Summary of Key Principles

What are Covariates?

Covariates are individual-specific variables that explain pharmacokinetic/pharmacodynamic (PKPD) variability. They help predict fixed effects (predictable sources of variability) and reduce random effects (unpredictable variability).

Most Important Covariates:

• Weight (size)
• Race
• Sex
• Renal function
• Age (especially in pediatrics)

Covariate Classification

1. By Source:

   • Intrinsic: weight, age, sex, race, renal function, genotype
   • Extrinsic: dose, compliance, smoking status

2. By Type:

   • Continuous: weight, age, renal function, dose
   • Categorical: sex, race, genotype, smoking status

Selection Criteria (in order of importance)

1. Biological plausibility - Does it make biological sense?
2. Extrapolation plausibility - Does the model extrapolate sensibly?
3. Clinical relevance - Is the effect size clinically meaningful?
4. Statistical significance - Is it statistically significant?

Standardization Principle

Always standardize to a 70 kg adult for population parameters:

• Makes parameters comparable across studies
• Facilitates interpretation and extrapolation

Continuous Covariate Models

1. Weight Effects (Theory-Based Allometric Scaling)

Theoretical Foundation:

• Clearance (CL) scales with metabolic rate ∝ Weight^0.75
• Volume (V) scales with body size ∝ Weight^1.0

Basic Allometric Model:

POPCL = THETA(1)                    ; Population CL for 70kg person
POPV = THETA(2)                     ; Population V for 70kg person
FSIZE_CL = (WT/70)^0.75            ; Size factor for CL
FSIZE_V = (WT/70)^1.0              ; Size factor for V
GRPCL = POPCL * FSIZE_CL           ; Group CL
GRPV = POPV * FSIZE_V              ; Group V
CL = GRPCL * EXP(ETA(1))           ; Individual CL
V = GRPV * EXP(ETA(2))             ; Individual V

Numeric Example:

• THETA(1) = 10 L/h (CL for 70kg person)
• THETA(2) = 50 L (V for 70kg person)
• Patient weight = 84 kg

FSIZE_CL = (84/70)^0.75 = 1.2^0.75 = 1.129
FSIZE_V = (84/70)^1.0 = 1.2^1.0 = 1.2
GRPCL = 10 * 1.129 = 11.29 L/h
GRPV = 50 * 1.2 = 60 L

2. Renal Function Effects

Additive Model for Parallel Clearance Pathways:

CL_total = CL_non-renal + CL_renal

Implementation:

FSIZE = (WT/70)^0.75
RF = CLCR/100                       ; Normalized renal function (100 mL/min = normal)
GRPCL = (THETA(1) + THETA(2) * RF) * FSIZE

Numeric Example:

• THETA(1) = 5 L/h (non-renal clearance for 70kg)
• THETA(2) = 8 L/h (renal clearance for 70kg with normal function)
• Patient: 84 kg, CLCR = 60 mL/min

FSIZE = (84/70)^0.75 = 1.129
RF = 60/100 = 0.6
GRPCL = (5 + 8 * 0.6) * 1.129 = (5 + 4.8) * 1.129 = 11.06 L/h

3. Age Effects (Empirical Models)

Linear Model:

FAGE = 1 + THETA(3) * (AGE - 20)

Exponential Model (Preferred):

FAGE = EXP(THETA(3) * (AGE - 20))

Numeric Example:

• THETA(3) = -0.01 per year (1% decrease per year after age 20)
• Patient: 65 years old

FAGE = EXP(-0.01 * (65 - 20)) = EXP(-0.45) = 0.638

This represents a 36% decrease in clearance compared to a 20-year-old.

Categorical Covariate Models

Sex Effects

Method 1 (Basic):

IF(SEX.EQ.1) THEN        ; Male = 1
    GRPCL = THETA(1) * FSIZE
ELSE                     ; Female = 0
    GRPCL = THETA(2) * FSIZE
ENDIF

Method 2 (Preferred - Multiplicative Factor):

IF(SEX.EQ.1) THEN        ; Male
    FSEX = 1
ELSE                     ; Female
    FSEX = THETA(3)
ENDIF
GRPCL = POPCL * FSIZE * FSEX

Method 3 (Linear Factor):

FSEX = 1 + THETA(3) * SEX
GRPCL = POPCL * FSIZE * FSEX

Numeric Example:

• THETA(3) = 0.8 (females have 80% of male clearance)
• Male patient (SEX = 1): FSEX = 1.0
• Female patient (SEX = 0): FSEX = 0.8

Complete Model Example

Final Integrated Model:

; Population parameters
POPCL = THETA(1)                    ; 10 L/h for 70kg male, age 20, normal renal function
POPV = THETA(2)                     ; 50 L for 70kg

; Covariate effects
FSIZE_CL = (WT/70)^0.75
FSIZE_V = (WT/70)^1.0
RF = CLCR_STD/100                   ; Standardized CLCR
FAGE = EXP(THETA(3) * (AGE - 20))
FSEX = 1 + THETA(4) * (1 - SEX)    ; SEX: Male=1, Female=0

; Group parameters
GRPCL = POPCL * FSIZE_CL * (1 + THETA(5) * RF) * FAGE * FSEX
GRPV = POPV * FSIZE_V

; Individual parameters
CL = GRPCL * EXP(ETA(1))
V = GRPV * EXP(ETA(2))

Numeric Example:

Patient Characteristics:

• Weight: 84 kg
• Age: 65 years
• Sex: Female (0)
• CLCR_STD: 60 mL/min

Parameters:

• THETA(1) = 10 L/h
• THETA(2) = 50 L
• THETA(3) = -0.01 per year
• THETA(4) = -0.2 (20% reduction for females)
• THETA(5) = 0.5 (50% contribution of renal clearance)

Calculations:

FSIZE_CL = (84/70)^0.75 = 1.129
FSIZE_V = (84/70)^1.0 = 1.2
RF = 60/100 = 0.6
FAGE = EXP(-0.01 * (65-20)) = 0.638
FSEX = 1 + (-0.2) * (1-0) = 0.8

GRPCL = 10 * 1.129 * (1 + 0.5 * 0.6) * 0.638 * 0.8
      = 10 * 1.129 * 1.3 * 0.638 * 0.8
      = 7.51 L/h

GRPV = 50 * 1.2 = 60 L

Statistical Testing

Likelihood Ratio Test (LRT)

• Compare nested models using NONMEM Objective Function Value (OFV)
• ΔOFV > 3.84 for p < 0.05 (1 degree of freedom)
• Use forward inclusion followed by backward elimination

Model Evaluation

• Visual Predictive Check (VPC) to assess covariate importance
• Examine ETA vs covariate plots before and after inclusion
• Ensure biological plausibility of parameter estimates

Key Recommendations

1. Always include allometric scaling for weight - don't test statistically
2. Use theory-based models when available (e.g., allometry)
3. Standardize all parameters to 70 kg
4. Consider biological plausibility over statistical significance
5. Use size-standardized renal function to avoid weight confounding
6. Validate models with VPC and diagnostic plots