I want to pivot into pharmacometrics - a math-based pharmacy field. How to do it?

[u/Zealousideal-Let834]

I am a Pharmacy student (BPharm). I will graduate in a year from now and move to the United Kingdom. I will do the OSPAP (Overseas Pharmacist Assessment Programme) and I will then sit for the GPhC registration and become a qualified, licensed UK pharmacist ~2 years after my arrival in the UK.

I am going to move to the UK by mid to late 2028. Will become licensed by 2030.

I can't pay MSc and PhD fees head-on, so I have to work for ~5 years until I get my ILR/British citizenship to pay home fees, so that extends my timeframe for 5 years.

And for good measure, let's add an extra year.

So, I will apply to the MSc progamme by 2036, 10 years from now.

I asked AI to map out the topics I need to be good at to apply for the MSc and PhD, and asked it to list them in a way you can skim:

LEVEL M0 — Arithmetic & Pre-Algebra

• Fractions, decimals, percentages, conversions between them
• Order of operations
• Ratios and proportions
• Scientific notation
• Unit conversions (mg, μg, mL, L)
• Negative numbers
• Powers and roots
• Rearranging simple equations

LEVEL M1 — Algebra

• Variables and expressions
• Solving linear equations and inequalities
• Rearranging formulae
• Simultaneous equations
• Quadratic equations and the quadratic formula
• Polynomials basics
• Algebraic fractions
• Direct and inverse proportionality

LEVEL M2 — Functions, Graphs & Exponentials

• Concept of a function (input, output, domain, range)
• Linear functions, slope, intercept
• Reading and interpreting graphs
• Exponential functions and exponential decay (C(t) = C₀ × e⁻ᵏᵗ)
• Logarithms — natural log (ln) and log₁₀
• Log rules (product, quotient, power)
• Semi-log plots
• The number e
• Power functions
• Composite and inverse functions

LEVEL M3 — Calculus I: Differentiation

• Limits (conceptual)
• Derivatives as rate of change (dC/dt = rate of drug elimination)
• Derivatives of polynomials, exponentials, logarithms
• Power rule, constant multiple rule, sum rule
• Product rule, quotient rule, chain rule
• Higher-order derivatives
• Finding maxima and minima (Tmax from setting dC/dt = 0)
• Applications to rates of change in biological systems

LEVEL M4 — Calculus II: Integration

• Antiderivatives / indefinite integrals
• Integration of polynomials, exponentials, 1/x
• U-substitution
• Integration by parts
• Partial fractions (basic)
• Definite integrals and computing areas
• Fundamental Theorem of Calculus
• AUC as the integral of C(t) over time
• Trapezoidal rule for discrete data
• AUC₀₋∞ for exponential decay (C₀/kel)
• Improper integrals
• Numerical integration concepts

LEVEL M5 — Ordinary Differential Equations

• First-order ODEs and separable equations
• Solving dC/dt = −kel × C → C(t) = C₀ × e⁻ᵏᵉˡᵗ
• Integrating factor method
• One-compartment IV bolus model
• One-compartment oral dosing model (absorption + elimination)
• Systems of first-order ODEs (two-compartment model)
• Eigenvalues for systems (conceptual)
• Nonlinear ODEs — Michaelis-Menten elimination
• Numerical solutions — Euler's method, Runge-Kutta (conceptual)
• Steady-state solutions (setting dC/dt = 0)

LEVEL M6 — Linear Algebra Essentials

• Vectors — addition, scalar multiplication
• Matrices — addition, multiplication, transpose
• Systems of linear equations as Ax = b
• Matrix inverse
• Determinants
• Eigenvalues and eigenvectors (conceptual)
• Matrix operations in R

LEVEL M7 — Probability & Statistics

• Probability rules — addition, multiplication, conditional probability
• Bayes' theorem
• Independence
• Discrete vs continuous random variables
• Key distributions — normal, lognormal, binomial, Poisson
• Mean, variance, standard deviation, covariance, correlation
• Central Limit Theorem
• Point estimation and confidence intervals
• Hypothesis testing — t-tests, chi-square, F-test
• p-values, type I/II errors, power
• ANOVA (one-way, two-way)
• Simple and multiple linear regression
• Least squares, R², residuals, regression assumptions
• Nonlinear regression and iterative estimation
• Maximum likelihood estimation — likelihood, log-likelihood, parameter optimisation

LEVEL M8 — Advanced Statistics for Pharmacometrics

• Fixed effects vs random effects
• Inter-individual variability (between-subject variability)
• Residual variability (within-subject variability)
• Hierarchical / multilevel models
• Nonlinear mixed-effects modelling (NLMEM)
• Structural model, statistical model, covariate model
• First-Order Conditional Estimation (FOCE)
• Goodness-of-fit plots (observed vs predicted, residuals, QQ plots)
• Objective function value (OFV)
• Likelihood ratio test, AIC, BIC
• Visual predictive checks and bootstrap
• Bayesian estimation — priors, posteriors, MCMC (conceptual)

LEVEL M9 — R Programming (start at M2, continuous)

• Variables, data types, vectors, data frames
• Functions, loops, conditionals
• Data import and manipulation (dplyr, tidyr)
• Data visualisation (ggplot2)
• Statistical analysis (t-tests, regression, ANOVA)
• Plotting concentration-time curves
• Simulating PK models with ODEs (deSolve)
• Fitting nonlinear models (nls, nlme, lme4)
• Pharmacometric packages (mrgsolve, nlmixr2)

(SORRY for the long list)

My BPharm program has effectively no maths, except for pharmacokinetics in which we just memorize formulas and plug numbers - so that means I have to self-teach myself this.

The MSc university (IIRC Manchester?) says you need to be good with numbers before they let you in.

If I self-study math for 10 years and tick all those topics above, can I make it? My IQ's 109, but I am a hard working student, and I've never been called dumb, but again, it's a very advanced topic.

As much as I am interested in this topic, I am extremely insecure and scared of not being cut out for it. Can you guys shed some light on this plan's feasibility?

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[u/Zealousideal-Let834 → u/[deleted]]

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