scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

Chronological Bias in Randomized Clinical Trials Arising from Different Types of Unobserved Time Trends

2014 ◽  
Vol 53 (06) ◽  
pp. 501-510 ◽  
Author(s):  
R.-D. Hilgers ◽  
M. Tamm
Keyword(s):  
Treatment Effect ◽  
Time Trends ◽  
Type I Error ◽  
Mean Squared Error ◽  
Block Size ◽  
T Test ◽  
Design Stage ◽  
Type I ◽  
Inflated Type ◽  
Block Sizes

SummaryBackground: In clinical trials patients are commonly recruited sequentially over time incurring the risk of chronological bias due to (unobserved) time trends. To minimize the risk of chronological bias, a suitable randomization procedure should be chosen.Objectives: Considering different time trend scenarios, we aim at a detailed evaluation of the extent of chronological bias under permuted block randomization in order to provide recommendations regarding the choice of randomization at the design stage of a clinical trial and to assess the maximum extent of bias for a realized sequence in the analysis stage.Methods: For the assessment of chronological bias we consider linear, logarithmic and stepwise trends illustrating typical changes during recruitment in clinical practice. Bias and variance of the treatment effect estimator as well as the empirical type I error rate when applying the t-test are investigated. Different sample sizes, block sizes and strengths of time trends are considered.Results: Using large block sizes, a notable bias exists in the estimate of the treatment effect for specific sequences. This results in a heavily inflated type I error for realized worst-case sequences and an enlarged mean squared error of the treatment effect estimator. Decreasing the block size restricts these effects of time trends. Already applying permuted block randomization with two blocks instead of the random allocation rule achieves a good reduction of the mean squared error and of the inflated type I error. Averaged over all sequences, the type I error of the t-test is far below the nominal significance level due to an overestimated variance.Conclusions: Unobserved time trends can induce a strong bias in the treatment effect estimate and in the test decision. Therefore, already in the design stage of a clinical trial a suitable randomization procedure should be chosen. According to our results, small block sizes should be preferred, but also medium block sizes are sufficient to restrict chronological bias to an acceptable extent if other contrary aspects have to be considered (e.g. serious risk of selection bias). Regardless of the block size, a blocked ANOVA should be used because the t-test is far too conservative, even for weak time trends.

scholarly journals A SIMULATION STUDY OF FIXED-B ASYMPTOTIC DISTRIBUTIONS IN LINEAR PANEL MODELS WITH FIXED EFFECTS

2020 ◽  
Vol 13 (2) ◽  
pp. 206-217
Author(s):  
Indah Rini Setyowati ◽  
Khairil Anwar Notodiputro ◽  
Anang Kurnia
Keyword(s):  
Panel Data ◽  
Asymptotic Distribution ◽  
Standard Method ◽  
Fixed Effects ◽  
Linear Models ◽  
Type I Error ◽  
Asymptotic Distributions ◽  
Type I ◽  
Test Statistic ◽  
Time Dimension

In linear models, panel data often violates the assumption that the error terms should be independent. As a result, the estimated variance is usually large and the standard inferential methods are not appropriate. The previous research developed an inference method to solve this problem using a variance estimator namely the Heteroskedasticity Autocorrelation Consistent of the Cross-Section Averages (HACSC), with some improvements. The test statistic of this method converges to the fixed-b asymptotic distribution. In this paper, the performance of the proposed inferential method is evaluated by means of simulation and compared with the standard method using plm package in R. Several comparisons regarding the Type I Error of these two methods have been carried out. The results showed that the statistical inference based on fixed-b asymptotic distribution out-perform the standard method, especially for the panel data with small number of individual and time dimension.

scholarly journals REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction

2021 ◽  
Author(s):  
Zaheer Ahmed ◽  
Alberto Cassese ◽  
Gerard van Breukelen ◽  
Jan Schepers
Keyword(s):  
Null Hypothesis ◽  
Type I Error ◽  
Type I ◽  
The Novel ◽  
Simulation Studies ◽  
Test Statistic ◽  
Clustering Model ◽  
Novel Method ◽  
Main Effects ◽  
Empirical Case Studies

AbstractWe present a novel method, REMAXINT, that captures the gist of two-way interaction in row by column (i.e., two-mode) data, with one observation per cell. REMAXINT is a probabilistic two-mode clustering model that yields two-mode partitions with maximal interaction between row and column clusters. For estimation of the parameters of REMAXINT, we maximize a conditional classification likelihood in which the random row (or column) main effects are conditioned out. For testing the null hypothesis of no interaction between row and column clusters, we propose a $$max-F$$ m a x - F test statistic and discuss its properties. We develop a Monte Carlo approach to obtain its sampling distribution under the null hypothesis. We evaluate the performance of the method through simulation studies. Specifically, for selected values of data size and (true) numbers of clusters, we obtain critical values of the $$max-F$$ m a x - F statistic, determine empirical Type I error rate of the proposed inferential procedure and study its power to reject the null hypothesis. Next, we show that the novel method is useful in a variety of applications by presenting two empirical case studies and end with some concluding remarks.

scholarly journals Another Warning about Median Reaction Time --- Version of 11 Feb 2020

2020 ◽  
Author(s):  
Jeff Miller
Keyword(s):  
Type I Error ◽  
Reaction Times ◽  
Error Rates ◽  
Type I ◽  
Experimental Conditions ◽  
Type I Error Rates ◽  
Correction Technique ◽  
Inflated Type ◽  
The Mean ◽  
Rt Distributions

Contrary to the warning of Miller (1988), Rousselet and Wilcox (2020) argued that it is better to summarize each participant’s single-trial reaction times (RTs) in a given condition with the median than with the mean when comparing the central tendencies of RT distributions across experimental conditions. They acknowledged that median RTs can produce inflated Type I error rates when conditions differ in the number of trials tested, consistent with Miller’s warning, but they showed that the bias responsible for this error rate inflation could be eliminated with a bootstrap bias correction technique. The present simulations extend their analysis by examining the power of bias-corrected medians to detect true experimental effects and by comparing this power with the power of analyses using means and regular medians. Unfortunately, although bias-corrected medians solve the problem of inflated Type I error rates, their power is lower than that of means or regular medians in many realistic situations. In addition, even when conditions do not differ in the number of trials tested, the power of tests (e.g., t-tests) is generally lower using medians rather than means as the summary measures. Thus, the present simulations demonstrate that summary means will often provide the most powerful test for differences between conditions, and they show what aspects of the RT distributions determine the size of the power advantage for means.

scholarly journals Generalized additive models and inflated type I error rates of smoother significance tests

2011 ◽  
Vol 55 (1) ◽  
pp. 366-374 ◽  
Author(s):  
Robin L. Young ◽  
Janice Weinberg ◽  
Verónica Vieira ◽  
Al Ozonoff ◽  
Thomas F. Webster
Keyword(s):  
Type I Error ◽  
Generalized Additive Models ◽  
Error Rates ◽  
Additive Models ◽  
Type I ◽  
Significance Tests ◽  
Type I Error Rates ◽  
Inflated Type

scholarly journals A novel gene-set association test based on variance-gamma distribution

2018 ◽  
Vol 28 (9) ◽  
pp. 2868-2875
Author(s):  
Zhongxue Chen ◽  
Qingzhong Liu ◽  
Kai Wang
Keyword(s):  
Gamma Distribution ◽  
Type I Error ◽  
Null Distribution ◽  
Real Data ◽  
Association Test ◽  
P Value ◽  
Type I ◽  
Test Statistic ◽  
Data Set ◽  
Variance Gamma

Several gene- or set-based association tests have been proposed recently in the literature. Powerful statistical approaches are still highly desirable in this area. In this paper we propose a novel statistical association test, which uses information of the burden component and its complement from the genotypes. This new test statistic has a simple null distribution, which is a special and simplified variance-gamma distribution, and its p-value can be easily calculated. Through a comprehensive simulation study, we show that the new test can control type I error rate and has superior detecting power compared with some popular existing methods. We also apply the new approach to a real data set; the results demonstrate that this test is promising.

No counts, no variance: allowing for loss of degrees of freedom when assessing biological variability from RNA-seq data

2017 ◽  
Vol 16 (2) ◽  
Author(s):  
Aaron T. L. Lun ◽  
Gordon K. Smyth
Keyword(s):  
Software Package ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Linear Models ◽  
Type I Error ◽  
Real Data ◽  
Type I ◽  
Rna Seq ◽  
Study Gene Expression ◽  
Complex Models

AbstractRNA sequencing (RNA-seq) is widely used to study gene expression changes associated with treatments or biological conditions. Many popular methods for detecting differential expression (DE) from RNA-seq data use generalized linear models (GLMs) fitted to the read counts across independent replicate samples for each gene. This article shows that the standard formula for the residual degrees of freedom (d.f.) in a linear model is overstated when the model contains fitted values that are exactly zero. Such fitted values occur whenever all the counts in a treatment group are zero as well as in more complex models such as those involving paired comparisons. This misspecification results in underestimation of the genewise variances and loss of type I error control. This article proposes a formula for the reduced residual d.f. that restores error control in simulated RNA-seq data and improves detection of DE genes in a real data analysis. The new approach is implemented in the quasi-likelihood framework of the edgeR software package. The results of this article also apply to RNA-seq analyses that apply linear models to log-transformed counts, such as those in the limma software package, and more generally to any count-based GLM where exactly zero fitted values are possible.

Parametric Alternatives to the Analysis of Variance

1982 ◽  
Vol 7 (3) ◽  
pp. 207-214 ◽  
Author(s):  
Jennifer J. Clinch ◽  
H. J. Keselman
Keyword(s):  
Monte Carlo ◽  
Analysis Of Variance ◽  
Monte Carlo Methods ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
F Test ◽  
Assumption Violations ◽  
Mean Equality

The ANOVA, Welch, and Brown and Forsyth tests for mean equality were compared using Monte Carlo methods. The tests’ rates of Type I error and power were examined when populations were non-normal, variances were heterogeneous, and group sizes were unequal. The ANOVA F test was most affected by the assumption violations. The test proposed by Brown and Forsyth appeared, on the average, to be the “best” test statistic for testing an omnibus hypothesis of mean equality.

scholarly journals Capturing the Dynamical Repertoire of Single Neurons with Generalized Linear Models

2017 ◽  
Vol 29 (12) ◽  
pp. 3260-3289 ◽  
Author(s):  
Alison I. Weber ◽  
Jonathan W. Pillow
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Spike Timing ◽  
Process Models ◽  
Type I ◽  
Linear Filters ◽  
Recurrent Point ◽  
Response Properties ◽  
Electrophysiological Recordings ◽  
Wide Range

A key problem in computational neuroscience is to find simple, tractable models that are nevertheless flexible enough to capture the response properties of real neurons. Here we examine the capabilities of recurrent point process models known as Poisson generalized linear models (GLMs). These models are defined by a set of linear filters and a point nonlinearity and are conditionally Poisson spiking. They have desirable statistical properties for fitting and have been widely used to analyze spike trains from electrophysiological recordings. However, the dynamical repertoire of GLMs has not been systematically compared to that of real neurons. Here we show that GLMs can reproduce a comprehensive suite of canonical neural response behaviors, including tonic and phasic spiking, bursting, spike rate adaptation, type I and type II excitation, and two forms of bistability. GLMs can also capture stimulus-dependent changes in spike timing precision and reliability that mimic those observed in real neurons, and can exhibit varying degrees of stochasticity, from virtually deterministic responses to greater-than-Poisson variability. These results show that Poisson GLMs can exhibit a wide range of dynamic spiking behaviors found in real neurons, making them well suited for qualitative dynamical as well as quantitative statistical studies of single-neuron and population response properties.

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