Insulin Secretion and Hepatic Extraction during Euglycemic Clamp Study: Modelling of Insulin and C-peptide data

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1 Insulin Secretion and Hepatic Extraction during Euglycemic Clamp Study: Modelling of Insulin and C-peptide data Chantaratsamon Dansirikul Mats O Karlsson Division of Pharmacokinetics and Drug Therapy Department of Pharmaceutical Biosciences Uppsala University

2 Goal & Aim Goal: To develop an integrated glucose-insulin model GIR INSULIN EFFECT GLUCOSE Glu-P KIE KI Ins-E Ins-C KA Ins abs. cpt ktr K K KIE Ins depot. cpt (Q) + KIE Glu-C KGI Ins-E KIE exogenous Insulin KG (-HE)*R liver - KGE - R Glu-E + β cell C-peptide KGE KGE Insulin production Glu-E - C-peptide glucose production KGE Aim: to characterize endogenous insulin secretion profile and to estimate hepatic extraction of insulin

3 Insulin Secretion Introduction Insulin Secretion & C-peptide Secretion: basal & prandial Direct assessment of insulin secretion from blood concentration is not so easy! ~50% (40-85%) -3 is lost during single pass through liver C-peptide Co-secreated with insulin from beta-cell on an equimolar basis A negligible amount is lost during single pass through the liver 4 A measure of pre-hepatic insulin secretion. Cobelli C, et al. Diabetes 37: 3-3 (88). Tura A, et al. Am J Physiol Endocrinol Metab 8: E-74 (00) 3. Meier JJ, et al. Diabetes 54: 4-5 (005) 4. Polonsky K, et al. J Clin Invest 7:4-3 (83) 3

4 Data 4-hour Euglycemic clamp study C-peptide & Insulin Data 5 healthy volunteers 3 samples/subject C-peptide (pmol/l) QL=33 pmol/l none < QL QL=0 pmol/l 3% < QL

5 Methods Modelling NONMEM VI Log-transformed data Estimation method First Order Conditional Estimation (FOCE) method Laplacian method (handling of data below quantification limit (BQL)) 5

6 Methods Model & Modelling Steps C-peptide data: Population disposition parameters were fixed Insulin pre-hepatic secretion (R) was characterised using a flexible staircase input model β-cell liver R CP-C KCP CP-P Sequential approach C-peptide & Insulin data: Population disposition parameters of insulin were fixed 3 Pre-hepatic secretion (R) estimated from C-peptide data was used Hepatic extraction (HE) of insulin Van Cauter E, et al. Diabetes 4: () ; Lindberg-freijs A et al. Biopharmaceutics & Drug Disposition 5: 75-8 (4); 3 Silber H, et al. J Clin Pharmacol (in press) Ins KI (-HE)*R β-cell liver R CP-C KCP CP-P

7 Step Results C-peptide secretion (Pre-hepatic secretion of Insulin) describe data simulate new data DV IPRE PRED Visual Predictive Check e.g. 0% PI Observations/Individual predictions/population predictions ID: ID: ID:3 ID: ID:7 ID:8 ID:4 ID: ID:0 ID: ID: ID:3 ID: ID:5 ID: Time (min) Numerical Predictive Check e.g. obtained based on 000 simulated datasets %Observation (5%CI) Expectation above simulated median 4.7 (8.-7.8) 50 below simulated median 50.3 (8.-7.8) 50 above simulated 0%PI 4. (0-.) 5 below simulated 0%PI 7. (0-5.4) 5 above simulated 50%PI. (8.-44.) 5 below simulated 50%PI 3. (8.-45.) 5 7

8 Issue 3% of Insulin data are BQL Step QL = 0 pmol/l (horizontal line) Replacement BQL data with QL/

9 Method How to handle BQL? Step Omission BQL data Replacement observation QL/ for all BQL data QL/ for the first BQL data, discard the rest Replacing with zero Likelihood approach: maximizing likelihood... For all data taken into account likelihood of a BQL observation being below QL e.g. F_FLAG functionality in NONMEM VI For data above QL conditional on the likelihood of being above QL e.g. YLO functionality in NONMEM VI

10 Results Hepatic Extraction (HE) of Insulin Step Slightly different parameter estimates Method HE P-RV Typical 5%CI Typical 5%CI. Omission ( ) 0.3 ( ). QL/ 0.8 ( ) ( ) 3. F_FLAG 0.5 ( ) 0.75 ( ) HE= hepatic extraction, P-RV = proportional residual variablity (on untransformed scale), 5%CI = bootstrap 5% confidence interval (000 bootstrap samples) Neither the inclusion of additive residual error (fixed or estimated) nor ETA on EPS improved OFV value for each method 0

11 QL/ or F_FLAG, which method should I go for? Step Criteria Relevance for comparison QL/ Results F_FLAG Objective function value (OFV) no inapplicable inapplicable Goodness of fit plots (GOF) limited Model estimation stability yes Different initial estimates stable stable Bootstrapping 74% Cov step success 7% Cov step success Bias & Imprecision yes ME < % ME < % (Simulation & re-estimation ) RMSE < 0% RMSE < 0% Numercial Predictive Check yes (slightly better) Run time yes < 0 min < 0 min 00 datasets was simulated using final estimates from each method. Parameters were then re-estimated. Mean error (ME) and root mean squared error (RMSE) were computed and presented as a percentage of the true value.

12 Results Numerical Predictive Check Step % observation above 0% and 50% prediction interval (PI) % observations above expectation QL/ The 5% confidence interval (CI) is obtained based on 000 simulated datasets F_FLAG observed 5%CI observed 5%CI 0%PI %PI % BQL observation simulated from each method method %BQL observation observed 5%CI QL/ F_FLAG The 5% confidence interval (CI) is obtained based on 000 simulated datasets

13 Conclusions Endogenous insulin secretion profile was well characterized using a flexible staircase input model In the presence of BQL data, F_FLAG method was chosen Theoretically appealing Slightly better with numerical predictive check 3

14 Discussion Issue: I Selection among different methods of handling BQL Original Question How to select which method to be used to handle BQL when the OFV (and GOF) can not be used? Approach Model estimation stability Bias & imprecision (simulation & re-estimation) Numerical Predictive Check Run time What else can be considered? 4

15 Discussion Issue: II Flexible staircase input model & Endogenous secretion Flexible Staircase Input Model Secretion rate is the same within a time interval Changes are characterised using staircase function Secretion at baseline and fraction of changes are estimated Secretion Rate (pmol/min) ID C-peptide (pmol/l) ID ID Any comments? 5