1. Describing patient variability, 2. Minimizing patient variability, 3. Describing and Minimizing Intraindividual

Transcription

1 1. Describing patient variability, 2. Minimizing patient variability, 3. Describing and Minimizing Intraindividual Variability. 4. Improving the reporting of lab assay results. Roger Jelliffe MD, Alan Schumitzky, David Bayard, Michael Neely, Michael Van Guilder, Andreas Botnen, Aida Bustad Laboratory of Applied Pharmacokinetics Univ. of So. Calif. School of Medicine AAVPT BE Conference, DC, June 2010

2 Set Specific Targets, not windows. Hit them most Precisely.

3 Describing Patient Variability Find covariates such as body weight, renal function, BSA, etc, to minimize variability. Use nonparametric population modeling methods.

4 A Parametric Population Model Joint Density

5 A Population Model, made by Breugel

6 What is the IDEAL Pop Model? The correct structural PK/PD Model. The collection of each subject s exactly known parameter values for that model. This is impossible. But you would have multiple, often genetically polymorphic, individual models, one for each subject. Usual statistical summaries can also be obtained, but usually will lose info. How best approach this ideal? NP!

7 Caratheodory, Lindsay, Mallet theorems We don t need to look at the infinity of all continuous distributions. The most likely (ML) distribution, given the data, CAN BE FOUND in a DISCRETE COLLECTION of points, up to 1 per subject. Each point (support point) has an estimate of each parameter value, and of the probability of those values. No assumptions about the shape of the distribution.

8 An NP Population Model, made by Mallet

9 NP can find sub-populations that would be missed by parametric techniques. True two-parameter density Smoothed empirical density of 20 samples from true density

10 NP vs. parametric methods, cont d. Best parametric representation using normality assumption Smoothed NP results

11 A Clinical Population Seventeen patients 1000 mg Amikacin IM qd for 5 doses 8-10 levels per patient, usually 4-5 on day 1-2, and 4-5 on day 5-6, Microbiological assay, SD = x Conc Ccr range ml/min/1.73 M 2

12 Describing variability in the clinical environment IIV = Gamma x (assay error SD polynomial) so, IIV = Gamma x ( x Conc) Gamma = 3.7

13 Amikacin Results: Parameterization as Ka, Vs, and Ks With, Median/CV% IT2B NPEM NPAG Ka 1.352/ / /21.24 Vs.2591/ / /17.38 Ks / / /15.76

14 Amikacin - Log Likelihood, Ka, Vs, and Ks, with and without gamma Without IT2B NPEM NPAG Log - Lik With Log - Lik

15 Estimates from Pop Medians, Ka, Vs, Ks parameterization, no /with IT2B NPEM NPAG r 2 =.814/ / /.880 ME =.979/ / /.169 MSE = 55.47/ / /29.70

16 Conclusions All parameter values pretty similar Less apparent variation seen with IT2B But log likelihood the least NPEM, NPAG more likely param distribs No spuriously high param correlations NPAG most likely param distributions NPEM, NPAG best suited for MM dosage Likelihoods are exact. Therefore, NPEM, NPAG are consistent, precise.

17 Now, Managing Patient Variability

18 Multiple Model (MM) Design of Doses. Think of the blue slide again. Start with the multiple support points in the NP pop model. Give a candidate dose regimen to each support point. See the multiple predictions. Compute their overall weighted squared error from the target goal. Find the regimen having least weighted squared error in target goal achievement. Most precise.

19 What s the best one dose fits all? 1. Use an NP pop model. 2. Have your covariates in the model. 3. Select a target goal. 4. Use an MM dosage design to hit the target most precisely. 5. Take this documented dose through the FDA.

20 Therefore, in addition to finding covariates, The DOSE ITSELF becomes an important tool to minimize variability about target response.

21 7/14/ Continuous IV Vanco. Regimen based on means is given to all subjects. Dangerous!!

22 Vanco, continuous IV. MM regimen. 7/14/

23 Probability [%] Percentile Distance Concentration in central compartment [ug/ml]

24 Bayes Theorem Previous data = past experience = population model. That is the Bayesian Prior (prior to now) estimates probability of an event (parameter value or distribution) based on that past experience. New data from patient. Reconcile past + new. This is the Bayesian posterior - (individual pt model). This finds the most likely compromise between the 2 data sets.

25 A mathematician named Bayes - Mooned people in various ways. He would show off his prior to any admirer, But to see his posterior You payes!

26 7.1. Monitoring the Patient and getting MM Bayesian posteriors. Pop Model Bayesian MM Posterior

27 7.2 MAP Bayesian reaches out Can reach out toward an unusual patient But the MAP point misses the true patient Held back toward the prior. Shrinkage, the compromise. Also, only 1 point. No graphic view of uncertainties. What to do?

28 7.3 Hybrid Bayesian posterior Start with MAP Bayesian. It reaches out, but not fully. Pop prior holds it back. Add new support points nearby, inside and mostly outside, to AUGMENT the pop model for the coming patient data. Then do MM Bayesian on ALL the support points.

29 Population model v, k support points

30 Estimates with MM posterior

31 Augmented hybrid pop model support points

32 Hybrid Bayesian posterior v,k, points

33 Estimates with hybrid MM posterior

34 Concentration in central compartment [ug/ml] WgtAvg Time [hours]

35 Concentration in central compartment [ug/ml] [%] 9.62 [%] 9.49 [%] 8.98 [%] WgtAvg Time [hours]

36

37 Probability [%] Percentile Distance Concentration in central compartment [ug/ml]

38 Describing and Managing Intra-individual Variability

39 Bayesian analysis for very unstable patients: interacting multiple model (IMM) fitting Limitation of all current Bayesian methods: assume only 1 set of fixed parameters to fit the data. Sequential MAP or MM Bayesian same as fitting all data at once. Relax this assumption. Let the true patient change during data analysis if more likely to do so. The Bayesian posterior can change with each new dose or serum level if more likely Hits evasive targets better. IMM.

40 MAP,MM IMM Errors in tracking serum conc: Sequential MAP, MM, and IMM Bayesian posteriors

41 C o n c e n t r a t i o n i n c e n t r a l c o m p a r t m MM Bayesian (Alison Thomson et al) W g t A v g T i m e [ h o u rs ]

42 C o n c e n t r a t i o n i n c e n t r a l c o m p a r t m e n t [ u g / m L ] Sequential IMM Bayesian (Alison Thomson et al) W g t A v g T i m e [ h o u rs ]

43 Summary of Bayesian fitting MAP - Only 1 point but reaches out somewhat. MM multiple points richer. Each point now has a Bayesian posterior probability. Hybrid best features of both. Still richer in relevant support points. But still has fixed parameter values. IMM- Changing parameter values if more likely.

44 Improving the Description and Reporting of Lab Assay Errors Using CV% is suboptimal. As measurement gets lower, CV% gets greater, think must censor low lab results. THIS IS AN ILLUSION! There is NO NEED to censor low data, or to have any LOQ!

45 Instead, Describe Assay Errors by Fisher Info: Fisher Info = 1/Variance of a data point. Need to estimate the SD of every TDM serum level that goes through the lab assay system. Variance = SD 2 Fisher info = 1/Variance = Weight. Assay Error Polynomial (AEP): SD = A 0 C 0 + A 1 C 1 + A 2 C 2 + A 3 C 3 Store it in the software.

46 SD CV% CV% SD Concentration (ug/ml) 5

47 Assay CV% versus Fisher Information Assume, for example, 10% assay CV If conc = 10, SD = 1, var = 1, weight = 1 If conc = 20, SD = 2, var = 4, weight = ¼ (aha!! That s the difference from CV%!) So a % error (the assay CV) is NOT the optmal measure of the error! Big limitation!! As conc approaches zero, CV% approaches infinity! Big limitation! Think must censor data! But assay SD, var, weight always finite. Fisher info is a better measure of assay error. Big advantage!!! NO LOQ! Big advantage! Everyone else uses Fisher info. Only the lab guys don t.

48 How about HIV, etc, assays? Drive the result to ZERO and document it! Never settle for <50 copies, etc! Same for HCV, Philadelphia chromosome, etc.

49 How get assay error polynomial? 1. Get samples a blank, a low one, a middle one, a high one, and the highest one, over the assay working range. 2. Divide each sample into at least 5 aliquots. 3. Get mean and SD of each sample. 4. Fit a polynomial to the relationship between assay mean and SD. 5. SD = A 0 C 0 + A 1 C 1 + A 2 C 2 + A 3 C 3 6. Then have good error estimate for each single result, to give good weight to data. 7. Store polynomial in the software

50 How about residual analysis? Don t ask if the stuff is there or not, and set a socially acceptable number of SD s above the blank. There are many policies for handling censored data. None is better that the measured result itself. The measurement itself is the best estimator of the true value.