Individual Parameters

The [individual_parameters] block defines how population parameters (theta), random effects (eta), and covariates combine to produce individual PK parameters.

Syntax

PARAM = expression

Each line assigns a PK parameter using an arithmetic expression that can reference:

Theta parameters — names defined in [parameters] (e.g. TVCL, TVV)
Eta random effects — names defined as omega parameters (e.g. ETA_CL, ETA_V)
Covariates — column names from the data file (e.g. WT, CRCL)
Constants — numeric literals (e.g. 70, 0.75)

Supported operators and functions

Operator / Function	Example
`+`, `-`, `*`, `/`	`TVCL * WT / 70`
`^` (power)	`(WT/70)^0.75`
`exp()`	`exp(ETA_CL)`
`log()`, `ln()`	`log(TVCL)`
`sqrt()`	`sqrt(WT)`
`abs()`	`abs(ETA_CL)`
`inv_logit()`, `logit()`	`inv_logit(logit(THETA_F) + ETA_F)`
Parentheses	`TVCL * (WT/70)^0.75`
Comparisons (in `if` conditions)	`WT > 70`, `SEX == 1`
Logical (in `if` conditions)	`&&`, `\\|\\|`, `!`
Inline conditional	`if (SEX == 1) TVCL * 1.5 else TVCL`

Conditional logic (`if` / `else`)

Two forms are supported and may be combined freely.

Block form

[individual_parameters]
  if (WT > 70) {
    CL = TVCL * (WT / 70)^0.75 * exp(ETA_CL)
  } else if (SEX == 1) {
    CL = TVCL * 1.2 * exp(ETA_CL)
  } else {
    CL = TVCL * exp(ETA_CL)
  }
  V = TVV * exp(ETA_V)

Conditions support <, <=, >, >=, ==, != and logical operators (&&, ||, !). Note: use == only for integer-coded covariates — exact float comparison is unreliable for continuous values.

Inline (ternary) form

[individual_parameters]
  CL = if (SEX == 1) TVCL * 1.5 else TVCL
  V  = TVV  * exp(ETA_V)

Both then and else branches are required in the inline form.

Interaction with mu-referencing

When a parameter is assigned inside an if block, mu-reference detection is skipped for that parameter (the ETA→THETA link is no longer unconditional). Unconditional assignments continue to be detected normally.

To keep mu-referencing on a covariate-adjusted parameter, bury the conditional inside the covariate term:

CL = TVCL * (if (WT > 70) (WT/70)^0.75 else 1.0) * exp(ETA_CL)

Common parameterisations

Exponential (log-normal) random effects

The standard approach for PK parameters that must be positive:

[individual_parameters]
  CL = TVCL * exp(ETA_CL)
  V  = TVV  * exp(ETA_V)
  KA = TVKA * exp(ETA_KA)

Allometric scaling with covariates

[individual_parameters]
  CL = TVCL * (WT/70)^0.75 * exp(ETA_CL)
  V  = TVV  * (WT/70)^1.0  * exp(ETA_V)

Estimated covariate effects

Use additional theta parameters for covariate exponents:

[parameters]
  theta TVCL(0.134, 0.001, 10.0)
  theta THETA_WT(0.75, 0.01, 2.0)
  theta THETA_CRCL(0.5, 0.01, 2.0)

[individual_parameters]
  CL = TVCL * (WT/70)^THETA_WT * (CRCL/100)^THETA_CRCL * exp(ETA_CL)

Logit-normal bioavailability

Use inv_logit(logit(THETA_F) + ETA_F) to constrain bioavailability to (0, 1). The starting value for THETA_F is on the (0, 1) scale — whatever fraction you specify is what the optimiser uses as the typical F:

[parameters]
  theta THETA_F(0.70, 0.001, 0.999)  # typical bioavailability = 70%
  omega ETA_F ~ 0.10                 # BSV on the logit scale

[individual_parameters]
  F = inv_logit(logit(THETA_F) + ETA_F)

When ETA_F = 0, F_i = THETA_F exactly (logit and inv_logit cancel).
The estimated THETA_F in output is directly interpretable as typical F.
omega ETA_F is variance on the logit scale — not the variance of F itself.

The alternative inv_logit(THETA_F + ETA_F) is also supported, where THETA_F is on the logit scale (e.g. logit(0.70) ≈ 0.847).

Additive random effects

For parameters where the subject-level deviation is additive (e.g. lag time in hours):

TLAG = TVTLAG + ETA_TLAG

ETA_TLAG follows N(0, ω_TLAG), so individual lag times are normally distributed around TVTLAG.

Automatic mu-referencing

When a line matches one of the detected patterns:

PARAM = THETA * exp(ETA)                      # multiplicative / log-normal
PARAM = THETA * <anything> * exp(ETA)         # with covariate terms
PARAM = exp(log(THETA) + ETA)                 # canonical MU form
PARAM = THETA + ETA                           # additive

ferx records the ETA→THETA mapping and re-centres the inner-loop ETA search at each outer iteration — reproducing NONMEM / nlmixr2 mu-referencing without requiring an explicit MU_i line.

Patterns not detected (falls back to eta = 0 start):

Two or more free thetas in the product (TVCL * TVSCALE * exp(ETA_CL)) — ambiguous anchor
Compound eta expressions inside exp (exp(ETA_CL + ETA_OCC))

Set mu_referencing = false in [fit_options] to disable detection entirely. See Fit Options.

Covariate detection

Any uppercase identifier in the expression that does not match a theta name or eta name is automatically treated as a covariate. The covariate value is read from the corresponding column in the data file (case-insensitive match).

For example, in CL = TVCL * (WT/70)^0.75 * exp(ETA_CL):

TVCL — theta parameter
ETA_CL — omega parameter
WT — covariate column (must exist in the CSV)

PK parameter names

The left-hand side of each assignment must map to a recognised PK slot:

Name	PK parameter
`CL`	Clearance
`V` or `V1`	Volume of distribution (central)
`Q`	Intercompartmental clearance
`V2`	Peripheral volume 1
`Q3`	Intercompartmental clearance 2 (3-cpt)
`V3`	Peripheral volume 2 (3-cpt)
`KA`	Absorption rate constant
`F`	Bioavailability (default 1.0 if omitted)

For ODE models, parameter names are user-defined and passed as a flat vector to the ODE right-hand side.