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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
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Updated: Jul 6, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Copula-based markov chain logistic regression modeling on binomial time series data.

Pepi Novianti1,2, Gunardi1, Dedi Rosadi1

  • 1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia.

Methodsx
|January 3, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel copula-based Markov chain logistic regression model for binomial time series data with covariates. Maximum Likelihood Estimation (MLE) accurately estimates model parameters, revealing variable relationships and time dependencies.

Keywords:
Asymptotic propertiesAutoregressiveClayton, Conditional probabilityCopula-Based Markov Chain Logistic Regression ModelCount time seriesFrankGumbelMaximum likelihood estimation

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Statistical Modeling

Background:

  • Traditional time series models often struggle with binomial data and covariate inclusion.
  • Copula functions offer a flexible way to model joint distributions and dependencies.
  • Markov chain models capture sequential dependencies in data.

Purpose of the Study:

  • To develop a copula-based Markov chain logistic regression model for binomial time series data.
  • To incorporate covariate variables into the time series model.
  • To estimate model parameters, including logistic regression and copula parameters, using Maximum Likelihood Estimation (MLE).

Main Methods:

  • Utilized a copula-based Markov chain approach to model binomial time series.
  • Integrated logistic regression for modeling the probability of success with covariates.
  • Employed bivariate copula functions (Clayton, Gumbel, Frank) and Maximum Likelihood Estimation (MLE) for parameter estimation.

Main Results:

  • MLE demonstrated accurate parameter estimation for the proposed model.
  • The model effectively captures relationships between dependent and independent variables.
  • The model successfully estimates the time dependency of the binomial time series data.

Conclusions:

  • The copula-based Markov chain logistic regression model is a viable approach for analyzing binomial time series with covariates.
  • MLE is an efficient method for parameter estimation in this complex model.
  • The model provides insights into both variable associations and temporal dynamics.