Identifying predictors of resilience to stressors in single-arm studies of pre-post change.

Many older adults experience a major stressor at some point in their lives. The ability to recover well after a major stressor is known as resilience. An important goal of geriatric research is to identify factors that influence resilience to stressors. Studies of resilience in older adults are typically conducted with a single-arm where everyone experiences the stressor. The simplistic approach of regressing change versus baseline yields biased estimates due to mathematical coupling and regression to the mean (RTM). We develop a method to correct the bias. We extend the method to include covariates. Our approach considers a counterfactual control group and involves sensitivity analyses to evaluate different settings of control group parameters. Only minimal distributional assumptions are required. Simulation studies demonstrate the validity of the method. We illustrate the method using a large, registry of older adults (N  =7239) who underwent total knee replacement (TKR). We demonstrate how external data can be utilized to constrain the sensitivity analysis. Naive analyses implicated several treatment effect modifiers including baseline function, age, body-mass index (BMI), gender, number of comorbidities, income, and race. Corrected analysis revealed that baseline (pre-stressor) function was not strongly linked to recovery after TKR and among the covariates, only age and number of comorbidities were consistently and negatively associated with post-stressor recovery in all functional domains. Correction of mathematical coupling and RTM is necessary for drawing valid inferences regarding the effect of covariates and baseline status on pre-post change. Our method provides a simple estimator to this end.

A unified Bayesian framework for bias adjustment in multiple comparisons from clinical trials.

In clinical trials, multiple comparisons arising from various treatments/doses, subgroups, or endpoints are common. Typically, trial teams focus on the comparison showing the largest observed treatment effect, often involving a specific treatment pair and endpoint within a subgroup. These findings frequently lead to follow-up pivotal studies, many of which do not confirm the initial positive results. Selection bias occurs when the most promising treatment, subgroup, or endpoint is chosen for further development, potentially skewing subsequent investigations. Such bias can be defined as the deviation in the observed treatment effects from the underlying truth. In this article, we propose a general and unified Bayesian framework to address selection bias in clinical trials with multiple comparisons. Our approach does not require a priori specification of a parametric distribution for the prior, offering a more flexible and generalized solution. The proposed method facilitates a more accurate interpretation of clinical trial results by adjusting for such selection bias. Through simulation studies, we compared several methods and demonstrated their superior performance over the normal shrinkage estimator. We recommended the use of Bayesian Model Averaging estimator averaging over Gaussian Mixture Models as the prior distribution based on its performance and flexibility. We applied the method to a multicenter, randomized, double-blind, placebo-controlled study investigating the cardiovascular effects of dulaglutide.

Perceptual narrowing continues throughout childhood: Evidence from specialization of face processing.

Face recognition shows a long trajectory of development and is known to be closely associated with the development of social skills. However, it is still debated whether this long trajectory is perceptually based and what the role is of experience-based refinements of face representations throughout development. We examined the effects of short and long-term experienced stimulus history on face processing, using regression biases of face representations towards the experienced mean. Children and adults performed same-different judgments in a serial discrimination task where two consecutive faces were drawn from a distribution of morphed faces. The results show that face recognition continues to improve after 9 years of age, with more pronounced improvements for own-race faces. This increased narrowing with age is also indicated by similar use of stimulus statistics for own-race and other-race faces in children, contrary to the different use of the overall stimulus history for these two face types in adults. Increased face proficiency in adulthood renders the perceptual system less tuned to other-race face statistics. Altogether, the results demonstrate associations between levels of specialization and the extent to which perceptual representations become narrowly tuned with age.

Initial soil organic carbon stocks govern changes in soil carbon: Reality or artifact?

Changes in soil organic carbon (SOC) storage have the potential to affect global climate; hence identifying environments with a high capacity to gain or lose SOC is of broad interest. Many cross-site studies have found that SOC-poor soils tend to gain or retain carbon more readily than SOC-rich soils. While this pattern may partly reflect reality, here we argue that it can also be created by a pair of statistical artifacts. First, soils that appear SOC-poor purely due to random variation will tend to yield more moderate SOC estimates upon resampling and hence will appear to accrue or retain more SOC than SOC-rich soils. This phenomenon is an example of regression to the mean. Second, normalized metrics of SOC change-such as relative rates and response ratios-will by definition show larger changes in SOC at lower initial SOC levels, even when the absolute change in SOC does not depend on initial SOC. These two artifacts create an exaggerated impression that initial SOC stocks are a major control on SOC dynamics. To address this problem, we recommend applying statistical corrections to eliminate the effect of regression to the mean, and avoiding normalized metrics when testing relationships between SOC change and initial SOC. Careful consideration of these issues in future cross-site studies will support clearer scientific inference that can better inform environmental management.

No Placebo Effect beyond Regression to the Mean on the Six Minute Walk Test in Pulmonary Arterial Hypertension Trials.

In drug studies, patients are often included when the disease activity is high. This will make any treatment appear to lessen disease activity, although the improvement is biased by selection. This effect is known as regression towards the mean (RTM). We aimed at investigating drug trials in Pulmonary Arterial Hypertension (PAH) using the 6-minute walking distance test (6MWD) as a primary outcome for the phenomenon of RTM. An existing registry of 43 open label studies and 23 randomized controlled trials conducted between 1990 and 2009 was used as the data source. Data analysis was carried out for 18 randomized controlled trials (RCTs) and 24 open label studies out of this registry. Data were analyzed for verum and placebo arms of the RCTs separately, as well as for the open label arms. In the verum arms, the overall effect given as 33.2 m (95% CI: 25.7; 40.6]); 6MWD was slightly lower than the effect in the observational studies, with 44.6 m (95% CI: [25.4; 63.8]). After studying and interpreting the data, we found that regression towards the mean plays only a minor role in PAH studies. In particular, placebo effects in the RCTs were negligibly small, with a mean 6MWD of -2.5 m (95% CI: [-9.8; 4.7]) in the placebo arm. Therefore, our analysis indicates that results of non-randomized observational studies can be regarded as valid tools for gaining valid clinical effects in patients with PAH.

Regression to the mean in latent change score models: an example involving breastfeeding and intelligence.

BACKGROUND: Latent change score models are often used to study change over time in observational data. However, latent change score models may be susceptible to regression to the mean. Earlier observational studies have identified a positive association between breastfeeding and child intelligence, even when adjusting for maternal intelligence. METHOD: In the present study, we investigate regression to the mean in the case of breastfeeding and intelligence of children. We used latent change score modeling to analyze intergenerational change in intelligence, both from mothers to children and backward from children to mothers, in the 1979 National Longitudinal Survey of Youth (NLSY79) dataset (N = 6283). RESULTS: When analyzing change from mothers to children, breastfeeding was found to have a positive association with intergenerational change in intelligence, whereas when analyzing backward change from children to mothers, a negative association was found. CONCLUSIONS: These discrepant findings highlight a hidden flexibility in the analytical space and call into question the reliability of earlier studies of breastfeeding and intelligence using observational data.

Embodiment and learning of abstract concepts (such as algebraic topology and regression to the mean).

This video is a proof of concept that ideas from embodied cognition can be used to understand how the brain and cognitive systems deal with very abstract concepts. The video teaches regression to the mean using three ideas. The first idea is directly related to embodied cognition: abstract concepts are grounded in perceptual, motor, and emotional systems by using successive levels of grounding within an extended procedure. The second idea is that this sort of grounding often requires formal instruction: a teacher needs to develop the sequence in which the concepts are grounded and the methods of grounding. That is, at least some abstract concepts are unlikely to be learned through an individual's unstructured interactions with the world. The third idea is that humans are hyper-social, thus making formal instruction possible. To the extent that the viewer learns the abstract concept of regression to the mean, then the video demonstrates how an embodied theory of abstract concepts could work.

Adjusting for bias in the mean for primary and secondary outcomes when trials are in sequence.

When designing a clinical trial, one key aspect of the design is the sample size calculation. The sample size calculation tends to rely on a target or expected difference. The expected difference can be based on the observed data from previous studies, which results in bias. It has been reported that large treatment effects observed in trials are often not replicated in subsequent trials. If these values are used to design subsequent studies, the sample sizes may be biased which results in an unethical study. Regression to the mean (RTM) is one explanation for this. If only health technologies which meet a particular continuation criterion (such as p<0.05 in the first study) are progressed to a second confirmatory trial, it is highly likely that the observed effect in the second trial will be lower than that observed in the first trial. It will be shown how when moving from one trial to the next, a truncated normal distribution is inherently imposed on the first study. This results in a lower observed effect size in the second trial. A simple adjustment method is proposed based on the mathematical properties of the truncated normal distribution. This adjustment method was confirmed using simulations in R and compared with other previous adjustments. The method can be applied to the observed effect in a trial, which is being used in the design of a second confirmatory trial, resulting in a more stable estimate for the 'true' treatment effect. The adjustment accounts for the bias in the primary and secondary endpoints in the first trial with the bias being affected by the power of that study. Tables of results have been provided to aid implementation, along with a worked example. In summary, there is a bias introduced when the point estimate from one trial is used to assist the design of a second trial. It is recommended that any observed point estimates be used with caution and the adjustment method developed in this article be implemented to significantly reduce this bias.

Selection bias, investment decisions and treatment effect distributions.

When making decisions regarding the investment and design for a Phase 3 programme in the development of a new drug, the results from preceding Phase 2 trials are an important source of information. However, only projects in which the Phase 2 results show promising treatment effects will typically be considered for a Phase 3 investment decision. This implies that, for those projects where Phase 3 is pursued, the underlying Phase 2 estimates are subject to selection bias. We will in this article investigate the nature of this selection bias based on a selection of distributions for the treatment effect. We illustrate some properties of Bayesian estimates, providing shrinkage of the Phase 2 estimate to counteract the selection bias. We further give some empirical guidance regarding the choice of prior distribution and comment on the consequences for decision-making in investment and planning for Phase 3 programmes.

Francis Galton's regression towards mediocrity and the stability of types.

A prevalent narrative locates the discovery of the statistical phenomenon of regression to the mean in the work of Francis Galton. It is claimed that after 1885, Galton came to explain the fact that offspring deviated less from the mean value of the population than their parents did as a population-level statistical phenomenon and not as the result of the processes of inheritance. Arguing against this claim, we show that Galton did not explain regression towards mediocrity statistically, and did not give up on his ideas regarding an inheritance process that caused offspring to revert to the mean. While the common narrative focuses almost exclusively on Galton's statistics, our arguments emphasize the anthropological and biological questions that Galton addressed. Galton used regression towards mediocrity to support the claim that some biological types were more stable than others and hence were resistant to evolutionary change. This view had implications concerning both natural selection and eugenics. The statistical explanation attributed to Galton appeared later, during the biometrician-mutationist debate in the early 1900s. It was in the context of this debate and specifically by the biometricians, that the development of the statistical explanation was originally attributed to Galton.

Interpretation of within-group change in randomised trials.

In medicine, it is common to observe improvement after intervention, at least partly because patients present for care in extremis and would have improved without intervention. Controlling for this counterfactual explanation for improvement is the principle reason to conduct a trial in which patients are randomised to treatment or a control group. Accordingly, it is not reasonable to infer that both interventions are effective when the groups show similar improvements in outcome.

Influence of pre-treatment blood pressure levels on antihypertensive drug benefits in diabetics: the roadmap experience.

Purpose: Most guidelines for treatment of hypertension in the setting of diabetes recommend a blood pressure (BP) target of <130/80 mmHg. However, uncertainty exists about the extent, effectiveness and safety of lowering BP in diabetics. To expand the evidence on this issue, we analysed data from the Randomised Olmesartan and Diabetes MicroAlbuminuria Prevention (ROADMAP) study population.Material: Substudy with blood pressure readings.Methods: The response after initiation of therapy and adequacy of BP control across patients with different BP levels at baseline were analysed.Results: BP at randomisation was 136.2(15.3)/80.6(9.5) [mean (SD)] mmHg with a range of 87-213/37-123 mmHg. At 1 year, mean BP was 127 (11.9)/75 (8.1) mmHg and the overall control rate (<130/80 mmHg) exceeded 61% in this population. The mean reductions in systolic [-9.4 (15.4) mmHg] and diastolic BP [-5.4 (9.5) mmHg] were highly dependent on the BP stage at Visit 1. At 1 year, treatment decreased the prevalence of patients with baseline BP levels of >160/100 from 9 to 2%[[mean BP change -31 (15.7)/ -14 (9.8) mmHg]] and of 140-159/90-99 mmHg from 32 to 11% [[mean BP change -16(12.7)/ -8.9 (8.7) mmHg]], with corresponding increases in the prevalence of patients with baseline BP levels of 120-139/80-99 from 48 to 65% [[mean BP change -4.1 (10.6)/ -3.1 (7.8) mmHg]]and of <120/80 from 11 to 22% [[mean BP change +5.9 (11.8)/+2.5 (8.6) mmHg]]. These effects did not change significantly thereafter and were maintained throughout follow-up.Conclusion: Blood pressure control is feasible in patients with diabetes without nephropathy, independent of baseline BP values. Asymmetric BP-lowering in the first year after starting therapy represents a true antihypertensive effect with sustainable shifts in BP severity.

Regression to the Mean in Measurements of Growth Rates in Geographic Atrophy.

INTRODUCTION: Comparison of patients with extremely high and low values of a given characteristic is a common strategy to gain insights into disease mechanisms, but this approach is particularly susceptible to regression to the mean (RTM). OBJECTIVE: The aim of this work was to determine RTM in growth rate measurements in patients with geographic atrophy (GA) secondary to age-related macular degeneration. METHODS: We conducted a retrospective analysis of the GAIN (NCT01694095) and its extension study, in which individuals 50 years or older with pure GA were followed for a minimum of 6 months. Two repeated and masked measurements of area of atrophy, both at baseline and final visits, were made, and growth rates were calculated for each. RTM was determined graphically and statistically, and the percentage of eyes misclassified as having fast and slow progression rates due to RTM was determined for different definitions of "fast" and "slow" growth. RESULTS: We included 112 eyes of 112 patients: 64.3% were females, the mean age was 78.1 (SD ±7.6) years, and the mean follow-up time was 3.2 (±2.2) years. There was RTM, which decreased when the mean of two measurements was used. The magnitude of RTM in growth rates ranged from 2 to 11 µm/year and led to misclassification of eyes considered to have fast and slow growth between 2.9 and 10.3% of the cases, depending on the definition of fast and slow growth. CONCLUSIONS: RTM was present in measurements of GA growth rate, but it had a modest impact on patient misclassification. Comparison of features between patients with extreme growth rates is a reasonable strategy, but RTM should be minimized by taking the mean of two measurements.

Investigating systematic bias in brain age estimation with application to post-traumatic stress disorders.

Brain age prediction using machine-learning techniques has recently attracted growing attention, as it has the potential to serve as a biomarker for characterizing the typical brain development and neuropsychiatric disorders. Yet one long-standing problem is that the predicted brain age is overestimated in younger subjects and underestimated in older. There is a plethora of claims as to the bias origins, both methodologically and in data itself. With a large neuroanatomical dataset (N = 2,026; 6-89 years of age) from multiple shared datasets, we show this bias is neither data-dependent nor specific to particular method including deep neural network. We present an alternative account that offers a statistical explanation for the bias and describe a simple, yet efficient, method using general linear model to adjust the bias. We demonstrate the effectiveness of bias adjustment with a large multi-modal neuroimaging data (N = 804; 8-21 years of age) for both healthy controls and post-traumatic stress disorders patients obtained from the Philadelphia Neurodevelopmental Cohort.

Correlation Between Baseline GFR and Subsequent Change in GFR in Norwegian Adults Without Diabetes and in Pima Indians.

RATIONALE & OBJECTIVE: An elevated glomerular filtration rate (GFR), or renal hyperfiltration, may predispose individuals to subsequent rapid GFR decline in diabetes, obesity, and metabolic syndrome. Although this hypothesis is supported by results of experimental studies, the importance of hyperfiltration at the population level remains controversial. We investigated whether higher baseline GFR predicts a steeper decline in GFR. STUDY DESIGN: Longitudinal cohort studies. SETTING & PARTICIPANTS: 1,594 middle-aged Norwegians without diabetes (the Renal Iohexol Clearance Survey [RENIS]) and 319 Pima Indians (83% with type 2 diabetes). PREDICTOR: Baseline measured GFR using exogenous clearance methods. OUTCOMES: Change in measured GFR over time. ANALYTICAL APPROACH: Linear mixed regression models fit to assess the correlation between the random intercept (reflecting baseline GFR) and random slope (change in GFR over time). RESULTS: Mean baseline GFRs were 104.0 ± 20.1 (SD) and 149.4 ± 43.3 mL/min, and median follow-up durations were 5.6 (IQR, 5.2-6.0) and 9.1 (IQR, 4.0-15.0) years in the RENIS and Pima cohorts, respectively. Correlation between baseline GFR (random intercept) and slope of GFR decline was -0.31 (95% CI, -0.40 to -0.23) in the RENIS cohort and -0.41 (95% CI, -0.55 to -0.26) in the Pima cohort, adjusted for age, sex, height, and weight, suggesting that higher baseline GFRs were associated with steeper GFR decline rates. LIMITATIONS: Different methods for measuring GFR in the 2 cohorts. Renal hyperfiltration may not reflect higher single-nephron GFR. GFR decline is assumed to be linear, which may not match the actual pattern; observed correlations may arise from natural variation. CONCLUSIONS: Higher baseline GFR is associated with faster decline in GFR over time. If this relationship were causal, elevated GFR would represent a potentially modifiable risk factor for medium- to long-term GFR decline.

Regression to the mean for the bivariate binomial distribution.

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.

Birds with high lifetime reproductive success experience increased telomere loss.

Lifetime reproductive success (LRS) is what counts in terms of evolution, but investments in reproduction entail costs for an organism. The idea that telomere dynamics may be shaped in response to such costs is already established; however, we still lack information on whether this relation translates to overall fitness. Here, we quantified LRS (number of fledged young) and longitudinal telomere dynamics of small passerine birds-the blue tits ( Cyanistes caeruleus). We found that individual telomere erosion rate was positively associated with lifetime fledgling number. Birds with more fledged young experienced increased telomere attrition. We show that telomere attrition rate, but not telomere length, is related to individual fitness and suggest that telomere dynamics may underlie reproductive costs experienced by animals as a consequence of prioritizing their lifetime fitness. This is the first study, to our knowledge, to provide evidence that more pronounced telomere erosion is associated with higher fitness gain.

Ancillary factors in the treatment of orofacial pain: A topical narrative review.

Ancillary factors, not directly related to treatment, often play a significant role by affecting therapeutic outcome. A search of the literature was conducted including words related to the placebo phenomenon and orofacial diseases. Therefore, critical factors have been grouped into three major categories: (a) the natural course of the diseases; (b) the regression of the symptoms to their mean intensity; and (c) placebo response. This topical narrative review describes the elements mentioned above, provides an up-to-date overview of the hot topics and gaps in the field and indicates developing and future research direction of the orofacial pain field. Such a knowledge might be positively used during daily clinical practice to optimise the management of orofacial pain diseases, as well as in conducting future clinical trials for validating new interventions.

Quantifying the regression to the mean effect in Poisson processes.

Regression to the mean (RTM) can occur whenever an extreme observation is selected from a population and a later observation is closer to the population mean. A consequence of this phenomenon is that natural variability can be mistaken as real change. Simple expressions are available to quantify RTM when the underlying distribution is bivariate normal. However, there are many real-world situations, which are better approximated as a Poisson process. Examples include the number of hard disk failures during a year, the number of cargo ships damaged by waves, daily homicide counts in California, and the number of deaths per quarter attributable to acquired immune deficiency syndrome in Australia. In this paper, we derive expressions for quantifying RTM effects for the bivariate Poisson distribution for both the homogeneous and inhomogeneous cases. Statistical properties of our derivations have been evaluated through a simulation study. The asymptotic distributions of RTM estimators have been derived. The RTM effect for the number of people killed in road accidents in different regions of New South Wales (Australia) is estimated using maximum likelihood.

Most evidence for the compensation account of cognitive training is unreliable.

Cognitive training and brain stimulation studies have suggested that human cognition, primarily working memory and attention control processes, can be enhanced. Some authors claim that gains (i.e., post-test minus pretest scores) from such interventions are unevenly distributed among people. The magnification account (expressed by the evangelical "who has will more be given") predicts that the largest gains will be shown by the most cognitively efficient people, who will also be most effective in exploiting interventions. In contrast, the compensation account ("who has will less be given") predicts that such people already perform at ceiling, so interventions will yield the largest gains in the least cognitively efficient people. Evidence for this latter account comes from reported negative correlations between the pretest and the training/stimulation gain. In this paper, with the use of mathematical derivations and simulation methods, we show that such correlations are pure statistical artifacts caused by the widely known methodological error called "regression to the mean". Unfortunately, more advanced methods, such as alternative measures, linear models, and control groups do not guarantee correct assessment of the compensation effect either. The only correct method is to use direct modeling of correlations between latent true measures and gain. As to date no training/stimulation study has correctly used this method to provide evidence in favor of the compensation account, we must conclude that most (if not all) of the evidence should be considered inconclusive.