dfpoly {MBNMAdose}

Fractional polynomial dose-response function

Description

Fractional polynomial dose-response function

Usage

dfpoly(degree = 1, beta.1 = "rel", beta.2 = "rel", power.1 = 0, power.2 = 0)

Arguments

degree

The degree of the fractional polynomial as defined in Royston and Altman (1994)

beta.1

Pooling for the 1st fractional polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

beta.2

Pooling for the 2nd fractional polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

power.1

Value for the 1st fractional polynomial power (\gamma_1). Must take any numeric value in the set ⁠-2, -1, -0.5, 0, 0.5, 1, 2, 3⁠.

power.2

Value for the 2nd fractional polynomial power (\gamma_2). Must take any numeric value in the set ⁠-2, -1, -0.5, 0, 0.5, 1, 2, 3⁠.

Details

• \beta_1 represents the 1st coefficient.

• \beta_2 represents the 2nd coefficient.

• \gamma_1 represents the 1st fractional polynomial power

• \gamma_2 represents the 2nd fractional polynomial power

For a polynomial of degree=1:

{\beta_1}x^{\gamma_1}

For a polynomial of degree=2:

{\beta_1}x^{\gamma_1}+{\beta_2}x^{\gamma_2}

x^{\gamma} is a regular power except where \gamma=0, where x^{(0)}=ln(x). If a fractional polynomial power \gamma repeats within the function it is multiplied by another ln(x).

Value

An object of class("dosefun")

Dose-response parameters

Argument	Model specification
"rel"	Implies that relative effects should be pooled for this dose-response parameter separately for each agent in the network.
"common"	Implies that all agents share the same common effect for this dose-response parameter.
"random"	Implies that all agents share a similar (exchangeable) effect for this dose-response parameter. This approach allows for modelling of variability between agents.
numeric()	Assigned a numeric value, indicating that this dose-response parameter should not be estimated from the data but should be assigned the numeric value determined by the user. This can be useful for fixing specific dose-response parameters (e.g. Hill parameters in Emax functions) to a single value.

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

Royston P, Altman D (1994). “Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling.” Journal of the Royal Statistical Society: Series C, 43(3), 429-467.

Examples

# 1st order fractional polynomial a value of 0.5 for the power
dfpoly(beta.1="rel", power.1=0.5)

# 2nd order fractional polynomial with relative effects for coefficients
# and a value of -0.5 and 2 for the 1st and 2nd powers respectively
dfpoly(degree=2, beta.1="rel", beta.2="rel",
  power.1=-0.5, power.2=2)