On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

scholarly journals G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Florent Le Borgne ◽  
Arthur Chatton ◽  
Maxime Léger ◽  
Rémi Lenain ◽  
Yohann Foucher
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Statistical Power ◽  
Small Sample ◽  
Causal Effects ◽  
Small Samples ◽  
Support Vector ◽  
Sample Sizes ◽  
Super Learner ◽  
Small Sample Sizes

AbstractIn clinical research, there is a growing interest in the use of propensity score-based methods to estimate causal effects. G-computation is an alternative because of its high statistical power. Machine learning is also increasingly used because of its possible robustness to model misspecification. In this paper, we aimed to propose an approach that combines machine learning and G-computation when both the outcome and the exposure status are binary and is able to deal with small samples. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We proposed six different scenarios characterised by various sample sizes, numbers of covariates and relationships between covariates, exposure statuses, and outcomes. We have also illustrated the application of these methods, in which they were used to estimate the efficacy of barbiturates prescribed during the first 24 h of an episode of intracranial hypertension. In the context of GC, for estimating the individual outcome probabilities in two counterfactual worlds, we reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. In the investigated scenarios, G-computation associated with the super learner was a performant method for drawing causal inferences, even from small sample sizes.

Implications of Small Samples for Generalization: Adjustments and Rules of Thumb

2016 ◽  
Vol 41 (5) ◽  
pp. 472-505 ◽  
Author(s):  
Elizabeth Tipton ◽  
Kelly Hallberg ◽  
Larry V. Hedges ◽  
Wendy Chan
Keyword(s):  
Observational Studies ◽  
Small Sample ◽  
Average Treatment Effect ◽  
Small Samples ◽  
Sample Sizes ◽  
Random Samples ◽  
Rules Of Thumb ◽  
Large Populations ◽  
Small Sample Sizes ◽  
Combine Information

Background: Policy makers and researchers are frequently interested in understanding how effective a particular intervention may be for a specific population. One approach is to assess the degree of similarity between the sample in an experiment and the population. Another approach is to combine information from the experiment and the population to estimate the population average treatment effect (PATE). Method: Several methods for assessing the similarity between a sample and population currently exist as well as methods estimating the PATE. In this article, we investigate properties of six of these methods and statistics in the small sample sizes common in education research (i.e., 10–70 sites), evaluating the utility of rules of thumb developed from observational studies in the generalization case. Result: In small random samples, large differences between the sample and population can arise simply by chance and many of the statistics commonly used in generalization are a function of both sample size and the number of covariates being compared. The rules of thumb developed in observational studies (which are commonly applied in generalization) are much too conservative given the small sample sizes found in generalization. Conclusion: This article implies that sharp inferences to large populations from small experiments are difficult even with probability sampling. Features of random samples should be kept in mind when evaluating the extent to which results from experiments conducted on nonrandom samples might generalize.

Heart Rate Variability And Respiratory Muscle Strength In Patients With Type Ii Diabetes Practicing Pilates: A Randomized Clinical Trial

2021 ◽  
Vol 17 ◽  
Author(s):  
Samara Sousa Vasconcelos Gouveia ◽  
Guilherme Pertinni de Morais Gouveia ◽  
Leydnaya Maria Souza ◽  
Bruno Cunha da Costa ◽  
Gustavo Henrique Melo Sousa ◽  
...  
Keyword(s):  
Clinical Trial ◽  
Heart Rate ◽  
Heart Rate Variability ◽  
Muscle Strength ◽  
Normal Distribution ◽  
Randomized Clinical Trial ◽  
Respiratory Muscle ◽  
Control Group ◽  
Respiratory Muscle Strength

Purpose: This study aimed to analyze the effect of a Pilates protocol on respiratory muscle strength and heart rate variability (HRV) in patients with type 2 diabetes. Method: A randomized clinical trial (RBR-2gc2qj) was conducted with a type 2 diabetic target population. Patients practiced the Pilates protocol for 8 weeks, with two visits per week. The variables tested were maximum inspiratory pressure (MIP), maximum expiratory pressure (MEP), and HRV (time and frequency domains). All variables were tested for normal distribution. Using SPSS 21.0, analysis of variance was performed for variables with normal distribution, and the Wilcoxon and Friedman tests were used for variables that did not show a normal distribution, with a 5% significance level. Results: Forty-four participants were included in the study (intervention group: 22; control group: 22; mean age: 61.23 ± 8.49 years), most of whom were female (77.3%), married or in a consensual union (59.1%), had complete literacy (31.8%), and had an average body mass index of 26.96 ± 4.35 kg/m2. There were no significant differences in MIP and MEP before and after the protocol between the intervention and control groups. Regarding HRV, there were significant differences in autonomic modulation, especially between the moments before and during exercise and between the moments during and after exercise; however, it was not possible to determine which system (sympathetic or parasympathetic) is most involved in these changes. Conclusion: The exercise protocol based on the Pilates method did not alter respiratory muscle strength but promoted changes in HRV, especially between the moments before and during exercise and during and after exercise.

Control arm heterogeneity in trials for unselected advanced triple-negative breast cancer (aTNBC).

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. 1082-1082
Author(s):  
Kinisha Gala ◽  
Ankit Kalucha ◽  
Samuel Martinet ◽  
Anushri Goel ◽  
Kalpana Devi Narisetty ◽  
...  
Keyword(s):  
Clinical Trial ◽  
Clinical Trials ◽  
Sample Size ◽  
Single Agent ◽  
Progression Free Survival ◽  
Sample Sizes ◽  
Time To Event ◽  
Sample Size Calculations ◽  
Subgroup Analyses ◽  
Combination Regimens

1082 Background: Primary endpoints of clinical trials frequently include subgroup-analyses. Several solid cancers such as aTNBC are heterogeneous, which can lead to unpredictable control arm performance impairing accurate assumptions for sample size calculations. We explore the value of a comprehensive clinical trial results repository in assessing control arm heterogeneity with aTNBC as the pilot. Methods: We identified P2/3 trials reporting median overall survival (mOS) and/or median progression-free survival (mPFS) in unselected aTNBC through a systematic search of PubMed, clinical trials databases and conference proceedings. Trial arms with sample sizes ≤25 or evaluating drugs no longer in development were excluded. Due to inconsistency among PD-L1 assays, PD-L1 subgroup analyses were not assessed separately. The primary aim was a descriptive analysis of control arm mOS and mPFS across all randomized trials in first line (1L) aTNBC. Secondary aims were to investigate time-to-event outcomes in control arms in later lines and to assess time-trends in aTNBC experimental and control arm outcomes. Results: We included 33 trials published between June 2013-Feb 2021. The mOS of control arms in 1L was 18.7mo (range 12.6-22.8) across 5 trials with single agent (nab-) paclitaxel [(n)P], and 18.1mo (similar range) for 7 trials including combination regimens (Table). The mPFS of control arms in 1L was 4.9mo (range 3.8-5.6) across 5 trials with single-agent (n)P, and 5.6mo (range 3.8-6.1) across 8 trials including combination regimens. Control arm mOS was 13.1mo (range 9.4-17.4) for 3 trials in first and second line (1/2L) and 8.7mo (range 6.7-10.8) across 5 trials in 2L and beyond. R2 for the mOS best-fit lines across control and experimental arms over time was 0.09, 0.01 and 0.04 for 1L, 1/2L and 2L and beyond, respectively. Conclusions: Median time-to-event outcomes of control arms in 1L aTNBC show considerable heterogeneity, even among trials with comparable regimens and large sample sizes. Disregarding important prognostic factors at stratification can lead to imbalances between arms, which may jeopardize accurate sample size calculations, trial results and interpretation. Optimizing stratification and assumptions for power calculations is of utmost importance in aTNBC and beyond. A digitized trial results repository with precisely defined patient populations and treatment settings could improve accuracy of assumptions during clinical trial design.[Table: see text]

scholarly journals Conservative Estimations of Reliability With Limited Sampling

2007 ◽  
Author(s):  
Victor Picheny ◽  
Nam-Ho Kim ◽  
Raphael T. Haftka
Keyword(s):  
Normal Distribution ◽  
Thermal Loading ◽  
Bootstrap Method ◽  
Composite Panel ◽  
Small Samples ◽  
Normal Distribution Function ◽  
Limited Sampling ◽  
Bootstrap Approach ◽  
The Relationship ◽  
The Bootstrap Method

The objective of this paper is to provide a method of safely estimating reliability based on small samples. First, it is shown that the commonly used estimators of the parameters of the normal distribution function are biased, and they tend to lead to unconservative estimates of reliability. Then, two ways of making this estimation conservative are proposed: (1) adding constraints when a distribution is fitted to the data to bias it to be conservative, and (2) using the bootstrap method to estimate the bias needed for a given level of conservativeness. The relationship between the accuracy and the conservativeness of the estimates is explored for a normal distribution. In particular, detailed results are presented for the case when the goal is 95% likelihood to be conservative. The bootstrap approach is found to be more accurate for this level of conservativeness. It is then applied to the reliability analysis of a composite panel under thermal loading. Finally, we explore the influence of sample sizes and target probability of failure on estimates quality, and show that for a constant level of conservativeness, small samples and low probabilities can lead to a high risk of large overestimation while this risk is limited to a very reasonable value for samples above.

scholarly journals A refinement of normal approximation to Poisson binomial

2005 ◽  
Vol 2005 (5) ◽  
pp. 717-728 ◽  
Author(s):  
K. Neammanee
Keyword(s):  
Normal Distribution ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Standard Normal Distribution ◽  
Bernoulli Random Variables ◽  
Binomial Random Variable ◽  
Standard Normal ◽  
Correction Terms ◽  
Better Than

LetX1,X2,…,Xnbe independent Bernoulli random variables withP(Xj=1)=1−P(Xj=0)=pjand letSn:=X1+X2+⋯+Xn.Snis called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor's formula to improve the approximation by adding some correction terms. Our result is better than before and is of order1/nin the casep1=p2=⋯=pn.

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