DerivCumulHazard

Cumulative hazard (integral of hazard) and its first and second derivatives wrt regression parameters beta

Fits (excess) hazard, relative mortality ratio or marginal intensity models with multidimensional penalized splines allowing for
time-dependent effects, non-linear effects and interactions between several continuous covariates. In survival and net survival analysis, in addition to modelling the effect of time (via the baseline hazard), one has often to deal with several continuous covariates and model their functional forms, their time-dependent effects, and their interactions. Model specification becomes therefore a complex problem and penalized regression splines represent an appealing solution to that problem as splines offer the required flexibility while penalization limits overfitting issues. Current implementations of penalized survival models can be slow or unstable and sometimes lack some key features like taking into account expected mortality to provide net survival and excess hazard estimates. In contrast, survPen provides an automated, fast, and stable implementation (thanks to explicit calculation of the derivatives of the likelihood) and offers a unified framework for
multidimensional penalized hazard and excess hazard models. Later versions (>2.0.0) include penalized models for relative mortality ratio, and marginal intensity in recurrent event setting.
survPen may be of interest to those who 1) analyse any kind of time-to-event data: mortality, disease relapse, machinery breakdown, unemployment, etc 2) wish to describe the associated hazard and to understand which predictors impact its dynamics,
3) wish to model the relative mortality ratio between a cohort and a reference population, 4) wish to describe the marginal intensity for recurrent event data.
See Fauvernier et al. (2019a) <doi:10.21105/joss.01434> for an overview of the package and Fauvernier et al. (2019b) <doi:10.1111/rssc.12368> for the method.

Mathieu Fauvernier

survPen

Multidimensional Penalized Splines for (Excess) Hazard Models,
Relative Mortality Ratio Models and Marginal Intensity Models

Laurent Roche

Laurent Remontet

Zoe Uhry

Nadine Bossard

Elsa Coz

DerivCumulHazard function

<dl><dt>X_GL</dt>
<dd>list of matrices (<code>length(X.GL)=n.legendre</code>) for Gauss-Legendre quadrature</dd>
<dt>weights</dt>
<dd>vector of weights for Gauss-Legendre integration on [-1;1]</dd>
<dt>tm</dt>
<dd>vector of midpoints times for Gauss-Legendre integration; tm = 0.5*(t1 - t0)</dd>
<dt>n_legendre</dt>
<dd>number of nodes for Gauss-Legendre quadrature</dd>
<dt>n</dt>
<dd>number of individuals in the dataset</dd>
<dt>p</dt>
<dd>number of regression parameters</dd>
<dt>beta</dt>
<dd>vector of estimated regression parameters</dd>
<dt>expected</dt>
<dd>vector of expected hazard rates</dd>
<dt>type</dt>
<dd>"net", "overall" or "mult"</dd>
<dt>is_pwcst</dt>
<dd>True if there is a piecewise constant baseline specified. False otherwise</dd>
<dt>pwcst_weights</dt>
<dd>if is.pwcst is TRUE, matrix of weights giving the time contribution of each individual on each sub-interval. Otherwise NULL</dd></dl>

Arguments

Cumulative hazard (integral of hazard) and its first and second derivatives wrt regression parameters beta — DerivCumulHazard

<dl>

<dt>X_GL</dt>
<dd>list of matrices (<code>length(X.GL)=n.legendre</code>) for Gauss-Legendre quadrature</dd>


<dt>weights</dt>
<dd>vector of weights for Gauss-Legendre integration on [-1;1]</dd>


<dt>tm</dt>
<dd>vector of midpoints times for Gauss-Legendre integration; tm = 0.5*(t1 - t0)</dd>


<dt>n_legendre</dt>
<dd>number of nodes for Gauss-Legendre quadrature</dd>


<dt>n</dt>
<dd>number of individuals in the dataset</dd>


<dt>p</dt>
<dd>number of regression parameters</dd>


<dt>beta</dt>
<dd>vector of estimated regression parameters</dd>


<dt>expected</dt>
<dd>vector of expected hazard rates</dd>


<dt>type</dt>
<dd>"net", "overall" or "mult"</dd>


<dt>is_pwcst</dt>
<dd>True if there is a piecewise constant baseline specified. False otherwise</dd>


<dt>pwcst_weights</dt>
<dd>if is.pwcst is TRUE, matrix of weights giving the time contribution of each individual on each sub-interval. Otherwise NULL</dd>

</dl>

Get 50% off unlimited learning

DerivCumulHazard: Cumulative hazard (integral of hazard) and its first and second derivatives wrt regression parameters beta

Description

Usage

Value

Arguments