Emax dose-response function

demax(emax = "rel", ed50 = "rel", hill = NULL, p.expon = FALSE)

Arguments

emax: Pooling for Emax parameter. Can take "rel", "common", "random" or be assigned a numeric value (see details).
ed50: Pooling for ED50 parameter. Can take "rel", "common", "random" or be assigned a numeric value (see details).
hill: Pooling for Hill parameter. Can take "rel", "common", "random" or be assigned a numeric value (see details).
p.expon: A logical object to indicate whether ed50 and hill parameters should be expressed within the dose-response function on an exponential scale

Value

An object of class("dosefun")

Details

Emax represents the maximum response. exp(ED50) represents the dose at which 50% of the maximum response is achieved. exp(Hill) is the Hill parameter, which allows for a sigmoidal function.

Without Hill parameter: $$\frac{E_{max}\times{x}}{ET_{50}+x}$$

With Hill parameter: $$\frac{E_{max}\times{x^{hill}}}{ET_{50}\times{hill}}+x^{hill}$$

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

There are no references for Rd macro \insertAllCites on this help page.

Examples

# Model without a Hill parameter
demax(emax="rel", ed50="common")
#> $name
#> [1] "emax"
#> 
#> $fun
#> ~(emax * dose)/(ed50 + dose)
#> <environment: 0x55e2695cd1c0>
#> 
#> $p.expon
#> [1] FALSE
#> 
#> $params
#> [1] "emax" "ed50"
#> 
#> $nparam
#> [1] 2
#> 
#> $jags
#> [1] "(s.beta.1[agent[i,k]] * dose[i,k]) / (s.beta.2[agent[i,k]] + dose[i,k])"
#> 
#> $apool
#>     emax     ed50 
#>    "rel" "common" 
#> 
#> $bname
#>     emax     ed50 
#> "beta.1" "beta.2" 
#> 
#> attr(,"class")
#> [1] "dosefun"

# Model including a Hill parameter and defaults for Emax and ED50 parameters
demax(hill="common")
#> $name
#> [1] "emax"
#> 
#> $fun
#> ~(emax * (dose^hill))/((ed50^hill) + (dose^hill))
#> <environment: 0x55e26af65b00>
#> 
#> $p.expon
#> [1] FALSE
#> 
#> $params
#> [1] "emax" "ed50" "hill"
#> 
#> $nparam
#> [1] 3
#> 
#> $jags
#> [1] "(s.beta.1[agent[i,k]] * (dose[i,k] ^ s.beta.3[agent[i,k]])) / ((s.beta.2[agent[i,k]] ^ s.beta.3[agent[i,k]]) + (dose[i,k] ^ s.beta.3[agent[i,k]]))"
#> 
#> $apool
#>     emax     ed50     hill 
#>    "rel"    "rel" "common" 
#> 
#> $bname
#>     emax     ed50     hill 
#> "beta.1" "beta.2" "beta.3" 
#> 
#> attr(,"class")
#> [1] "dosefun"