MBNMAdose (version 0.4.3)

dfpoly: 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)

Value

An object of class("dosefun")

Arguments

degree

The degree of the fractional polynomial as defined in royston1994;textualMBNMAdose

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.

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().

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 \(ln(x)\).

References

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)