Martin Mächler

Last Name

Mächler

First Name

Martin

ORCID

0000-0002-8685-9910

Organisational unit

01434 - Lehre Mathematik

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Publications 1 - 6 of 6

Nested Archimedean Copulas Meet R: The nacopula Package
Hofert, Marius; Mächler, Martin (2011)
Journal of Statistical Software
The package nacopula provides procedures for constructing nested Archimedean copulas in any dimensions and with any kind of nesting structure, generating vectors of random variates from the constructed objects, computing function values and probabilities of falling into hypercubes, as well as evaluation of characteristics such as Kendall's tau and the tail-dependence coefficients. As by-products, algorithms for various distributions, including exponentially tilted stable and Sibuya distributions, are implemented. Detailed examples are given.
Are the same parameters measured at admission and in the ICU comparable in their predictive values for complication and mortality in severely injured patients?
Gröbli, Lea; Kalbas, Yannik; Kessler, Franziska; et al. (2025)
European Journal of Medical Research
Introduction Numerous studies have investigated variables that predict mortality and complications following severe trauma. These studies, however, mainly focus on admission values or a single variable. The aim of this study was to investigate the predictive quality of multiple routine clinical measurements (at admission and in the ICU). Methods Retrospective cohort study of severely injured patients treated at one Level 1 academic trauma centre. Inclusion criteria: severe injury (ISS ≥ 16 points), primary admission and complete data set. Exclusion criteria end-of-life treatment based on advanced directive, secondary transferred patients. Primary outcome: mortality, pneumonia, sepsis. Routine clinical parameters were stratified based on measurement timepoint into Group TB (Trauma Bay, admission) and into Group intensive care unit (ICU, 72 h after admission). Prediction of complications and mortality were calculated using two prediction methods: adaptive boosting (AdaBoost, artificial intelligence, AI) and LASSO regression analysis. Results Inclusion of 3668 cases. Overall mean age 45.5 ± 20 years, mean ISS 28.2 ± 15.1 points, incidence pneumonia 19.0%, sepsis 14.9%, death from haemorrhagic shock 4.1%, death from multiple organ failure 1.9%, overall mortality rate 26.8%. Highest predictive value for complications for Group TB include abbreviated injury scale (AIS), new injury severity score (NISS) and systemic Inflammatory Response Syndrome (SIRS) score. Highest predictive quality for complications for Group ICU include late lactate values, haematocrit, leukocytes, and CRP. Sensitivity and specificity of late prediction models using a 25% cutoff were 73.61% and 76.24%, respectively. Conclusions The predictive quality of routine clinical measurements strongly depends on the timepoint of the measurement. Upon admission, the injury severity and affected anatomical regions are more predictive, while during the ICU stay, laboratory parameters are better predictor of adverse outcomes. Therefore, the dynamics of pathophysiologic responses should be taken into consideration, especially during decision making of secondary definitive surgical interventions. Level of evidence: III (retrospective cohort study).
Fitting Linear Mixed-Effects Models Using lme4
Bates, Douglas; Mächler, Martin; Bolker, Ben; et al. (2015)
Journal of Statistical Software
Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.
Parallel and Other Simulations in R Made Easy: An End-to-End Study
Hofert, Marius; Mächler, Martin (2016)
Journal of Statistical Software
It is shown how to set up, conduct, and analyze large simulation studies with the new R package simsalapar (= simulations simplified and launched parallel). A simulation study typically starts with determining a collection of input variables and their values on which the study depends. Computations are desired for all combinations of these variables. If conducting these computations sequentially is too time-consuming, parallel computing can be applied over all combinations of select variables. The final result object of a simulation study is typically an array. From this array, summary statistics can be derived and presented in terms of flat contingency or LATEX tables or visualized in terms of matrix-like figures. The R package simsalapar provides several tools to achieve the above tasks. Warnings and errors are dealt with correctly, various seeding methods are available, and run time is measured. Furthermore, tools for analyzing the results via tables or graphics are provided. In contrast to rather minimal examples typically found in R packages or vignettes, an end-to-end, not-so-minimal simulation problem from the realm of quantitative risk management is given. The concepts presented and solutions provided by simsalapar may be of interest to students, researchers, and practitioners as a how-to for conducting realistic, large-scale simulation studies in R.
Causal Inference Using Graphical Models with the R Package pcalg
Kalisch, Markus; Mächler, Martin; Colombo, Diego; et al. (2012)
Journal of Statistical Software
The pcalg package for R can be used for the following two purposes: Causal structure learning and estimation of causal effects from observational data. In this document, we give a brief overview of the methodology, and demonstrate the package’s functionality in both toy examples and applications.
Variable length Markov chains: methodology, computing and software
Mächler, Martin; Bühlmann, Peter (2002)
Research Report / Seminar für Statistik, Eidgenössische Technische Hochschule (ETH)
We present a tutorial and new publicly available computational tools for variable length Markov chains (vlmc). vlmc’s are Markov chains with the additional at tractive structure that their memories depend on a variable number of lagged values, depending on how the actual past (the lagged values) looks like. They build a very flexible class of tree structured models for categorical time series. Fitting vlmc’s from data is a non-trivial computational task. We provide an efficient implementation of the so-called context algorithm which requires O(n log(n)) operations only. The imple mentation, which is publicly available, includes additional important new features and options: diagnostics, goodness of fit, simulation and bootstrap, residuals and tuning the context algorithm. Our tutorial is presented with a version in R which is available from the Comprehensive R Archive Network (CRAN 1997 ff.). The exposition is self contained, gives rigorous and partly new mathematical descriptions and is illustrated by analyzing a DNA sequence from the Epstein-Barr virus.

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Martin Mächler

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