A note on point estimation and interval estimation of the relative treatment effect under a simple crossover design

2021 ◽  
Author(s):  
Chii‐Dean Lin ◽  
Kung‐Jong Lui
Keyword(s):  
Treatment Effect ◽  
Interval Estimation ◽  
Crossover Design ◽  
Point Estimation ◽  
Relative Treatment Effect

scholarly journals Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

2014 ◽  
Vol 11 (2) ◽  
pp. 193-201
Author(s):  
Baghdad Science Journal
Keyword(s):  
Current Model ◽  
Survival Function ◽  
Information Matrix ◽  
Interval Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

Biostatistics 1: Basic Concepts

2010 ◽  
pp. 3-11
Author(s):  
M. Hassan Murad ◽  
Qian Shi
Keyword(s):  
Odds Ratio ◽  
Sampling Error ◽  
Interval Estimation ◽  
Point Estimation ◽  
Descriptive Data ◽  
Sample Size Calculations ◽  
Measures Of Dispersion ◽  
Basic Concepts ◽  
Error Bias

Chapter 1 reviews basic concepts of biostatistics. Topics include descriptive data, probability and odds, estimation and sampling error, hypothesis testing, and power and sample size calculations. The discussion of descriptive data includes types of data (discrete vs continuous and nominal vs ordinal), central tendency (mean, median, and mode), skewed distributions, and measures of dispersion (range, variance, standard deviation). Probability and odds are broken down into laws of probability, odds, odds ratio, relative risk, and probability distribution. The examination of estimation and sampling error covers concepts such as random error, bias, standard error, point estimation, and interval estimation.

Estimating Interval of the Number of Errors for Embedded Software Development Projects

2014 ◽  
Vol 2 (3) ◽  
pp. 40-50 ◽  
Author(s):  
Kazunori Iwata ◽  
Toyoshiro Nakasima ◽  
Yoshiyuki Anan ◽  
Naohiro Ishii
Keyword(s):  
Neural Network ◽  
Support Vector Machine ◽  
Software Development ◽  
Previous Investigation ◽  
Interval Estimation ◽  
Embedded Software ◽  
Point Estimation ◽  
Support Vector ◽  
Development Projects ◽  
Artificial Neural Network Ann

Previous investigation focused on the prediction of total and errors for embedded software development projects using an artificial neural network (ANN). However, methods using ANNs have reached their improvement limits, since an appropriate value is estimated using what is known as point estimation in statistics. This paper proposes a method for predicting the number of errors for embedded software development projects using interval estimation provided by a support vector machine and ANN.

scholarly journals Catalytic prior distributions with application to generalized linear models

2020 ◽  
Vol 117 (22) ◽  
pp. 12004-12010
Author(s):  
Dongming Huang ◽  
Nathan Stein ◽  
Donald B. Rubin ◽  
S. C. Kou
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Synthetic Data ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Predictive Distribution ◽  
Point Estimation ◽  
Tuning Parameter ◽  
Working Model ◽  
Coverage Accuracy

A catalytic prior distribution is designed to stabilize a high-dimensional “working model” by shrinking it toward a “simplified model.” The shrinkage is achieved by supplementing the observed data with a small amount of “synthetic data” generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate.

scholarly journals Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2084
Author(s):  
Ali Yousef ◽  
Ayman A. Amin ◽  
Emad E. Hassan ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Asymptotic Results ◽  
Squared Error Loss Function ◽  
Estimation Problems ◽  
Width Confidence Interval

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

scholarly journals Sharp bounds on the relative treatment effect for ordinal outcomes

Biometrics ◽  
2019 ◽  
Vol 76 (2) ◽  
pp. 664-669
Author(s):  
Jiannan Lu ◽  
Yunshu Zhang ◽  
Peng Ding
Keyword(s):  
Treatment Effect ◽  
Sharp Bounds ◽  
Relative Treatment Effect

scholarly journals Sequential point and interval estimation of scale parameter of exponential distribution

1995 ◽  
Vol 18 (2) ◽  
pp. 383-390
Author(s):  
Z. Govindarajulu
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Stopping Time ◽  
Interval Estimation ◽  
Location Parameter ◽  
Exact Expression ◽  
Point Estimation ◽  
Quadratic Loss ◽  
Negative Exponential Distribution ◽  
Negative Exponential

Sequential fixed-width confidence intervals are obtained for the scale parameterσwhen the location parameterθof the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

Error propagation in simulated treatment comparisons for multiple myeloma: Results from a simulation.

2020 ◽  
Vol 38 (15_suppl) ◽  
pp. e20523-e20523
Author(s):  
Eric Mackay ◽  
Justin Slater ◽  
Paul Arora ◽  
Kristian Thorlund ◽  
Audrey Beliveau ◽  
...  
Keyword(s):  
Multiple Myeloma ◽  
Treatment Effect ◽  
Comparative Effectiveness ◽  
Error Propagation ◽  
Covariate Adjustment ◽  
Relative Treatment Effect ◽  
Kaplan Meier ◽  
Adjustment Term ◽  
Treatment Comparisons ◽  
True Treatment Effect

e20523 Background: Comparing the effectiveness of multiple myeloma treatments presents a challenge due to the limited number of head-to-head trials with which to conduct indirect treatment comparisons. This is particularly true when subgroup analysis is of interest. In comparative effectiveness research Simulated Treatment Comparisons (STCs) are becoming increasingly common in the absence of head-to-head trials. STCs use estimates from limited IPD to adjust for covariate imbalance between trials, however the uncertainty from these estimates is generally ignored when estimating relative treatment effects. This study demonstrates the need to account for this uncertainty when conducting STCs for indications such as multiple myeloma. We introduce an STC method that accounts for the uncertainty due to covariate adjustment, and demonstrate its effectiveness via simulation. Methods: We simulated two single arm studies (N = 300 for both), each containing age and overall survival. We assume study 1 has individual patient data available, and study 2 only has aggregate age data and a digitized Kaplan-Meier curve. We compute a covariate adjustment term based on the mean age difference between the studies and the age coefficients from fitting a parametric survival model to the observed study 1 IPD. We then estimate the variance of this adjustment term via bootstrapping and incorporate this uncertainty into a Bayesian STC model which estimates the relative treatment effect for the two study datasets converted to a digitized Kaplan-Meier format. Results: The proportion of 95% credible intervals (CrI) that captured the true treatment effect was 86.8% without error propagation, whereas 92.0% of CrI’s captured the true treatment with error propagation. 94.9% of CrI’s contained the true treatment effect when using survival regression with the complete IPD. Conclusions: Failing to account for uncertainty from the covariate adjustment when conducting simulated treatment comparisons generally leads to underestimating the uncertainty of the relative treatment effect. This method better captures the uncertainty introduced when conducting an STC and has the potential to yield more reliable estimates of the comparative effectiveness of multiple myeloma treatments.

scholarly journals Austenite Grain Size Estimtion from Chord Lengths of Logarithmic-Normal Distribution

2017 ◽  
Vol 62 (4) ◽  
pp. 2015-2019
Author(s):  
H. Adrian ◽  
K. Wiencek
Keyword(s):  
Grain Size ◽  
Normal Distribution ◽  
Gamma Distribution ◽  
Interval Estimation ◽  
Random Variable ◽  
Point Estimation ◽  
Size Estimation ◽  
Present Contribution ◽  
Austenite Grain Size ◽  
The One

AbstractLinear section of grains in polyhedral material microstructure is a system of chords. The mean length of chords is the linear grain size of the microstructure. For the prior austenite grains of low alloy structural steels, the chord length is a random variable of gamma- or logarithmic-normal distribution. The statistical grain size estimation belongs to the quantitative metallographic problems. The so-called point estimation is a well known procedure. The interval estimation (grain size confidence interval) for the gamma distribution was given elsewhere, but for the logarithmic-normal distribution is the subject of the present contribution. The statistical analysis is analogous to the one for the gamma distribution.

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