Information on the distributions currently available within the
When fitting a Multi-Parameter Regression (MPR) model to data, the underlying distribution is selected
using the “
family” argument in the
mpr package includes distributions which have upto three parameters:
λ. This is a scale parameter which controls the overall magnitude of the hazard function and is typically the “interest” parameter in standard Single-Parameter Regression (SPR) models. The Multi-Parameter Regression (MPR) framework is more general and considers all parameters to be of interest.
γ. This is a shape parameter which controls the time evolution of the hazard.
ρ. This is an additional shape parameter which controls the time evolution of the hazard (available within the Burr and PGW distributions).
The MPR framework allows these parameters to depend on covariates as follows:
g1(λ) = x' β
g2(γ) = z' α
g3(ρ) = w' τ
where g1(.), g2(.) and g3(.) are appropriate link functions (log-link for positive parameters and identity-link for unconstrained parameters), x, z and w are covariate vectors, which may or may not contain covariates in common, and β, α and τ are the corresponding vectors of regression coefficients.
The distributions currently available are described below in terms of their hazard functions:
||λ γ t^(γ - 1)||λ > 0, γ > 0||SPR(λ) = PH|
||λ γ (λ t)^(γ - 1)||λ > 0, γ > 0||SPR(λ) = AFT|
||λ exp(γ t)||λ > 0, γ \in (-∞, ∞)||SPR(λ) = PH|
||λ γ t^(γ - 1) / (1 + λ t^γ)||λ > 0, γ > 0||SPR(λ) = PO|
||exp(γ t + λ) / (1+exp(γ t + λ))||λ \in (-∞, ∞), γ \in (-∞, ∞)||---|
||λ γ t^(γ - 1) / (1 + λ ρ t^γ)||λ > 0, γ > 0, ρ > 0||---|
||λ γ ρ t^(γ-1) (1+t^γ)^(ρ-1)||λ > 0, γ > 0, ρ > 0||SPR(λ) = PH|
The acronymns which appear in the table above are:
a Single-Parameter Regression (SPR) model where covariates enter through the scale parameter,
λ. For example, in the row corresponding to the
Weibull model, “SPR(λ)
= PH” means that the Weibull SPR(λ) model is a PH model. Thus, this standard parametric
PH model is generalised via the Weibull MPR model.
accelerated failure time.
power generalised Weibull.
1 2 3 4 5 6 7 8 9 10
# Veterans' administration lung cancer data data(veteran, package="survival") head(veteran) # Weibull MPR treatment model mpr(Surv(time, status) ~ list(~ trt, ~ trt), data=veteran, family="Weibull") # Burr MPR treatment model mpr(Surv(time, status) ~ list(~ trt, ~ trt, ~ trt), data=veteran, family="Burr")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.