Reliability of Pharmacodynamic Analysis by Logistic Regression

2000 ◽  
Vol 92 (4) ◽  
pp. 985-992 ◽  
Author(s):  
Wei Lu ◽  
James M. Bailey
Keyword(s):  
Logistic Regression ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Parameter Estimates ◽  
True Parameter ◽  
True Value ◽  
Coefficients Of Variation ◽  
Effect Relation ◽  
Log Normal ◽  
Multiple Patients

Background Many pharmacologic studies record data as binary yes-or-no variables, and analysis is performed using logistic regression. This study investigates the accuracy of estimation of the drug concentration associated with a 50% probability of drug effect (C50) and the term describing the steepness of the concentration-effect relation (gamma). Methods The authors developed a technique for simulating pharmacodynamic studies with binary yes-or-no responses. Simulations were conducted assuming either that each data point was derived from the same patient or that data were pooled from multiple patients in a population with log-normal distributions of C50 and gamma. Coefficients of variation were calculated. The authors also determined the percentage of simulations in which the 95% confidence intervals contained the true parameter value. Results The coefficient of variation of parameter estimates decreased with increasing n and gamma. The 95% confidence intervals for C50 estimation contained the true parameter value in more than 90% of the simulations. However, the 95% confidence intervals of gamma did not contain the true value in a substantial number of simulations of data from multiple patients. Conclusion The coefficient of variation of parameter estimates may be as large as 40-50% for small studies (n < or = 20). The 95% confidence intervals of C50 almost always contain the true value, underscoring the need for always reporting confidence intervals. However, when data from multiple patients is naively pooled, the estimates of gamma may be biased, and the 95% confidence intervals may not contain the true value.

scholarly journals Analyzing data from memory tasks - comparison of ANOVA, logistic regression and mixed logit model

Psihologija ◽  
2018 ◽  
Vol 51 (4) ◽  
pp. 469-488
Author(s):  
Milica Popovic-Stijacic ◽  
Ljiljana Mihic ◽  
Dusica Filipovic-Djurdjevic
Keyword(s):  
Logistic Regression ◽  
Confidence Intervals ◽  
Logit Model ◽  
Linear Models ◽  
Mixed Logit ◽  
Binary Logistic Regression ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Mixed Logit Model ◽  
Mixed Logit Models

We compared three statistical analyses over binary outcomes. As applying ANOVA over proportions violates at least two classical assumptions of linear models, two alternatives are described: the binary logistic regression and the mixed logit model. Firstly, we compared the effects obtained by the three methods over the same data from a previous memory research. All three methods gave similar results: the effects of the tasks and the number of sensory modalities were observed, but not their interaction. Secondly, by using the bootstrap estimates of the parameters, the efficacy of each method was explored. As predicted, the bootstrap parameter estimates of the ANOVA had large bias and standard errors, and consequently wide confidence intervals. On the other hand, the bootstrap parameter estimates of the binary logistic regression and the mixed logit models were similar ? both had low bias and standard errors and narrow confidence intervals.

scholarly journals Confidence intervals for the common coefficient of variation of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10004
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Daily Rainfall ◽  
Moisture Index ◽  
Interval Estimates ◽  
The Common ◽  
Log Normal ◽  
Confidence Interval Estimates

The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (nI < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.

Infinite Parameter Estimates in Logistic Regression: Opportunities, Not Problems

2002 ◽  
Vol 27 (2) ◽  
pp. 147-161 ◽  
Author(s):  
David Rindskopf
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Strict Sense ◽  
Hypothesis Tests ◽  
Infinite Slope ◽  
Alternative Method

Infinite parameter estimates in logistic regression are commonly thought of as a problem. This article shows that in principle an analyst should be happy to have an infinite slope in logistic regression, because it indicates that a predictor is perfect. Using simple approaches, hypothesis tests may be performed and confidence intervals calculated even when a slope is infinite. Some functions of parameters that are infinite are still well defined, and reasonable estimates of these quantities (in particular, LD50) may be obtained even when the maximum likelihood estimates do not, in a strict sense, exist. Surprisingly, these techniques can provide more reasonable and useful results than the most popular alternative method, exact logistic regression.

Reliability of Pharmacodynamic Analysis by Logistic Regression

2003 ◽  
Vol 99 (6) ◽  
pp. 1255-1262 ◽  
Author(s):  
Wei Lu ◽  
James G. Ramsay ◽  
James M. Bailey
Keyword(s):  
Logistic Regression ◽  
Coefficient Of Variation ◽  
Binary Data ◽  
Sparse Data ◽  
Unbiased Estimation ◽  
Data Sets ◽  
Data Set ◽  
True Value ◽  
Data Points ◽  
Data Point

Background Many pharmacologic studies record data as binary, yes-or-no, variables with analysis using logistic regression. In a previous study, it was shown that estimates of C50, the drug concentration associated with a 50% probability of drug effect, were unbiased, whereas estimates of gamma, the term describing the steepness of the concentration-effect relationship, were biased when sparse data were naively pooled for analysis. In this study, it was determined whether mixed-effects analysis improved the accuracy of parameter estimation. Methods Pharmacodynamic studies with binary, yes-or-no, responses were simulated and analyzed with NONMEM. The bias and coefficient of variation of C50 and gamma estimates were determined as a function of numbers of patients in the simulated study, the number of simulated data points per patient, and the "true" value of gamma. In addition, 100 sparse binary human data sets were generated from an evaluation of midazolam for postoperative sedation of adult patients undergoing cardiac surgery by random selection of a single data point (sedation score vs. midazolam plasma concentration) from each of the 30 patients in the study. C50 and gamma were estimated for each of these data sets by using NONMEM and were compared with the estimates from the complete data set of 656 observations. Results Estimates of C50 were unbiased, even for sparse data (one data point per patient) with coefficients of variation of 30-50%. Estimates of gamma were highly biased for sparse data for all values of gamma greater than 1, and the value of gamma was overestimated. Unbiased estimation of gamma required 10 data points per patient. The coefficient of variation of gamma estimates was greater than that of the C50 estimates. Clinical data for sedation with midazolam confirmed the simulation results, showing an overestimate of gamma with sparse data. Conclusion Although accurate estimations of C50 from sparse binary data are possible, estimates of gamma are biased. Data with 10 or more observations per patient is necessary for accurate estimations of gamma.

scholarly journals Bayesian Confidence Intervals for Coefficients of Variation of PM10 Dispersion

2021 ◽  
Vol 5 (2) ◽  
pp. 139-154
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Bayesian Approach ◽  
Normal Distributions ◽  
Coefficients Of Variation ◽  
The Difference ◽  
Log Normal ◽  
Log Normal Distribution ◽  
The Bayesian Approach

Herein, we propose the Bayesian approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. For the first case, the Bayesian approach was compared with large-sample, Chi-squared, and approximate fiducial approaches via Monte Carlo simulation. For the second case, the Bayesian approach was compared with the method of variance estimates recovery (MOVER), modified MOVER, and approximate fiducial approaches using Monte Carlo simulation. The results show that the Bayesian approach provided the best approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. To illustrate the performances of the confidence limit construction approaches with real data, they were applied to analyze real PM10 datasets from the Nan and Chiang Mai provinces in Thailand, the results of which are in agreement with the simulation results. Doi: 10.28991/esj-2021-01264 Full Text: PDF

scholarly journals A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions

2021 ◽  
Vol 50 (1) ◽  
pp. 261-278
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Bayesian Approaches ◽  
Normal Distributions ◽  
Generalized Confidence Interval ◽  
Coefficients Of Variation ◽  
The Difference ◽  
Highest Posterior Density

The coefficient of variation is widely used as a measure of data precision. Confidence intervals for a single coefficient of variation when the data follow a normal distribution that is symmetrical and the difference between the coefficients of variation of two normal populations are considered in this paper. First, the confidence intervals for the coefficient of variation of a normal distribution are obtained with adjusted generalized confidence interval (adjusted GCI), computational, Bayesian, and two adjusted Bayesian approaches. These approaches are compared with existing ones comprising two approximately unbiased estimators, the method of variance estimates recovery (MOVER) and generalized confidence interval (GCI). Second, the confidence intervals for the difference between the coefficients of variation of two normal distributions are proposed using the same approaches, the performances of which are then compared with the existing approaches. The highest posterior density interval was used to estimate the Bayesian confidence interval. Monte Carlo simulation was used to assess the performance of the confidence intervals. The results of the simulation studies demonstrate that the Bayesian and two adjusted Bayesian approaches were more accurate and better than the others in terms of coverage probabilities and average lengths in both scenarios. Finally, the performances of all of the approaches for both scenarios are illustrated via an empirical study with two real-data examples.

Confidence Intervals for the Coefficient of Variation for the Normal and Log Normal Distributions

Biometrika ◽  
1964 ◽  
Vol 51 (1/2) ◽  
pp. 25 ◽  
Author(s):  
L. H. Koopmans ◽  
D. B. Owen ◽  
J. I. Rosenblatt
Keyword(s):  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Normal Distributions ◽  
Log Normal
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