Quantifying the regression to the mean effect in Poisson processes

Khan, Mazhar; Olivier, Jake

doi:10.1002/sim.7850

Cited by 4 publications

(3 citation statements)

References 24 publications

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“…Regression to normal glucose regulation (RNGR) was defined as HbA1c <5.5% in the final visit to avoid the regression to the mean bias, 16 frequently observed in single measurements such as fasting glucose and 2-hour glucose. Prediabetes maintenance was defined as having at least one of the prediabetes criteria in the last visit.…”

Section: Methodsmentioning

confidence: 99%

Metabolomic markers of glucose regulation after a lifestyle intervention in prediabetes

Sevilla-González

Manning

Westerman

et al. 2022

BMJ Open Diab Res Care

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IntroductionDisentangling the specific factors that regulate glycemia from prediabetes to normoglycemia could improve type 2 diabetes prevention strategies. Metabolomics provides substantial insights into the biological understanding of environmental factors such as diet. This study aimed to identify metabolomic markers of regression to normoglycemia in the context of a lifestyle intervention (LSI) in individuals with prediabetes.Research design and methodsWe conducted a single-arm intervention study with 24 weeks of follow-up. Eligible study participants had at least one prediabetes criteria according to the American Diabetes Association guidelines, and body mass index between 25 and 45 kg/m2. LSI refers to a hypocaloric diet and >150 min of physical activity per week. Regression to normoglycemia (RNGR) was defined as achieving hemoglobin A1c (HbA1c) <5.5% in the final visit. Baseline and postintervention plasma metabolomic profiles were measured using liquid chromatography-tandem mass spectrometry. To select metabolites associated with RNGR, we conducted the least absolute shrinkage and selection operator-penalized regressions.ResultsThe final sample was composed of 82 study participants. Changes in three metabolites were significantly associated with regression to normoglycemia; N-acetyl-D-galactosamine (OR=0.54; 95% CI 0.32 to 0.82), putrescine (OR=0.90, 95% CI 0.81 to 0.98), and 7-methylguanine (OR=1.06; 95% CI 1.02 to 1.17), independent of HbA1c and weight loss. In addition, metabolomic perturbations due to LSI displayed enrichment of taurine and hypotaurine metabolism pathway (p=0.03) compatible with biomarkers of protein consumption, lower red meat and animal fats and higher seafood and vegetables.ConclusionsEvidence from this study suggests that specific metabolomic markers have an influence on glucose regulation in individuals with prediabetes after 24 weeks of LSI independently of other treatment effects such as weight loss.

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Section: Methodsmentioning

confidence: 99%

Metabolomic markers of glucose regulation after a lifestyle intervention in prediabetes

Sevilla-González

Manning

Westerman

et al. 2022

BMJ Open Diab Res Care

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show abstract

“…Using the definition of the total observed effect T ( y 0 , θ ) in Equation , Khan and Olivier derived expressions for T ( y 0 , θ ) under the assumption of the bivariate Poisson distribution of successive occurrences, given by

T (y_{0}, θ) = θ_{1} \frac{1 - F (y_{0} - 1 | θ_{0} + θ_{1})}{1 - F (y_{0} | θ_{0} + θ_{1})} - θ_{2},

where y 0 is the cut‐off point and

F false(y false| λ false) = \sum_{t = 0}^{y} e^{- λ} λ^{t} false/ t!

. The related expressions for RTM and intervention effects are given by

\begin{matrix} alignleft \\ align-1 R (y_{0}, θ) = θ_{1} \cdot \frac{P (y_{0} | θ_{0} + θ_{1})}{1 - F (y_{0} | θ_{0} + θ_{1})}, & align-2 \end{matrix}

where P ( y | λ ) = e − λ λ y / y !…”

Section: Regression To the Mean For The Bivariate Normal And Poisson mentioning

confidence: 99%

“…Gardner and Heady and Davis derived a formula for calculating the expected RTM effect under an assumption of bivariate normality of the pre and post observations. Similarly, Khan and Olivier derived expressions for the RTM effect assuming the bivariate Poisson distribution for pre and post counts.…”

Section: Introductionmentioning

confidence: 99%

Regression to the mean for the bivariate binomial distribution

Khan

Olivier

2019

Statistics in Medicine

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Regression to the mean (RTM) occurs when subjects having relatively high or low measurements are remeasured and found closer to the population mean. This phenomenon can potentially lead to an inaccurate conclusion in a pre-post study design. Expressions are available for quantifying RTM when the distribution of pre and post observations are bivariate normal and bivariate Poisson. However, situations exist where the response variables are the number of successes in a fixed number of trials and follow the bivariate binomial distribution. In this article, expressions for quantifying RTM effects are derived when the underlying distribution is the bivariate binomial. Unlike the normal and Poisson distributions, the correlation between pre and post observations can be either negative or positive under the bivariate binomial distribution and the severity of RTM is greater in the former case. The percentage relative difference is used to highlight the differences in quantifying RTM under the bivariate binomial distribution and normal and Poisson approximations to the bivariate binomial distribution. Expressions for estimating RTM using the method of maximum likelihood along with its asymptotic distribution are derived. A simulation study is conducted to empirically assess the statistical properties of the RTM estimator and its asymptotic distribution. Data examples using the number of obese individuals and the number of nonconforming cardboard cans are discussed. KEYWORDS bivariate binomial distribution, intervention effects, regression to the mean Statistics in Medicine. 2019;38:2391-2412.wileyonlinelibrary.com/journal/sim

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Regression to the mean: Estimation and adjustment under the bivariate normal distribution

Khan

Olivier

2022

Communications in Statistics - Theory and Methods

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Quantifying the regression to the mean effect in Poisson processes

Cited by 4 publications

References 24 publications

Metabolomic markers of glucose regulation after a lifestyle intervention in prediabetes

Metabolomic markers of glucose regulation after a lifestyle intervention in prediabetes

Regression to the mean for the bivariate binomial distribution

Regression to the mean: Estimation and adjustment under the bivariate normal distribution

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