedure to adjust Tukey’s step-down trend test results in adjustments across only 2(k-1) groups rather than (k-1) 2 groups. - This provides improved power, even over Monte Carol adjusted procedures, when their adjustment is over (k-1) 2 groups (at least for k=9). The power of this adjustment of Tukey’s trend test can be improved by using PROC MULTTEST, which is easy to implement. It can be proven that the Bonferroni procedure to adjust Tukey’s step-down trend test strongly controls the FWER. - The more powerful bootstrap adjusted modification appears to strongly control the FWER as well. It may be useful to follow up this “low level” screening with a criterion that provides a higher “drug synergy hurdle”. One possibility is to use the concept of “nonlinear blending” found in mixture experiments.

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16 Nonlinear Blending Compared to FDA’s EOHSA. total dose (molar) Total dose (molar) solid gray line of constant total dose (molar) Nonlinear blending is: “excess over highest single agent at total dose” as opposed to “excess over highest single agent (at component dose)” Therefore nonlinear blending is a stronger form of “synergy”. drug A drug B

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17 Why classical synergy indices do not generally work well for screening for combination drug synergy. Drug 1 Drug 2 Isobologram (e.g. 50%) d1+d2=A Point of 50% response We have Loewe synergy at the combination (d 1,d 2 ) if But what if one or both of the ED 50 ’s (or ED 60 ’s, etc.) do not exist?

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18 Problems with the Interaction Index Cannot always compute the interaction index! Monotherapies do not achieve Y = 50% Yet, excellent synergy exists At a 50:50 ratio!

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19 Nonlinear Blending. If the response increases as we move away from the single agent compounds, then we have “optimal nonlinear blending”. Optimal nonlinear blending can exist no matter what the shape of the dose response curves for the single agent compounds. This type of synergy is much stronger than “excess over highest single agent”. Compound A Compound B total amount, T3 Total amount, T3 line of constant total amount, T3 total amount, T2 total amount, T1 Combined compound response

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20 Nonlinear Blending: Weak and Strong Nonlinear Blending 0 50 100 Percent of drug 1 Response (percent) Response (percent) Weak nonlinear blending Strong nonlinear blending 0 100 50 0 100 25 75 25 75 Blending profiles for two different pairs of drugs at a given total (molar) dose For details see: Peterson, J. and Novick, S., “Nonlinear Blending: A Useful, General Concept for the Assessment of Combination Drug Synergy”, Journal of Receptors and Signal Transduction, vol.27, pp125-146.

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21 2187Y243X+2 187Y 0.5 729Y0.51/3 243Y0.51/31/9 81Y1X+81Y0.51/31/91/27 27Y1X+27Y0.51/31/91/27 9Y8/9 1X+9Y 0.51/31/91/27 3Y2/3 1X+3Y 0.51/31/91/27 1Y0.5 1X+1Y 1/3 3x+1Y 1/9 9X+1Y 1/27 27X+1Y 1/81 81X+1Y 01X3X9X27X81X243X729X2187X

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22 The testing process for strong nonlinear blending. drug A (nM) drug B (nM) 7 Rays (diagonals) of constant dose ratio. = actual data point = interpolated data point Plate A Percent of drug A Interpolated response 010050 Interpolated data points from plates A and B.

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23 50% Drug A Drug B Ten ‘Total (Molar) Dose’ Slices Through the Combination Drug Region 1% 50% 99% 7 diagonals (rays) This line only cuts across 4 true rays Percent of drug A Interpolated response 010050 Imputed values in blue plate A plate B 0% 50%99%

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24 The testing process for strong nonlinear blending. Percent of drug A Interpolated response 010050 Interpolated data points from plates A and B. 1. For each total dose (molar) amount, fit a cubic polynomial curve to the data. (For robustness sake, we fit the data using a rank transformation of the percent drug A levels.) 2. Using gridding, find the maximum mean response. 3. Using the ‘min’ test, test to see if the maximum mean response is greater than both mean responses associated with 0% and 100% of drug A. If so, then we have strong nonlinear blending at that total (molar) amount. 4. Adjust the min test p-values (e.g. using the Hommel adjustment) across the various total dose levels used.

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25 Summary for Screening for Strong Nonlinear Blending Strong nonlinear blending can, in a practical sense, address any situation that might come up in the screening of drug combinations. The classical synergy indices such as Loewe synergy index, Chou & Talalay, Bliss, etc. all have serious flaws with regard to computation or interpretation of synergy. If Loewe synergy can exist (e.g. both ED50’s exist) then the existence of strong nonlinear blending implies the existence of Loewe synergy. It may be possible to improve screening for ‘strong nonlinear blending’ by use of generalized additive models to automate fitting of response surfaces to 9 x 9 factorial plate designs. This is work for the future! For further details on Nonlinear Blending see: Peterson, J. and Novick, S., “Nonlinear Blending: A Useful, General Concept for the Assessment of Combination Drug Synergy”, Journal of Receptors and Signal Transduction, vol.27, pp125-146. Send e-mail to john.peterson@gsk.com for a copy.john.peterson@gsk.com

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