Mathematics and Statistics in Anesthesiology

2018 ◽  
Author(s):  
Daniel Mortlock
Keyword(s):  
Probability Theory ◽  
Data Analysis ◽  
Survey Design ◽  
Probability Distributions ◽  
Statistical Tests ◽  
Real World Data ◽  
Mathematical Functions ◽  
P Values ◽  
Bayesian Data Analysis ◽  
Probability And Statistics

Mathematics is the language of quantitative science, and probability and statistics are the extension of classical logic to real world data analysis and experimental design. The basics of mathematical functions and probability theory are summarized here, providing the tools for statistical modeling and assessment of experimental results. There is a focus on the Bayesian approach to such problems (ie, Bayesian data analysis); therefore, the basic laws of probability are stated, along with several standard probability distributions (eg, binomial, Poisson, Gaussian). A number of standard classical tests (eg, p values, the t-test) are also defined and, to the degree possible, linked to the underlying principles of probability theory. This review contains 5 figures, 1 table, and 15 references. Keywords: Bayesian data analysis, mathematical models, power analysis, probability, p values, statistical tests, statistics, survey design

scholarly journals The Nested_fit Data Analysis Program

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 14 ◽  
Author(s):  
Martino Trassinelli
Keyword(s):  
Data Analysis ◽  
Probability Distributions ◽  
Analysis Program ◽  
Large Database ◽  
Data Set ◽  
Lawn Mower ◽  
Bayesian Data Analysis ◽  
Bayesian Evidence ◽  
Spectral Profiles ◽  
Log Normal

We present here Nested_fit, a Bayesian data analysis code developed for investigations of atomic spectra and other physical data. It is based on the nested sampling algorithm with the implementation of an upgraded lawn mower robot method for finding new live points. For a given data set and a chosen model, the program provides the Bayesian evidence, for the comparison of different hypotheses/models, and the different parameter probability distributions. A large database of spectral profiles is already available (Gaussian, Lorentz, Voigt, Log-normal, etc.) and additional ones can easily added. It is written in Fortran, for an optimized parallel computation, and it is accompanied by a Python library for the results visualization.

scholarly journals An introduction to data analysis using the PyMC3 probabilistic programming framework: A case study with Gaussian Mixture Modeling

2019 ◽  
Author(s):  
Shi Xian Liew ◽  
Mohsen Afrasiabi ◽  
Joseph L. Austerweil
Keyword(s):  
Data Analysis ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Real World Data ◽  
Probabilistic Programming ◽  
Bayesian Data Analysis ◽  
Computational Speed ◽  
Recent Developments ◽  
Psychology Community

Recent developments in modern probabilistic programming have offered users many practical tools of Bayesian data analysis. However, the adoption of such techniques by the general psychology community is still fairly limited. This tutorial aims to provide non-technicians with an accessible guide to PyMC3, a robust probabilistic programming language that allows for straightforward Bayesian data analysis. We focus on a series of increasingly complex Gaussian mixture models – building up from fitting basic univariate models to more complex multivariate models fit to real-world data. We also explore how PyMC3 can be configured to obtain significant increases in computational speed by taking advantage of a machine’s GPU, in addition to the conditions under which such acceleration can be expected. All example analyses are detailed with step-by-step instructions and corresponding Python code.

Assessing variability in surgical decision making among attending neurosurgeons at an academic center

2020 ◽  
Vol 132 (6) ◽  
pp. 1970-1976
Author(s):  
Ashwin G. Ramayya ◽  
H. Isaac Chen ◽  
Paul J. Marcotte ◽  
Steven Brem ◽  
Eric L. Zager ◽  
...  
Keyword(s):  
Spine Surgery ◽  
Repeated Measures ◽  
Elective Surgery ◽  
Statistical Tests ◽  
Neurosurgical Procedures ◽  
P Values ◽  
Surgical Interventions ◽  
Radiology Reports ◽  
Operative Notes ◽  
First Time

OBJECTIVEAlthough it is known that intersurgeon variability in offering elective surgery can have major consequences for patient morbidity and healthcare spending, data addressing variability within neurosurgery are scarce. The authors performed a prospective peer review study of randomly selected neurosurgery cases in order to assess the extent of consensus regarding the decision to offer elective surgery among attending neurosurgeons across one large academic institution.METHODSAll consecutive patients who had undergone standard inpatient surgical interventions of 1 of 4 types (craniotomy for tumor [CFT], nonacute redo CFT, first-time spine surgery with/without instrumentation, and nonacute redo spine surgery with/without instrumentation) during the period 2015–2017 were retrospectively enrolled (n = 9156 patient surgeries, n = 80 randomly selected individual cases, n = 20 index cases of each type randomly selected for review). The selected cases were scored by attending neurosurgeons using a need for surgery (NFS) score based on clinical data (patient demographics, preoperative notes, radiology reports, and operative notes; n = 616 independent case reviews). Attending neurosurgeon reviewers were blinded as to performing provider and surgical outcome. Aggregate NFS scores across various categories were measured. The authors employed a repeated-measures mixed ANOVA model with autoregressive variance structure to compute omnibus statistical tests across the various surgery types. Interrater reliability (IRR) was measured using Cohen’s kappa based on binary NFS scores.RESULTSOverall, the authors found that most of the neurosurgical procedures studied were rated as “indicated” by blinded attending neurosurgeons (mean NFS = 88.3, all p values < 0.001) with greater agreement among neurosurgeon raters than expected by chance (IRR = 81.78%, p = 0.016). Redo surgery had lower NFS scores and IRR scores than first-time surgery, both for craniotomy and spine surgery (ANOVA, all p values < 0.01). Spine surgeries with fusion had lower NFS scores than spine surgeries without fusion procedures (p < 0.01).CONCLUSIONSThere was general agreement among neurosurgeons in terms of indication for surgery; however, revision surgery of all types and spine surgery with fusion procedures had the lowest amount of decision consensus. These results should guide efforts aimed at reducing unnecessary variability in surgical practice with the goal of effective allocation of healthcare resources to advance the value paradigm in neurosurgery.

scholarly journals Pain Pharmacotherapy in a Large Cohort of Patients with Osteoarthritis: A Real-World Data Analysis

2021 ◽  
Author(s):  
Noga Fallach ◽  
Gabriel Chodick ◽  
Matanya Tirosh ◽  
Elon Eisenberg ◽  
Omri Lubovsky
Keyword(s):  
Data Analysis ◽  
Real World ◽  
Large Cohort ◽  
Real World Data ◽  
World Data
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