pammtools Survival Analysis with Generalized Additive Mixed Models

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# <strong><code>pammtools</code></strong> <br> Survival Analysis with Generalized Additive Mixed Models
## R Medicine 2020
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### <br><br><br><strong>Andreas Bender (<i class='fa fa-twitter'><span class='citation'>@adibender</span></i>)</strong>, <br>Fabian Scheipl, Philipp Kopper
### <br><br><br>Department of Statistics, LMU Munich

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**Time-to-event Analysis** (Survival Analysis) requires special methods because

- outcome can not always be fully observed (**censoring**, **truncation**)

- covariate values can change over time (**time-varying covariates**)

- covariate effects can change over time (**time-varying effects**)

- competing events prevent observation of the event of interest (**competing risks**)

- observation units transition between different states (**recurrent events**, **multi-state models**)
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Hitorically Survival Analysis dominated by Cox type models

Many **Survival Models** can be represented **as Poisson Regression** (on transformed data)

- Piece-wise Exponential Model (PEM; estimation based on GLM) <br>
e.g., <a name=cite-laird_covariance_1981></a><a name=cite-friedman_piecewise_1982></a>[Laird and Olivier (1981)](http://www.jstor.org/stable/2287816); [Friedman (1982)](http://www.jstor.org/stable/2240502)

- Piece-wise exponential Additive Mixed Model (PAMM; estimation based on GAMM) <br>
e.g., <a name=cite-cai_mixed_2002></a><a name=cite-bender_generalized_2018></a>[Cai, Hyndman, and Wand (2002)](http://dx.doi.org/10.1198/106186002862); [Bender, Groll, and Scheipl (2018)](https://doi.org/10.1177/1471082X17748083)

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`$\ra$` Use any method/R package for Survival Analysis that supports optimization
of Poisson Likelihood (e.g., GAMMs via **`mgcv`**; <a name=cite-wood_generalized_2017></a>[Wood (2017)](#bib-wood_generalized_2017))

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.font200[Survival Analysis as Poisson Regression]

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.font150[Data in "standard" time-to-event format] <br>
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.font150[Data in PED format] <br>
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