Harmonization of CSF and imaging biomarkers in Alzheimer's disease: Need and practical applications for genetics studies and preclinical classification.

In Alzheimer's disease (AD) research, cerebrospinal fluid (CSF) Amyloid beta (Aß), Tau and pTau are the most accepted and well validated biomarkers. Several methods and platforms exist to measure those biomarkers, leading to challenges in combining data across studies. Thus, there is a need to identify methods that harmonize and standardize these values. We used a Z-score based approach to harmonize CSF and amyloid imaging data from multiple cohorts and compared GWAS results using this approach with currently accepted methods. We also used a generalized mixture model to calculate the threshold for biomarker-positivity. Based on our findings, our normalization approach performed as well as meta-analysis and did not lead to any spurious results. In terms of dichotomization, cutoffs calculated with this approach were very similar to those reported previously. These findings show that the Z-score based harmonization approach can be applied to heterogeneous platforms and provides biomarker cut-offs consistent with the classical approaches without requiring any additional data.

Researchers in rheumatology should avoid categorization of continuous predictor variables.

BACKGROUND: Rheumatology researchers often categorize continuous predictor variables. We aimed to show how this practice may alter results from observational studies in rheumatology. METHODS: We conducted and compared the results of two analyses of the association between our predictor variable (percentage change in body mass index [BMI] from baseline to four years) and two outcome variable domains of structure and pain in knee and hip osteoarthritis. These two outcome variable domains covered 26 different outcomes for knee and hip combined. In the first analysis (categorical analysis), percentage change in BMI was categorized as ≥ 5% decrease in BMI, < 5% change in BMI, and ≥ 5% increase in BMI, while in the second analysis (continuous analysis), it was left as a continuous variable. In both analyses (categorical and continuous), we used generalized estimating equations with a logistic link function to investigate the association between the percentage change in BMI and the outcomes. RESULTS: For eight of the 26 investigated outcomes (31%), the results from the categorical analyses were different from the results from the continuous analyses. These differences were of three types: 1) for six of these eight outcomes, while the continuous analyses revealed associations in both directions (i.e., a decrease in BMI had one effect, while an increase in BMI had the opposite effect), the categorical analyses showed associations only in one direction of BMI change, not both; 2) for another one of these eight outcomes, the categorical analyses suggested an association with change in BMI, while this association was not shown in the continuous analyses (this is potentially a false positive association); 3) for the last of the eight outcomes, the continuous analyses suggested an association of change in BMI, while this association was not shown in the categorical analyses (this is potentially a false negative association). CONCLUSIONS: Categorization of continuous predictor variables alters the results of analyses and could lead to different conclusions; therefore, researchers in rheumatology should avoid it.

Should responder analyses be conducted on continuous outcomes?

Continuous outcomes are often dichotomized to classify trial subjects as responders or nonresponders, with the difference in rates of response between treatment and control defined as the "responder effect." In this article, we caution that dichotomization of continuous interval outcomes may not be best practice. Defining clinical benefit or harm for continuous interval outcomes as the difference between the means of treatment and control, that is, the "continuous treatment effect," we examine the case where treatment and control outcomes are normally distributed and differ only in location. For this case, continuous treatment effects may be considered clinically relevant if they exceed a prespecified minimum clinically important difference. In contrast, using minimum clinically important differences as dichotomization thresholds will not ensure clinically relevant responder effects. For example, in some situations, increasing the threshold may actually relax the criterion for effectiveness by increasing the calculated responder effect. Using responder effects to quantitatively assess benefit or risk of investigational drugs for continuous interval outcomes presents interpretational challenges. In particular, when the dichotomization threshold is halfway between the treatment and control outcome means, the responder effect is at a maximum with a magnitude monotonically related to the number of standard deviations between the mean outcomes of treatment and control. Large responder effect benefits may therefore reflect clinically unimportant continuous treatment effects amplified by small standard deviations, and small responder effect risks may reflect either clinically important continuous treatment effects minimized by large standard deviations, or selection of a dichotomization threshold not providing maximum responder effect.

Simple method for cutoff point identification in descriptive high-throughput biological studies.

BACKGROUND: Rapid development of high-throughput omics technologies generates an increasing interest in algorithms for cutoff point identification. Existing cutoff methods and tools identify cutoff points based on an association of continuous variables with another variable, such as phenotype, disease state, or treatment group. These approaches are not applicable for descriptive studies in which continuous variables are reported without known association with any biologically meaningful variables. RESULTS: The most common shape of the ranked distribution of continuous variables in high-throughput descriptive studies corresponds to a biphasic curve, where the first phase includes a big number of variables with values slowly growing with rank and the second phase includes a smaller number of variables rapidly growing with rank. This study describes an easy algorithm to identify the boundary between these phases to be used as a cutoff point. DISCUSSION: The major assumption of that approach is that a small number of variables with high values dominate the biological system and determine its major processes and functions. This approach was tested on three different datasets: human genes and their expression values in the human cerebral cortex, mammalian genes and their values of sensitivity to chemical exposures, and human proteins and their expression values in the human heart. In every case, the described cutoff identification method produced shortlists of variables (genes, proteins) highly relevant for dominant functions/pathways of the analyzed biological systems. CONCLUSIONS: The described method for cutoff identification may be used to prioritize variables in descriptive omics studies for a focused functional analysis, in situations where other methods of dichotomization of data are inaccessible.

A Bayesian modified Ising model for identifying spatially variable genes from spatial transcriptomics data.

A recent technology breakthrough in spatial molecular profiling (SMP) has enabled the comprehensive molecular characterizations of single cells while preserving spatial information. It provides new opportunities to delineate how cells from different origins form tissues with distinctive structures and functions. One immediate question in SMP data analysis is to identify genes whose expressions exhibit spatially correlated patterns, called spatially variable (SV) genes. Most current methods to identify SV genes are built upon the geostatistical model with Gaussian process to capture the spatial patterns. However, the Gaussian process models rely on ad hoc kernels that could limit the models' ability to identify complex spatial patterns. In order to overcome this challenge and capture more types of spatial patterns, we introduce a Bayesian approach to identify SV genes via a modified Ising model. The key idea is to use the energy interaction parameter of the Ising model to characterize spatial expression patterns. We use auxiliary variable Markov chain Monte Carlo algorithms to sample from the posterior distribution with an intractable normalizing constant in the model. Simulation studies using both simulated and synthetic data showed that the energy-based modeling approach led to higher accuracy in detecting SV genes than those kernel-based methods. When applied to two real spatial transcriptomics (ST) datasets, the proposed method discovered novel spatial patterns that shed light on the biological mechanisms. In summary, the proposed method presents a new perspective for analyzing ST data.

Analysis of an incomplete binary outcome dichotomized from an underlying continuous variable in clinical trials.

In many clinical trials, outcomes of interest are binary-valued. It is not uncommon that a binary-valued outcome is dichotomized from a continuous outcome at a threshold of clinical interest. To analyze such data, common approaches include (a) fitting a generalized linear mixed model (GLMM) to the dichotomized longitudinal binary outcome; and (b) the multiple imputation (MI) based method: imputing missing values in the continuous outcome, dichotomizing it into a binary outcome, and then fitting a generalized linear model to the "complete" data. We conducted comprehensive simulation studies to compare the performance of the GLMM versus the MI-based method for estimating the risk difference and the logarithm of odds ratio between two treatment arms at the end of study. In those simulation studies, we considered a range of multivariate distribution options for the continuous outcome (including a multivariate normal distribution, a multivariate t-distribution, a multivariate log-normal distribution, and the empirical distribution from a real clinical trial data) to evaluate the robustness of the estimators to various data-generating models. Simulation results demonstrate that both methods work well under those considered distribution options, but the MI-based method is more efficient with smaller mean squared errors compared to the GLMM. We further applied both the GLMM and the MI-based method to 29 phase 3 diabetes clinical trials, and found that the MI-based method generally led to smaller variance estimates compared to the GLMM.

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes.

We propose a novel response-adaptive randomization procedure for multi-armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non-myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response-adaptive algorithm based on the Gittins index for the multi-armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969-978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi-armed setting, there are efficiency and patient benefit gains of using a response-adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response-adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi-armed trial context.

Informative frailty indices from binarized biomarkers.

Frailty indices (FIs) based on continuous valued health data, such as obtained from blood and urine tests, have been shown to be predictive of adverse health outcomes. However, creating FIs from such biomarker data requires a binarization treatment that is difficult to standardize across studies. In this work, we explore a "quantile" methodology for the generic treatment of biomarker data that allows us to construct an FI without preexisting medical knowledge (i.e. risk thresholds) of the included biomarkers. We show that our quantile approach performs as well as, or even slightly better than, established methods for the National Health and Nutrition Examination Survey and the Canadian Study of Health and Aging data sets. Furthermore, we show that our approach is robust to cohort effects within studies as compared to other data-based methods. The success of our binarization approaches provides insight into the robustness of the FI as a health measure, and the upper limits of the FI observed in various data sets, and also highlights general difficulties in obtaining absolute scales for comparing FIs between studies.

The P Value Line Dance: When Does the Music Stop?

When should a trial stop? Such a seemingly innocent question evokes concerns of type I and II errors among those who believe that certainty can be the product of uncertainty and among researchers who have been told that they need to carefully calculate sample sizes, consider multiplicity, and not spend P values on interim analyses. However, the endeavor to dichotomize evidence into significant and nonsignificant has led to the basic driving force of science, namely uncertainty, to take a back seat. In this viewpoint we discuss that if testing the null hypothesis is the ultimate goal of science, then we need not worry about writing protocols, consider ethics, apply for funding, or run any experiments at all-all null hypotheses will be rejected at some point-everything has an effect. The job of science should be to unearth the uncertainties of the effects of treatments, not to test their difference from zero. We also show the fickleness of P values, how they may one day point to statistically significant results; and after a few more participants have been recruited, the once statistically significant effect suddenly disappears. We show plots which we hope would intuitively highlight that all assessments of evidence will fluctuate over time. Finally, we discuss the remedy in the form of Bayesian methods, where uncertainty leads; and which allows for continuous decision making to stop or continue recruitment, as new data from a trial is accumulated.

Using a dose-finding benchmark to quantify the loss incurred by dichotomization in Phase II dose-ranging studies.

While there is recognition that more informative clinical endpoints can support better decision-making in clinical trials, it remains a common practice to categorize endpoints originally measured on a continuous scale. The primary motivation for this categorization (and most commonly dichotomization) is the simplicity of the analysis. There is, however, a long argument that this simplicity can come at a high cost. Specifically, larger sample sizes are needed to achieve the same level of accuracy when using a dichotomized outcome instead of the original continuous endpoint. The degree of "loss of information" has been studied in the contexts of parallel-group designs and two-stage Phase II trials. Limited attention, however, has been given to the quantification of the associated losses in dose-ranging trials. In this work, we propose an approach to estimate the associated losses in Phase II dose-ranging trials that is free of the actual dose-ranging design used and depends on the clinical setting only. The approach uses the notion of a nonparametric optimal benchmark for dose-finding trials, an evaluation tool that facilitates the assessment of a dose-finding design by providing an upper bound on its performance under a given scenario in terms of the probability of the target dose selection. After demonstrating how the benchmark can be applied to Phase II dose-ranging trials, we use it to quantify the dichotomization losses. Using parameters from real clinical trials in various therapeutic areas, it is found that the ratio of sample sizes needed to obtain the same precision using continuous and binary (dichotomized) endpoints varies between 70% and 75% under the majority of scenarios but can drop to 50% in some cases.

Spurious interaction as a result of categorization.

BACKGROUND: It is common in applied epidemiological and clinical research to convert continuous variables into categorical variables by grouping values into categories. Such categorized variables are then often used as exposure variables in some regression model. There are numerous statistical arguments why this practice should be avoided, and in this paper we present yet another such argument. METHODS: We show that categorization may lead to spurious interaction in multiple regression models. We give precise analytical expressions for when this may happen in the linear regression model with normally distributed exposure variables, and we show by simulations that the analytical results are valid also for other distributions. Further, we give an interpretation of the results in terms of a measurement error problem. RESULTS: We show that, in the case of a linear model with two normally distributed exposure variables, both categorized at the same cut point, a spurious interaction will be induced unless the two variables are categorized at the median or they are uncorrelated. In simulations with exposure variables following other distributions, we confirm this general effect of categorization, but we also show that the effect of the choice of cut point varies over different distributions. CONCLUSION: Categorization of continuous exposure variables leads to a number of problems, among them spurious interaction effects. Hence, this practice should be avoided and other methods should be considered.

The Promise of Selecting Individuals from the Extremes of Exposure in the Analysis of Gene-Physical Activity Interactions.

BACKGROUND: Dichotomization using the lower quartile as cutoff is commonly used for harmonizing heterogeneous physical activity (PA) measures across studies. However, this may create misclassification and hinder discovery of new loci. OBJECTIVES: This study aimed to evaluate the performance of selecting individuals from the extremes of the exposure (SIEE) as an alternative approach to reduce such misclassification. METHOD: For systolic and diastolic blood pressure in the Framingham Heart Study, we performed a genome-wide association study with gene-PA interaction analysis using three PA variables derived by SIEE and two other dichotomization approaches. We compared number of loci detected and overlap with loci found using a quantitative PA variable. In addition, we performed simulation studies to assess bias, false discovery rates (FDR), and power under synergistic/antagonistic genetic effects in exposure groups and in the presence/absence of measurement error. RESULTS: In the empirical analysis, SIEE's performance was neither the best nor the worst. In most simulation scenarios, SIEE was consistently outperformed in terms of FDR and power. Particularly, in a scenario characterized by antagonistic effects and measurement error, SIEE had the least bias and highest power. CONCLUSION: SIEE's promise appears limited to detecting loci with antagonistic effects. Further studies are needed to evaluate SIEE's full advantage.

The Impact of Item Misspecification and Dichotomization on Class and Parameter Recovery in LCA of Count Data.

Mixture analysis of count data has become increasingly popular among researchers of substance use, behavioral analysis, and program evaluation. However, this increase in popularity seems to have occurred along with adoption of some conventions in model specification based on arbitrary heuristics that may impact the validity of results. Findings from a systematic review of recent drug and alcohol publications suggested count variables are often dichotomized or misspecified as continuous normal indicators in mixture analysis. Prior research suggests that misspecifying skewed distributions of continuous indicators in mixture analysis introduces bias, though the consequences of this practice when applied to count indicators has not been studied. The present work describes results from a simulation study examining bias in mixture recovery when count indicators are dichotomized (median split; presence vs. absence), ordinalized, or the distribution is misspecified (continuous normal; incorrect count distribution). All distributional misspecifications and methods of categorizing resulted in greater bias in parameter estimates and recovery of class membership relative to specifying the true distribution, though dichotomization appeared to improve class enumeration accuracy relative to all other specifications. Overall, results demonstrate the importance of accurately modeling count indicators in mixture analysis, as misspecification and categorizing data can distort study outcomes.

Potential Information Loss Due to Categorization of Minimum Inhibitory Concentration Frequency Distributions.

A bacterial isolate's susceptibility to antimicrobial is expressed as the lowest drug concentration inhibiting its visible growth, termed minimum inhibitory concentration (MIC). The susceptibilities of isolates from a host population at a particular time vary, with isolates with specific MICs present at different frequencies. Currently, for either clinical or monitoring purposes, an isolate is most often categorized as Susceptible, Intermediate, or Resistant to the antimicrobial by comparing its MIC to a breakpoint value. Such data categorizations are known in statistics to cause information loss compared to analyzing the underlying frequency distributions. The U.S. National Antimicrobial Resistance Monitoring System (NARMS) includes foodborne bacteria at the food animal processing and retail product points. The breakpoints used to interpret the MIC values for foodborne bacteria are those relevant to clinical treatments by the antimicrobials in humans in whom the isolates were to cause infection. However, conceptually different objectives arise when inference is sought concerning changes in susceptibility/resistance across isolates of a bacterial species in host populations among different sampling points or times. For the NARMS 1996-2013 data for animal processing and retail, we determined the fraction of comparisons of susceptibility/resistance to 44 antimicrobial drugs of twelve classes of a bacterial species in a given animal host or product population where there was a significant change in the MIC frequency distributions between consecutive years or the two sampling points, while the categorization-based analyses concluded no change. The categorization-based analyses missed significant changes in 54% of the year-to-year comparisons and in 71% of the slaughter-to-retail within-year comparisons. Hence, analyses using the breakpoint-based categorizations of the MIC data may miss significant developments in the resistance distributions between the sampling points or times. Methods considering the MIC frequency distributions in their entirety may be superior for epidemiological analyses of resistance dynamics in populations.

Contextuality in canonical systems of random variables.

Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Sample size determination for fold-increase endpoints defined by paired interval-censored data.

Medical studies often define binary end-points by comparing the ratio of a pair of measurements at baseline and end-of-study to a clinically meaningful cut-off. For example, vaccine trials may define a response as at least a four-fold increase in antibody titers from baseline to end-of-study. Accordingly, sample size is determined based on comparisons of proportions. Since the pair of measurements is quantitative, modeling the bivariate cumulative distribution function to estimate the proportion gives more precise results than using dichotomization of data. This is known as the distributional approach to the analysis of proportions. However, this can be complicated by interval-censoring. For example, due to the nature of some laboratory measurement methods, antibody titers are interval-censored. We derive a sample size formula based on the distributional approach for paired interval-censored data. We compare the sample size requirement in detecting an intervention effect using the distributional approach to a conventional approach of dichotomization. Some practical guidance on applying the sample size formula is given.

Effects of categorization method, regression type, and variable distribution on the inflation of Type-I error rate when categorizing a confounding variable.

The loss of signal associated with categorizing a continuous variable is well known, and previous studies have demonstrated that this can lead to an inflation of Type-I error when the categorized variable is a confounder in a regression analysis estimating the effect of an exposure on an outcome. However, it is not known how the Type-I error may vary under different circumstances, including logistic versus linear regression, different distributions of the confounder, and different categorization methods. Here, we analytically quantified the effect of categorization and then performed a series of 9600 Monte Carlo simulations to estimate the Type-I error inflation associated with categorization of a confounder under different regression scenarios. We show that Type-I error is unacceptably high (>10% in most scenarios and often 100%). The only exception was when the variable categorized was a continuous mixture proxy for a genuinely dichotomous latent variable, where both the continuous proxy and the categorized variable are error-ridden proxies for the dichotomous latent variable. As expected, error inflation was also higher with larger sample size, fewer categories, and stronger associations between the confounder and the exposure or outcome. We provide online tools that can help researchers estimate the potential error inflation and understand how serious a problem this is.

Limitations of Separating Athletes into High or Low-Risk Groups based on a Cut-Off. A Clinical Commentary.

Background: Athlete injury risk assessment and management is an important, yet challenging task for sport and exercise medicine professionals. A common approach to injury risk screening is to stratify athletes into risk groups based on their performance on a test relative to a cut-off threshold. However, one potential reason for ineffective injury prevention efforts is the over-reliance on identifying these 'at-risk' groups using arbitrary cut-offs for these tests and measures. The purpose of this commentary is to discuss the conceptual and technical issues related to the use of a cut-off in both research and clinical practice. Clinical Question: How can we better assess and interpret clinical tests or measures to enable a more effective injury risk assessment in athletes? Key Results: Cut-offs typically lack strong biologic plausibility to support them; and are typically derived in a data-driven manner and thus not generalizable to other samples. When a cut-off is used in analyses, information is lost, leading to potentially misleading results and less accurate injury risk prediction. Dichotomizing a continuous variable using a cut-off should be avoided. Using continuous variables on its original scale is advantageous because information is not discarded, outcome prediction accuracy is not lost, and personalized medicine can be facilitated. Clinical Application: Researchers and clinicians are encouraged to analyze and interpret the results of tests and measures using continuous variables and avoid relying on singular cut-offs to guide decisions. Injury risk can be predicted more accurately when using continuous variables in their natural form. A more accurate risk prediction will facilitate personalized approaches to injury risk mitigation and may lead to a decline in injury rates. Level of Evidence: 5.

A Bayesian finite mixture model approach to evaluate dichotomization method for correlated ELISA tests.

In diagnostic accuracy studies, a commonly employed approach involves dichotomizing continuous data and subsequently analyzing them using a Bayesian latent class model (BLCM), often relying on binomial or multinomial distributions, rather than preserving their continuous nature. However, this procedure can inadvertently lead to less reliable outcomes due to the inherent loss of information when converting the original continuous measurements into binary values. Through comprehensive simulations, we demonstrated the limitations and disadvantages of dichotomizing continuous biomarkers from two correlated tests. Our findings highlighted notable disparities between the true values and the model estimates as a result of dichotomization. We discovered the crucial significance of selecting a reference test with high diagnostic accuracy in test evaluation in order to obtain reliable estimates of test accuracy and prevalences. Our study served as a call to action for veterinary researchers to exercise caution when utilizing dichotomization.

Standardization of continuous and categorical covariates in sparse penalized regressions.

In sparse penalized regressions, candidate covariates of different units need to be standardized beforehand so that the coefficient sizes are directly comparable and reflect their relative impacts, which leads to fairer variable selection. However, when covariates of mixed data types (e.g. continuous, binary or categorical) exist in the same dataset, the commonly used standardization methods may lead to different selection probabilities even when the covariates have the same impact on or level of association with the outcome. In this paper, we propose a novel standardization method that targets at generating comparable selection probabilities in sparse penalized regressions for continuous, binary or categorical covariates with the same impact. We illustrate the advantages of the proposed method in simulation studies, and apply it to the National Ambulatory Medical Care Survey data to select factors related to the opioid prescription in the US.