Create a list containing the parameters of a single fitted parametric or flexible parametric survival model.
params_surv(coefs, dist, aux = NULL)
coefs  A list of length equal to the number of parameters in the
survival distribution. Each element of the list is a matrix of samples
of the regression coefficients under sampling uncertainty used to predict
a given parameter. All parameters are expressed on the real line (e.g.,
after log transformation if they are defined as positive). Each element
of the list may also be an object coercible to a matrix such as a


dist  Character vector denoting the parametric distribution. See "Details". 
aux  Auxiliary arguments used with splines, fractional polynomial, or piecewise exponential models. See "Details". 
An object of class params_surv
, which is a list containing coefs
,
dist
, and n_samples
. n_samples
is equal to the
number of rows in each element of coefs
, which must be the same. The coefs
element is always converted into a list of matrices. The list may also contain
aux
if a spline, fractional polynomial, or piecewise exponential model is
used.
Survival is modeled as a function of \(L\) parameters \(\alpha_l\). Letting \(F(t)\) be the cumulative distribution function, survival at time \(t\) is given by $$1  F(t  \alpha_1(x_{1}), \ldots, \alpha_L(x_{L})).$$ The parameters are modeled as a function of covariates, \(x_l\), with an inverse transformation function \(g^{1}()\), $$\alpha_l = g^{1}(x_{l}^T \beta_l).$$ \(g^{1}()\) is typically \(exp()\) if a parameter is strictly positive and the identity function if the parameter space is unrestricted.
The types of distributions that can be specified are:
exponential
or exp
Exponential distribution. coef
must contain the rate
parameter on the log scale and the same parameterization as in
stats::Exponential
.
weibull
or weibull.quiet
Weibull distribution. The first
element of coef
is the shape
parameter (on the log scale) and the second
element is the scale
parameter (also on the log scale). The parameterization is
that same as in stats::Weibull
.
weibullPH
Weibull distribution with a proportional hazards
parameterization. The first element of coef
is the shape
parameter
(on the log scale) and the second element is the scale
parameter
(also on the log scale). The parameterization is
that same as in flexsurv::WeibullPH
.
gamma
Gamma distribution. The first
element of coef
is the shape
parameter (on the log scale) and the second
element is the rate
parameter (also on the log scale). The parameterization is
that same as in stats::GammaDist
.
lnorm
Lognormal distribution. The first
element of coef
is the meanlog
parameter (i.e., the mean of survival on
the log scale) and the second element is the sdlog
parameter (i.e.,
the standard deviation of survival on the log scale). The parameterization is
that same as in stats::Lognormal
. The coefficients predicting the meanlog
parameter are untransformed whereas the coefficients predicting the sdlog
parameter are defined on the log scale.
gompertz
Gompertz distribution. The first
element of coef
is the shape
parameter and the second
element is the rate
parameter (on the log scale). The parameterization is
that same as in flexsurv::Gompertz
.
llogis
Loglogistic distribution. The first
element of coef
is the shape
parameter (on the log scale) and the second
element is the scale
parameter (also on the log scale). The parameterization is
that same as in flexsurv::Llogis
.
gengamma
Generalized gamma distribution. The first
element of coef
is the location parameter mu
, the second
element is the scale parameter sigma
(on the log scale), and the
third element is the shape parameter Q
. The parameterization is
that same as in flexsurv::GenGamma
.
survspline
Survival splines. Each element of coef
is a parameter of the
spline model (i.e. gamma_0
, gamma_1
, \(\ldots\)) with length equal
to the number of knots (including the boundary knots). See below for details on the
auxiliary arguments. The parameterization is that same as in flexsurv::Survspline
.
fracpoly
Fractional polynomials. Each element of coef
is a parameter of the
fractional polynomial model (i.e. gamma_0
, gamma_1
, \(\ldots\)) with length equal
to the number of powers plus 1. See below for details on the auxiliary arguments
(i.e., powers
).
pwexp
Piecewise exponential distribution. Each element of coef
is
rate parameter for a distinct time interval. The times at which the rates
change should be specified with the auxiliary argument time
(see below
for more details).
fixed
A fixed survival time. Can be used for "nonrandom" number
generation. coef
should contain a single parameter, est
, of the fixed
survival times.
Auxiliary arguments for spline models should be specified as a list containing the elements:
knots
A numeric vector of knots.
scale
The survival outcome to be modeled
as a spline function. Options are "log_cumhazard"
for the log cumulative hazard;
"log_hazard"
for the log hazard rate; "log_cumodds"
for the log cumulative odds;
and "inv_normal"
for the inverse normal distribution function.
timescale
If "log"
(the default), then survival is modeled as a spline function
of log time; if "identity"
, then it is modeled as a spline function of time.
Auxiliary arguments for fractional polynomial models should be specified as a list containing the elements:
powers
A vector of the powers of the fractional polynomial with each element chosen from the following set: 2. 1, 0.5, 0, 0.5, 1, 2, 3.
Auxiliary arguments for piecewise exponential models should be specified as a list containing the element:
time
A vector equal to the number of rate parameters giving the times at which the rate changes.
Furthermore, when splines (with scale = "log_hazard"
) or fractional
polynomials are used, numerical methods must be used to compute the cumulative
hazard and for random number generation. The following additional auxiliary arguments
can therefore be specified:
cumhaz_method
Numerical method used to compute cumulative hazard
(i.e., to integrate the hazard function). Always used for fractional polynomials
but only used for splines if scale = "log_hazard"
.
Options are "quad"
for adaptive quadrature and "riemann"
for Riemann sum.
random_method
Method used to randomly draw from
an arbitrary survival function. Options are "invcdf"
for the inverse CDF and
"discrete"
for a discrete time approximation that randomly samples
events from a Bernoulli distribution at discrete times.
step
Step size for computation of cumulative hazard with
numerical integration. Only required when using "riemann"
to compute the
cumulative hazard or using "discrete"
for random number generation.
n < 10 params < params_surv( coefs = list( shape = data.frame( intercept = rnorm(n, .5, .23) ), scale = data.frame( intercept = rnorm(n, 12.39, 1.49), age = rnorm(n, .09, .023) ) ), dist = "weibull" ) summary(params)#> parameter term mean sd 2.5% 97.5% #> 1: shape intercept 0.55088444 0.20690627 0.3793033 0.9404121 #> 2: scale intercept 11.29702797 1.62742924 8.7760297 13.1101035 #> 3: scale age 0.08523438 0.02072153 0.1221598 0.0595469params#> A "params_surv" object #> #> Summary of coefficients: #> parameter term mean sd 2.5% 97.5% #> 1: shape intercept 0.55088444 0.20690627 0.3793033 0.9404121 #> 2: scale intercept 11.29702797 1.62742924 8.7760297 13.1101035 #> 3: scale age 0.08523438 0.02072153 0.1221598 0.0595469 #> #> Number of parameter samples: 10 #> Distribution: weibull