PHARM/PCS V5 · Procedures
PHARM/PCS Procedures: All 48 Calculations
The procedures are grouped the same way as in the app. Choose a procedure to see what it computes, what you enter, and how to read the results.
Dosage and Statistics
Procedures 1 to 7
- 1Dosage and Concentration: Drug Stock SolutionsWork out how much stock solution to draw for a dosing solution of a given molarity and volume, and how much sodium chloride makes it isotonic.
- 2Mean, Standard Deviation and Confidence LimitsSummarize a set of replicate measurements: the mean, its scatter, and how tightly the population mean is pinned down, at a 90%, 95%, or 99% confidence level.
- 3Linear Regression IFit a least-squares straight line to paired x and y data and get the slope and intercept, or predict y at any x.
- 4Linear Regression II: Lines Through OriginFit a straight line forced through zero, for data where theory says zero input must give zero response.
- 5Analysis of the Regression LineFit a straight line and report everything needed to defend it: slope, both intercepts, the correlation coefficient, standard errors, and confidence limits.
- 6Parallel Lines I: Test for ParallelismTest whether two or more regression lines share a slope, the check that must pass before any relative potency calculation.
- 7Parallel Lines II: Construction of Parallel LinesCombine two parallel lines into one best common slope, weighted by how well each line is determined, and redraw both lines with it.
Dose-Response and Potency
Procedures 8 to 11
- 8Graded Dose-ResponseFit a graded dose-response line and get the A50, the dose giving half the maximal effect, with confidence limits.
- 9Quantal Dose-Response: ProbitsTurn percent-responding data into probits and read the ED50, ED16, and ED84 straight from a fitted line.
- 10Relative Potency IFind how many times more potent a test drug is than a standard, from a 2 and 2 assay or from full dose-response lines.
- 11Relative Potency II: Statistical AnalysisPut confidence limits on a potency ratio, the step that makes the ratio defensible in a report or a publication.
Receptor Pharmacology
Procedures 12 to 17
- 12Dissociation Constant I: Agonists (Furchgott Method)Estimate a full agonist's dissociation constant KA from dose-response curves measured before and after partial irreversible receptor blockade.
- 13Dissociation Constant II: Partial AgonistsEstimate a partial agonist's dissociation constant Kp by comparing its equieffective concentrations with those of a full agonist.
- 14Dissociation Constant III: Perturbation MethodsGet the forward and reverse rate constants of a drug-receptor reaction, and the dissociation constant K, from relaxation times measured after a rapid perturbation.
- 15pA2 Analysis I: Schild PlotEstimate a competitive antagonist's pA2 from dose ratios at several antagonist concentrations, with the slope test that checks the competitive model.
- 16pA2 Analysis II: Time-Dependent MethodEstimate pA2 from a single antagonist concentration by following the agonist dose ratio as the antagonist washes out, and get its half-life as well.
- 17pA2 Analysis III: Constrained PlotEstimate pA2 with the Schild slope fixed at −1, the tighter estimate to use once simple competitive antagonism is confirmed.
Enzyme Kinetics
Procedures 18 to 20
- 18Enzyme Kinetics I: Michaelis-Menten EquationEstimate Vmax and KM from initial-velocity data across substrate concentrations, using the Lineweaver-Burk double-reciprocal fit.
- 19Enzyme Kinetics II: Competitive InhibitionCompare an inhibited and an uninhibited Lineweaver-Burk line to get KI for an inhibitor that competes with substrate at the active site.
- 20Enzyme Kinetics III: Noncompetitive InhibitionGet KI for an inhibitor that lowers Vmax without changing the enzyme's apparent affinity for substrate.
Drug Decay and Binding
Procedures 21 to 25
- 21First-Order Drug DecayGet the first-order rate constant k for a decomposing drug from concentration-time data, and with it a half-life or shelf-life.
- 22Scatchard PlotGet the dissociation constant K and the total binding-site concentration from equilibrium binding data, with honest asymmetric limits on K.
- 23Henderson-Hasselbalch EquationFind the ratio of ionized to unionized drug at a given pH, the starting point for questions about absorption and partitioning.
- 24Exponential Growth and DecayFit a single exponential to time-course data and get the rate constant, the coefficient, and the half-life, each with confidence limits.
- 25Area Under a Curve: Trapezoidal and Simpson's RulesCompute the area under a curve from tabulated points by the trapezoidal rule, and by Simpson's rule when the spacing allows it.
Pharmacokinetics
Procedures 26 to 32
- 26Pharmacokinetics I: Constant Infusion, First-Order EliminationWork out the steady-state concentration of a drug given by constant IV infusion, or the infusion rate needed to reach a target level.
- 27Pharmacokinetics II: Multiple Intravenous InjectionsFor repeated IV doses at a fixed interval, find the steady-state peak, trough, and mean concentrations, and how many doses it takes to get there.
- 28Pharmacokinetics III: Volume of DistributionEstimate the apparent volume of distribution from an IV bolus concentration-time profile, by back-extrapolating the elimination phase.
- 29Pharmacokinetics IV: Plasma Concentration-Time DataFrom an oral dose's plasma profile, get the absorption and elimination rate constants, the peak time, AUC, and F/Vd, by the method of residuals.
- 30Pharmacokinetics V: Renal ClearanceCompute renal clearance two ways: from total urinary excretion over AUC, and from excretion rate against plasma concentration.
- 31Pharmacokinetics VI: Renal Excretion Data Following IV AdministrationSeparate total elimination from renal excretion after an IV dose, using urine collections alone.
- 32Pharmacokinetics VII: Multiple Dosing from Absorptive SiteFor repeated oral doses, find the steady-state mean and peak concentrations and the time to reach 95% of steady state.
ANOVA and Comparisons
Procedures 33 to 38, 44
- 33Analysis of Variance I: One-WayTest whether three or more group means differ in one omnibus test, rather than a string of t-tests, with groups of any size.
- 34Analysis of Variance II: Two-Way, Single ObservationTest a treatment effect and a blocking effect together, with one observation for each combination, so the blocking absorbs nuisance variation.
- 35Analysis of Variance III: Two-Way, with ReplicationTest two factors and their interaction, with several observations in every combination, to see whether the factors act independently.
- 36Newman-Keuls TestAfter a significant ANOVA, find which pairs of group means differ, using the studentized range, with groups of any size.
- 37Duncan Multiple Range TestAfter a significant ANOVA with equal group sizes, compare every pair of means using Duncan's graduated protection levels.
- 38Least Significant Difference TestAfter a significant ANOVA, compute a single least significant difference and see which pairs of means exceed it.
- 44Dunnett's Test (Comparison with a Control)Compare each treatment group with a single control after ANOVA, the more powerful choice when control comparisons are all you need.
Pairwise and Nonparametric
Procedures 39 to 43, 45
- 39t-Test I: Grouped DataTest whether two independent group means differ, with Student's t and a pooled variance, even when the groups differ in size.
- 40t-Test II: Paired DataTest whether paired measurements differ, such as before and after on the same subject, with each subject serving as its own control.
- 41Ratio of MeansPut honest confidence limits on the ratio of two means with Fieller's theorem, for fold-changes, relative bioavailability, or potency.
- 42Chi-Square TestTest whether two categorical variables are associated, from a contingency table of counts, with Yates' correction applied automatically to 2×2 tables.
- 43Proportions: Confidence LimitsPut exact confidence limits on a single proportion, such as a response rate, that stay within 0 and 1 even for small samples.
- 45Mann-Whitney U-TestCompare two independent groups without assuming normal data, by ranking every observation, when outliers or skew rule out a t-test.
Special Methods
Procedures 46 to 48
- 46Litchfield and Wilcoxon I: Confidence Limits of ED50Estimate an ED50 or LD50 with 95% confidence limits from all-or-none dose-response data, using every dose, including the 0% and 100% groups.
- 47Litchfield and Wilcoxon IIGo beyond the ED50: get ED16 and ED84 with confidence limits, and compare two drugs with a potency ratio and its limits.
- 48Differential EquationsSolve a first-order differential equation numerically by the fourth-order Runge-Kutta method, for kinetic models that have no closed-form answer.
Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.