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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Kaplan-Meier Approach01:24

Kaplan-Meier Approach

The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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 squares (OLS)...
What are Estimates?01:06

What are Estimates?

It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such as the mean,...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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ESTIMATION IN A SEMI-PARAMETRIC TWO-STAGE RENEWAL REGRESSION MODEL.

Statistica Sinica·2010
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Four causes of cadaveric kidney transplant failure: a competing risk analysis.

American journal of transplantation : official journal of the American Society of Transplantation and the American Society of Transplant Surgeons·2002
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Related Experiment Video

Updated: May 21, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Estimation in a semi-Markov transformation model.

Dorota M Dabrowska1

  • 1University of California, USA.

The International Journal of Biostatistics
|June 29, 2012
PubMed
Summary

This study introduces transformation models for analyzing censored semi-Markov and modulated renewal processes, enhancing disease progression modeling in biomedical research. The methods offer robust estimation and confidence bands for critical transition probabilities.

Area of Science:

  • Biostatistics
  • Survival Analysis
  • Longitudinal Data Analysis

Background:

  • Semi-Markov and modulated renewal processes are key for multi-state models in longitudinal failure time data analysis.
  • Biomedical applications often use these models to represent disease progression through distinct patient states.
  • Existing proportional hazard model extensions have limitations for complex censored processes.

Purpose of the Study:

  • To propose transformation models for analyzing censored semi-Markov and modulated renewal processes.
  • To extend regression analysis capabilities for multi-state longitudinal data.
  • To provide robust methods for estimating parameters and confidence bands in complex survival models.

Main Methods:

  • Utilizing transformation models for censored semi-Markov and modulated renewal processes.

Related Experiment Videos

Last Updated: May 21, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

  • Developing estimation techniques for finite and infinite dimensional parameters.
  • Extending the Gaussian multiplier method for confidence band construction.

    • Main Results:

    • Demonstrated the application of transformation models to censored semi-Markov and modulated renewal processes.
    • Successfully estimated parameters and constructed confidence bands for transition probabilities.
    • Illustrated the utility of the proposed methods with a transplant outcome dataset.

    Conclusions:

    • Transformation models offer a flexible and powerful framework for analyzing complex multi-state processes.
    • The proposed methods provide reliable tools for understanding disease progression and patient outcomes.
    • This approach advances the analysis of censored longitudinal failure time data in biomedical research.