View source: R/dose.functions.R
dfpoly | R Documentation |
Fractional polynomial dose-response function
dfpoly(degree = 1, beta.1 = "rel", beta.2 = "rel", power.1 = 0, power.2 = 0)
degree |
The degree of the fractional polynomial as defined in \insertCiteroyston1994;textualMBNMAdose |
beta.1 |
Pooling for the 1st fractional polynomial coefficient. Can take |
beta.2 |
Pooling for the 2nd fractional polynomial coefficient. Can take |
power.1 |
Value for the 1st fractional polynomial power ( |
power.2 |
Value for the 2nd fractional polynomial power ( |
\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)
.
An object of class("dosefun")
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()
.
# 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)
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