grad

Numerical gradient for a function at a given value (internal).

R implementation of generalized survival models (GSMs), smooth accelerated failure time (AFT) models and Markov multi-state models. For the GSMs, g(S(t|x))=eta(t,x) for a link function g, survival S at time t with covariates x and a linear predictor eta(t,x). The main assumption is that the time effect(s) are smooth <doi:10.1177/0962280216664760>. For fully parametric models with natural splines, this re-implements Stata's 'stpm2' function, which are flexible parametric survival models developed by Royston and colleagues. We have extended the parametric models to include any smooth parametric smoothers for time. We have also extended the model to include any smooth penalized smoothers from the 'mgcv' package, using penalized likelihood. These models include left truncation, right censoring, interval censoring, gamma frailties and normal random effects <doi:10.1002/sim.7451>, and copulas. For the smooth AFTs, S(t|x) = S_0(t*eta(t,x)), where the baseline survival function S_0(t)=exp(-exp(eta_0(t))) is modelled for natural splines for eta_0, and the time-dependent cumulative acceleration factor eta(t,x)=\int_0^t exp(eta_1(u,x)) du for log acceleration factor eta_1(u,x). The Markov multi-state models allow for a range of models with smooth transitions to predict transition probabilities, length of stay, utilities and costs, with differences, ratios and standardisation.

Mark Clements

rstpm2

Smooth Survival Models, Including Generalized Survival Models

Xing-Rong Liu

Benjamin Christoffersen

Paul Lambert

Lasse Hjort Jakobsen

Alessandro Gasparini

Gordon Smyth

Patrick Alken

Simon Wood

Rhys Ulerich

grad function

<dl> <dt>func</dt>
<dd>Function taking a vector argument x (returns a vector of length&gt;=1)</dd> <dt>x</dt>
<dd>vector of arguments for where the gradient is wanted.</dd> <dt>...</dt>
<dd>other arguments to the function</dd> <dt>method</dt>
<dd>string argument to determine whether to use the fast two sided
 calculation or use a Richardson extrapolation.</dd></dl>

Arguments

Author

gradient function (internal function)
   — grad

<dl>

 <dt>func</dt>
<dd>Function taking a vector argument x (returns a vector of length&gt;=1)</dd>

 <dt>x</dt>
<dd>vector of arguments for where the gradient is wanted.</dd>

 <dt>...</dt>
<dd>other arguments to the function</dd>

 <dt>method</dt>
<dd>string argument to determine whether to use the fast two sided
 calculation or use a Richardson extrapolation.</dd>

</dl>

gradient function (internal function)

grad: gradient function (internal function)

Description

Usage

Value

Arguments

Author

Details

See Also