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Expression (CovariateModel)

Define relationship between parameters and covariates

Description

The Expression property is a character vector or cell array of character vectors, where each character vector represents the relationship between a parameter and one or more covariates. The Expression property denotes fixed effects with the prefix theta, and random effects with the prefix eta.

Each expression must be in the form:

parameterName = relationship

This example of an expression defines the relationship between a parameter (volume) and a covariate (weight), with fixed effects, but no random effects:

CovModelObj.Expression = {'volume = theta1 + theta2*weight'};

This table illustrates expression formats for some common parameter-covariate relationships.

Parameter-Covariate RelationshipExpression Format
Linear with random effectCl = theta1 + theta2*WEIGHT + eta1
Exponential without random effectCl = exp(theta_Cl + theta_Cl_WT*WEIGHT)
Exponential, WEIGHT centered by mean, has random effectCl = exp(theta1 + theta2*(WEIGHT - mean(WEIGHT)) + eta1)
Exponential, log(WEIGHT), which is equivalent to power modelCl = exp(theta1 + theta2*log(WEIGHT) + eta1)
Exponential, dependent on WEIGHT and AGE, has random effectCl = exp(theta1 + theta2*WEIGHT + theta3*AGE + eta1)
Inverse of probit, dependent on WEIGHT and AGE, has random effectCl = probitinv(theta1 + theta2*WEIGHT + theta3*AGE + eta1)
Inverse of logit, dependent on WEIGHT and AGE, has random effectCl = logitinv(theta1 + theta2*WEIGHT + theta3*AGE + eta1)

    Tip   To simultaneously fit data from multiple dose levels, use a CovariateModel object as an input argument to sbiofitmixed, and omit the random effect (eta) from the Expression property in the CovariateModel object.

The Expression property must meet the following requirements:

  • The expressions are valid MATLAB® code.

  • Each expression is linear with a transformation.

  • There is exactly one expression for each parameter.

  • In each expression, a covariate is used in at most one term.

  • In each expression, there is at most one random effect (eta)

  • Fixed effect (theta) and random effect (eta) names are unique within and across expressions. That is, each covariate has its own fixed effect.

    Tip   Use the getCovariateData method to view the covariate data when writing equations for the Expression property of a CovariateModel object.

    Tip   Use the verify method to check that the Expression property of a CovariateModel object meets the conditions described previously.

Characteristics

Applies toObject: CovariateModel
Data typeCharacter vector or cell array of character vectors
Data valuesparameterName = relationship
AccessRead/write

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