Covariate Models¶

Comprehensive guide for incorporating patient characteristics into population PK/PD models.

Overview¶

Covariate models explain part of the inter-individual variability by relating parameters to measurable patient characteristics.

using NeoPKPD

# Allometric scaling: CL and V based on weight
covariate_model = CovariateModel([
    CovariateEffect(:CL, :WT, 70.0, PowerCovariate(), 0.75),
    CovariateEffect(:V, :WT, 70.0, PowerCovariate(), 1.0)
])

Mathematical Foundation¶

General Covariate Model¶

Parameters are adjusted based on covariate values:

\[\theta_i = \theta_{pop} \cdot f(cov_i, \beta)\]

Where: - \(\theta_i\) = Individual parameter - \(\theta_{pop}\) = Population typical value - \(f(cov_i, \beta)\) = Covariate function - \(\beta\) = Covariate coefficient

Order of Application¶

Covariates first: Adjust typical value for covariates
IIV second: Apply random effects to covariate-adjusted value
IOV third: Apply occasion-specific effects

\[\theta_{ij} = \theta_{pop} \cdot f(cov_i) \cdot e^{\eta_i + \kappa_{ij}}\]

Covariate Effect Types¶

Power Model¶

Most common for body size effects:

\[\theta_i = \theta_{pop} \cdot \left(\frac{cov_i}{ref}\right)^{\beta}\]

# Allometric scaling
power_effect = CovariateEffect(
    :CL,                    # Target parameter
    :WT,                    # Covariate name
    70.0,                   # Reference value
    PowerCovariate(),       # Effect type
    0.75                    # Exponent (β)
)

# Common allometric exponents:
# Clearance: 0.75 (3/4 power)
# Volume: 1.0 (proportional to body size)
# Half-life: 0.25 (1/4 power)

Linear Model¶

For effects proportional to deviation from reference:

\[\theta_i = \theta_{pop} \cdot (1 + \beta \cdot (cov_i - ref))\]

# Age effect on clearance
linear_effect = CovariateEffect(
    :CL,
    :AGE,
    45.0,                   # Reference age
    LinearCovariate(),
    -0.01                   # -1% per year above reference
)

# For a 65-year-old:
# CL = CL_pop * (1 + (-0.01) * (65 - 45))
# CL = CL_pop * (1 - 0.20) = 0.80 * CL_pop

Exponential Model¶

For multiplicative effects:

\[\theta_i = \theta_{pop} \cdot e^{\beta \cdot (cov_i - ref)}\]

# Renal function effect
exp_effect = CovariateEffect(
    :CL,
    :CRCL,                  # Creatinine clearance
    100.0,                  # Reference (normal)
    ExpCovariate(),
    0.005                   # Effect coefficient
)

# For CRCL = 50 mL/min:
# CL = CL_pop * exp(0.005 * (50 - 100))
# CL = CL_pop * exp(-0.25) = 0.78 * CL_pop

CovariateEffect Structure¶

Class Definition¶

struct CovariateEffect{K<:CovariateKind}
    param::Symbol              # Target parameter (:CL, :V, etc.)
    covariate::Symbol          # Covariate name (:WT, :AGE, etc.)
    ref::Float64               # Reference value
    kind::K                    # PowerCovariate, LinearCovariate, ExpCovariate
    beta::Float64              # Effect coefficient
end

Creating Effects¶

# Power effect
effect1 = CovariateEffect(:CL, :WT, 70.0, PowerCovariate(), 0.75)

# Linear effect
effect2 = CovariateEffect(:CL, :AGE, 45.0, LinearCovariate(), -0.008)

# Exponential effect
effect3 = CovariateEffect(:CLR, :CRCL, 100.0, ExpCovariate(), 0.007)