MIPK (Model Independent Pharmaco-Kinetics)

Transcription

1 MIPK (Model Independent Pharmaco-Kinetics) Martin Micbael SAS Institute Mancbester, UK Introduction MlPK is the working name of a SAS/AF application, currently under development in SAS Institute, designed to perform model-independent (non-compartmental) pharmacokinetic analysis of plasmal serum concentration data and urine concentration data from single-dose and multiple-dose pharmacokinetic studies. The application is a semi-batch program that runs against data from a complete pharmacokinetic study rather than individual concentration-time profiles. However the latter can be made the unit of analysis. Functional Components The functional components of the application are as follows: 1. Data Capture Four options are currently implemented: a b c d direct data entry, retrieve data from a SAS dataset, retrieve data from an external file (via SAS/ASSIST-), retrieve data from a Siphar DB file. In the latter three cases, the original data are preserved. A local copy is made by the application. 2. Data Maintenance Data available to the application can be edited. All edits are audit-trailed. Individual concentration-time pairs can be flagged as outliers (to be excluded from analysis). In addition, detection and/or quantification limits can be set and edited for a study. 577

2 3. Pharmacokinetic Analysis The following plasma/serum parameters are currently calculated for each profile in the study: a Cmax Taken as the maximum observed concentration b Tmax Taken as the sampling time of the maximum observed concentration c Ke The terminal elimination rate, calculated as the absolute value of the slope of the regression of the log-concentration on time through the terminal section of the concentration-time profile. The start time of the regression can be determined automatically by the program (using a combined R-squared and empirical runs test criterion), set as a constant for all profiles in the study, set as a fixed number of sampling times for all profiles in the study or set individually for each profile or a subset of profiles. The regression can only be performed on concentrations measured after Tmax and only then if there are at least three measurable concentrations at or after Tmax. d The terminal half-life, calculated as the ratio of the natural log of 2 to Ke. e AUC(O-Tn) The Area Under the Curve from time 0 to Tn, the time of the last measurable concentration. Four methods of calculation are available: i ii Linear-trapezoidal over the whole curve, Log-trapezoidal over the whole curve, iii Linear-trapezoidal up to the start of regression, log-trapezoidal thereafter, 578

3 IV Linear-trapezoidal if the concentration at a given time is greater than or equal to the concentration measured at the previous sampling time, log-trapezoidal otherwise. f AUC (O-infinity) Calculated as the AUC (O-Tn) plus AUC (Tn-infinity). The latter portion is calculated, byintegration, as the ratio of the last measurable concentration, Cn, to the value of Ke. g 100 x (AUC (Tn-infinity) I AUC (O-inrmity» Extrapolated portion of the AUC as a percentage of the AUC (O-infinity). h AUMC (0-Tn) Area under the first moment curve calculated using the linear trapezoidal rule. i AUMC (O-infmity) Calculated as AUMC (O-Tn) plus AUMC (Tn-infinity). The latter is calculated by integration. j 100 x (AUMC (Tn-infinity) I AUMC (O-infmity) Extrapolated portion of the AUMC as a percentage of the AUMC (O-infinity). k MRT Mean Residence Time calculated as the ratio of AUMC (O-infinity) to AUC (O-infinity). If the latter has been calculated by a method other than the linear trapezoidal rule, it is re-ca1culated using this method in order to calculate MRT. I CLp Total plasma clearance calculated as the ratio of dose to the AUC (O-infinity). m Varea The volume of distribution calculated as the ratio of clearance to the elimination rate. n Vss The volume of distribution at steady state, calcu1ated as the product of MRT and clearance. The two volumes are only calculated for intravenous drug administration. 579

4 I!,"! 1 i f. ;, " ;' : }, 1: j :: c, } l v. t: :,,',., il- r: ir t:, i: -i: 4. All kinetic parameters are stored in a permanent SAS dataset. Incremental AUCs and AUMCs. at each sampling time are calculated and stored. In addition, at each sampling time used in the regression, the expected concentration and percentage deviation of the observed from the expected concentration is calculated. NB: Handling of Non-Detected or Trace Concentrations Concentrations below the detection and/or quantification limits (ND Values) at Time 0 are treated as true zeroes. Single ND values 'sandwiched' between measurable concentrations and ND values at the end of the profile are ignored. Two ND values in succession terminate the measurable portion of the profile for the purposes of analysis. The pharmacokinetic analysis of urinary concentration data is not currently implemented. It is planned to include the calculation of the elimination rate and elimination half-life and total urinary elimination of the drug. Also, where both plasma and urinary data are available for a study, renal clearance will be calculated. Graphics Five options are currently available: a b c Semi-log plot of concentration against time for each profile. The regression line, non-detected and trace values and outliers are displayed. Semi-log plot of concentration against time for each subject/volunteer in the study, showing separate lines for each profile for the subject, ' Linear plot of concentration against time for each subject/volunteer in the study, showing separate lines for each profile for the subject, d Semi-log plot of concentration against time for each treatment/dose study, showing separate lines for each subject, in the e Median plot of concentration against time for each treatment/ dose in the study. Mean and geometric mean plots will also be available. 5. Listings The application includes the options to produce listings in report format of the concentration data (see Example Output 1) and of the kinetic parameters (see Example Output 2). The summary statistics that appear at the bottom of each column of data can be set by the user. 580

5 In addition, comprehensive reports of the analysis of each profile can optionally be produced (see Example Output 3 and 4). 6. Sunultaries The application includes the options to produce summary statistics of the kinetic parameters, again in report-quality format (see Example Output 5), including mean, standard deviation, standard error, geometric mean, confidence intervals for the mean and geometric mean, median, range and interquartile range. 7. Statistical Analysis It is planned to include the statistical analysis of kinetic parameters for the study, including bioequivalence tests and tests for kinetic linearity. Quality Assurance, Validation and Documentation It is planned to validate all computations within the application to regulatory standards. A set of test profiles and output willbe supplied with the application. A full set of user documentation, including detailed information on all computations, will be supplied with the application. Required Products It is currently envisaged that the application will require Base SAS, SAS/FSP, SAS/Graph and SASIStat and, optionally, SAS/Insight and SASI Assist. "ailal>ility It is planned to make the application available as a supported SAS product. At present, it is not possible to give a firm estimate of the date of the first release. The possibility of integrating the application into SAS/PH-Clinical to enable the users to fully integrate pharmacokinetic and clinical data is currently being explored. 581

6 Example Output 1,,1 j study MAINR Main Example Dataset Concentration (ng/ml)- at each Scheduled Assessment, by Treatment and Subject - j f f;' (, } i,' r!, f ii \' B!>i i: ). :1- Measurement Time (hh:mm) Subject 10 0:00 0:30 1:00 1:30 2:00 1 NO NO NO NO NO NO NO NO NO NO (n) (10) ( 11) (10) (9 ) (10) Mean NO Std oev :00 4:00 5: NO (10) (10) (10) ,- 1, t, ; l'.' Measurement Time (hh:mm) Subject 10 6:00 8:00 10:00 12:00 18:00 I * Tr Tr (n) (10) (10) (10) (10) (9) Mean Std oev :00 36:00 48:00 NO NO NO Tr Tr NO (10) (10) (10) Tr Trace (taken as 1.5 nglml in means) NO = Not Detected (taken as 0.5 nglml in means) * Outlier (excluded from Means) 582

7 Example Output 2 study : MAINR Main Example Dataset NON-COMPARTMENTAL PHARMACOKINETIC ANALYSIS Pharmacokinetic Parameters, by Treatment and Subject Subject Cmax AUC{O-inf) MRT Thalf ID (ng/ml) (ng.hr/ml) n Mean Std Dev Median

8 Example Output 3, 1 study : MAINR Main Example Dataset! NON-COMPARTMENTAL PHARMACOKINETIC ANALYSIS Number : 3 Subject : 3 Period : 1 1. DETERMINATION OF STARTING TIME OF TERMINAL REGRESSION Time n Intercept Slope (ng/ml) R-Square Half-Life F 5.48 F 5.50 F = Stopping condition met. n 4 Start Time = 6 Intercept Slope R-Squared = = = (ng/ml) EFFECT OF REMOVING EACH TIMElCONCENTRATION PAIR Time Conc'n R-Square Change (nglml) # # Half-Life (hr ) # = Concentration has 'strong' influence in regression 2. CONCENTRATION DATA Time Concentration (ng/ml) 0 NO NO NO = Not Detected (Concentration"< 1mg) 584

9 Example Output 3 (Continued) study : MAINR Main Example Dataset NON-COMPARTMENTALPHARMACOKINETIC ANALYSIS (Continued) Number : 3 Subject : 3 Period : 1 2. CONCENTRATION DATA (Continued) Time Concentration (ng/ml) 6.27 * 5.58 * 4.06 * 3.71* 12 0 outlier ND ND ND * = Included in terminal regression ND = Not Detected (Concentration < 1mg) o = Outlier 3. PHARMACOKINETIC PARAMETERS Tmax Cmax (ng/ml) Last Used Conc'n Time (Tn) Last Used Conc'n (Cn) (ng/ml) AUC(O-Tn) (ng.hr/ml) AUC(0-24hr) (ng.hr/ml) AUMC(O-Tn) (ng.hr2/ml) AUC(O-inf} (ng.hr/ml) % AUC(O-Inf} Extrapolated AUC(O-inf) (ng.hr/ml) AUMC(O-inf) (ng.hr2/ml) % AUMC(O-Inf) Extrapolated Extrap. Time 0 Conc'n (ng/ml) Ke (/hr) Thalf MRT F.CLp (ml/min) : : % % Observed Observed Observed Observed Linear + Log Trap'l Extrapolation Linear Trap'l AUC(O-Tn)+cn/Ke (Cn*100)/(Ke*AUC(0-Tn» Lin Trap'l+Cn/Ke (for MRT) AUMC(O-Tn)+(Cn*Tn)/ke+ Cn/Ke2 (100/AUMC(O-Inf)}* «Cn*Tn)/Ke+Cn/Ke2) From Regression -Slope loge2/ke AUMC(O-Inf}/AUC(O-Inf) Dose/AUC(o-inf) 585

10 Example Output 4 study : MAINR Main Example Dataset NON-COMPARTMENTAL PHARMACOKINETIC ANALYSIS Number : 3 Subject : 3 Period : 1 Time Interval Calc'n AUC % of AUC % of (t-1)-t (t-1)-t AuC(o-inf) o-t AUC (O-inf) (ng.hr/ml) (ng.hr/ml) Lin Trap Lin Trap Lin Trap Lin Trap Lin Trap Lin Trap Lin Trap Log Trap Log Trap Log Trap inf Extrap Automatic Regression Start-Time Selection. Model. concentration = * exp( Estimated Time Concentration Concentration (ng/ml) (ng/ml) 0 ND ND * * * * Outlier ND ND ND 0.12 * time) Percentage Residual (%) * ND = Included in Terminal Regression Not Detected 586

11 '"1t'"t'''L1L'''r".,.t*-, iu±'i.;e.j'i"t.. l'.f:,;k.. i i 'c. c,t!-. <.",...'>..,{:"'"'Tr,\;:"'"'<{':;..,n",',-.,:,-, ;:...: ry ":, Study MAINR Main Example Dataset NON-COMPARTMENTAL PHARMACOKINETIC ANALYSIS Pharmacokinetic Parameters, by Treatment Cmax n 10 (ng/ml) Missing 0 Mean Standard Deviation 't CI for Mean 11.35, Median Minimum-Maximum 11.95, Inter-Quartile Range 12.73, Geometric Mean % CI for Geom Mean 12.01, AUG(0-24hr) n (ng.hr/ml) Missing Mean Standard Deviation 95% CI for Mean Median Minimum-Maximum Inter-Quartile Range Geometric Mean 95% CI for Geom Mean 10 AUC(O-inf) n: 0 (ng.hr/ml) Missing: Mean: Standard Deviation: , % CI for Mean: Median: 97.83, Minimum-Maximum: , Inter-Quartile Range: Geometric Mean: , % CI for Geom Mean: , , , , 148 S -I"C o c::: "0 c::: Ul V1 00 '-l Ke n: 10 (/hr) Missing: 0 Mean: Standard Deviation: % CI for Mean: , Median: Minimum-Maximum: , Inter-Quartile Range: , 0.07l5 Geometric Mean: 't CI for Geom Mean: , Thalf n: Missing: Mean: Standard Deviation: 95% CI for Mean: Median: Minimum-Maximum: Inter-Quartile Range: Geometric Mean: 95\ CI for Geom Mean: 10 AUMC(O-inf) n: 0 (ng.hr2/m1) Missing: Mean: 1.92 Standard Deviation: 8.73, % CI for Mean: Median: 6.58, Minimum-Maximum: 9.69, Inter-Quartile Range: 9.92 Geometric Mean: 8.55, % CI for Geom Mean: , , , , 2076 MRT n 10 Missing 0 Mean Standard Deviation % CI for Mean 11.13, Median Minimum-Maximum 8.69, Inter-Quartile Range 12.23, Geometric Mean % CI for Geom Mean 10.97, 14.27