# rstpm2 v1.5.1

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## Smooth Survival Models, Including Generalized Survival Models

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>. 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.

## Readme

### rstpm2: An R package for link-based survival models

#### NOTE: versions 1.4.1 and 1.4.2 of rstpm2 included a critical bug in the predict function for type in "hr", "sdiff", "hdiff", "meansurvdiff", "meanhr", "or", "marghr" or "uncured".

## Introduction

This package provides link-based survival models that extend the Royston-Parmar models, a family of flexible parametric models. There are two main classes included in this package:

A. The class `stpm2`

is an R version of `stpm2`

in Stata with some extensions, including:

Multiple links (log-log, -probit, -logit);

Left truncation and right censoring (with experimental support for interval censoring);

Relative survival;

Cure models (where we introduce the

`nsx`

smoother, which extends the`ns`

smoother);Predictions for survival, hazards, survival differences, hazard differences, mean survival, etc;

Functional forms can be represented in regression splines or other parametric forms;

The smoothers for time can use any transformation of time, including no transformation or log(time).

B. Another class `pstpm2`

is the implementation of the penalised models and corresponding penalized likelihood estimation methods. The main aim is to represent another way to deal with non-proportional hazards and adjust for potential continuous confounders in functional forms, not limited to proportional hazards and linear effect forms for all covariates. Functional forms can be represented in penalized regression splines (all `mgcv`

smoothers ) or other parametric forms.

## Some examples

The default for the parametric model is to use the Royston Parmar model, which uses a natural spline for the transformed baseline for log(time) with a log-log link.

```
require(rstpm2)
data(brcancer)
fit <- stpm2(Surv(rectime,censrec==1)~hormon,data=brcancer,df=3)
plot(fit,newdata=data.frame(hormon=0),type="hazard")
```

The default for the penalised model is similar, using a thin-plate spline for the transformed baseline for log(time) with a log-log link. The advantage of the penalised model is that there is no need to specify the knots or degrees of freedom for the baseline smoother.

```
fit <- pstpm2(Surv(rectime,censrec==1)~hormon,data=brcancer)
plot(fit,newdata=data.frame(hormon=0),type="hazard")
```

## Functions in rstpm2

Name | Description | |

coef<- | Generic method to update the coef in an object. | |

cox.tvc | Test for a time-varying effect in the coxph model | |

eform.stpm2 | S3 method for to provide exponentiated coefficents with confidence intervals. | |

stpm2-class | Class "stpm2" ~~~ | |

markov_msm | Predictions for continuous time, nonhomogeneous Markov multi-state models using parametric and penalised survival models. | |

lines.stpm2 | S3 methods for lines | |

tvcCoxph-class | Class "tvcCoxph" | |

brcancer | German breast cancer data from Stata. | |

colon | Colon cancer. | |

aft | Parametric accelerated failure time model with smooth time functions | |

incrVar | Utility that returns a function to increment a variable in a data-frame. | |

predictnl | Estimation of standard errors using the numerical delta method. | |

legendre.quadrature.rule.200 | Legendre quadrature rule for n=200. | |

grad | gradient function (internal function) | |

pstpm2-class | Class "pstpm2" | |

aft-class | Class "stpm2" ~~~ | |

numDeltaMethod | Calculate numerical delta method for non-linear predictions. | |

Rstpm2-package | Flexible parametric survival models. | |

plot-methods | plots for an stpm2 fit | |

rstpm2-internal | Internal functions for the rstpm2 package. | |

nsx | Generate a Basis Matrix for Natural Cubic Splines (with eXtensions) | |

nsxD | Generate a Basis Matrix for the first derivative of Natural Cubic Splines (with eXtensions) | |

residuals-methods | Residual values for an stpm2 or pstpm2 fit | |

vuniroot | Vectorised One Dimensional Root (Zero) Finding | |

gsm | Parametric and penalised generalised survival models | |

popmort | Background mortality rates for the colon dataset. | |

predict.nsx | Evaluate a Spline Basis | |

predict-methods | Predicted values for an stpm2 or pstpm2 fit | |

predictnl-methods | ~~ Methods for Function predictnl ~~ | |

No Results! |

## Vignettes of rstpm2

## Last month downloads

## Details

Type | Package |

Date | 2019-10-28 |

LinkingTo | Rcpp,RcppArmadillo |

URL | http://github.com/mclements/rstpm2 |

BugReports | http://github.com/mclements/rstpm2/issues |

License | GPL-2 | GPL-3 |

LazyData | yes |

NeedsCompilation | yes |

Packaged | 2019-11-05 07:48:56 UTC; marcle |

Repository | CRAN |

Date/Publication | 2019-11-05 23:00:05 UTC |

imports | bbmle (>= 1.0.20) , deSolve , fastGHQuad , graphics , mgcv , parallel , Rcpp (>= 0.10.2) , stats , utils |

suggests | eha , ggplot2 , lattice , mstate , readstata13 , testthat |

depends | methods , R (>= 3.0.2) , splines , survival |

linkingto | RcppArmadillo |

Contributors | Gordon Smyth, Simon Wood, Xing-Rong Liu, Paul Lambert, Lasse Hjort Jakobsen, Alessandro Gasparini, Patrick Alken, Rhys Ulerich |

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