The meaning of significant mean group differences for biomarker discovery

Over the past decade, biomarker discovery has become a key goal in psychiatry to aid in the more reliable diagnosis and prognosis of heterogeneous psychiatric conditions and the development of tailored therapies. Nevertheless, the prevailing statistical approach is still the mean group comparison between “cases” and “controls,” which tends to ignore within-group variability. In this educational article, we used empirical data simulations to investigate how effect size, sample size, and the shape of distributions impact the interpretation of mean group differences for biomarker discovery. We then applied these statistical criteria to evaluate biomarker discovery in one area of psychiatric research—autism research. Across the most influential areas of autism research, effect size estimates ranged from small (d = 0.21, anatomical structure) to medium (d = 0.36 electrophysiology, d = 0.5, eye-tracking) to large (d = 1.1 theory of mind). We show that in normal distributions, this translates to approximately 45% to 63% of cases performing within 1 standard deviation (SD) of the typical range, i.e., they do not have a deficit/atypicality in a statistical sense. For a measure to have diagnostic utility as defined by 80% sensitivity and 80% specificity, Cohen’s d of 1.66 is required, with still 40% of cases falling within 1 SD. However, in both normal and nonnormal distributions, 1 (skewness) or 2 (platykurtic, bimodal) biologically plausible subgroups may exist despite small or even nonsignificant mean group differences. This conclusion drastically contrasts the way mean group differences are frequently reported. Over 95% of studies omitted the “on average” when summarising their findings in their abstracts (“autistic people have deficits in X”), which can be misleading as it implies that the group-level difference applies to all individuals in that group. We outline practical approaches and steps for researchers to explore mean group comparisons for the discovery of stratification biomarkers.

Monitoring Mortality Caused by COVID-19 Using Gamma-Distributed Variables Based on Generalized Multiple Dependent State Sampling

More recently in statistical quality control studies, researchers are paying more attention to quality characteristics having nonnormal distributions. In the present article, a generalized multiple dependent state (GMDS) sampling control chart is proposed based on the transformation of gamma quality characteristics into a normal distribution. The parameters for the proposed control charts are obtained using in-control average run length (ARL) at specified shape parametric values for different specified average run lengths. The out-of-control ARL of the proposed gamma control chart using GMDS sampling is explored using simulation for various shift size changes in scale parameters to study the performance of the control chart. The proposed gamma control chart performs better than the existing multiple dependent state sampling (MDS) based on gamma distribution and traditional Shewhart control charts in terms of average run lengths. A case study with real-life data from ICU intake to death caused by COVID-19 has been incorporated for the realistic handling of the proposed control chart design.

Estimating the Uncertainty of a Small Area Estimator Based on a Microsimulation Approach

Spatial microsimulation encompasses a range of alternative methodological approaches for the small area estimation (SAE) of target population parameters from sample survey data down to target small areas in contexts where such data are desired but not otherwise available. Although widely used, an enduring limitation of spatial microsimulation SAE approaches is their current inability to deliver reliable measures of uncertainty—and hence confidence intervals—around the small area estimates produced. In this article, we overcome this key limitation via the development of a measure of uncertainty that takes into account both variance and bias, that is, the mean squared error. This new approach is evaluated via a simulation study and demonstrated in a practical application using European Union Statistics on Income and Living Conditions data to explore income levels across Italian municipalities. Evaluations show that the approach proposed delivers accurate estimates of uncertainty and is robust to nonnormal distributions. The approach provides a significant development to widely used spatial microsimulation SAE techniques.

Growth Mixture Modeling With Nonnormal Distributions: Implications for Data Transformation

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality assumption and using data transformation on repeated measures. Based on unconditional GMM with two latent trajectories, data were generated under different sample sizes (300, 800, and 1500), skewness (0.7, 1.2, and 1.6) and kurtosis (2 and 4) of outcomes, numbers of time points (4 and 8), and class proportions (0.5:0.5 and 0.25:0.75). Of the four distributions, it was found that skew- t GMM had the highest accuracy in terms of parameter estimation. In GMM based on data transformations, the adjusted logarithmic method was more effective in obtaining unbiased parameter estimates than the use of van der Waerden quantile normal scores. Even though adjusted logarithmic transformation in nonnormal GMM reduced computation time, skew- t GMM produced much more accurate estimation and was more robust over a range of simulation conditions. This study is significant in that it considers different levels of kurtosis and class proportions, which has not been investigated in depth in previous studies. The present study is also meaningful in that investigated the applicability of data transformation to nonnormal GMM.

Distribution of Xanthomonas hortorum pv. carotae Populations in Naturally Infested Carrot Seed Lots

Bacterial blight of carrot (Daucus carota subsp. sativus), caused by the plant-pathogenic bacterium Xanthomonas hortorum pv. carotae, is a common seedborne disease of carrot wherever the crop is grown. Carrot seed lots were evaluated to determine the variability and distribution of populations of X. hortorum pv. carotae among individual carrot seeds. Twenty-four carrot seed lots harvested between 2014 and 2016 were subjected to a bulk seed wash dilution-plate assay to obtain mean X. hortorum pv. carotae levels. Mean infestation levels resulting from the bulk seed wash assays among the 24 seed lots ranged from 1.2 × 107 and 9.6 × 108 CFU/g seed and averaged 3.6 × 108 CFU/g seed. Individual seeds from the same 24 lots were also tested with a scaled-down wash assay of individual seeds. Among the 1,380 seeds that were individually assayed, 475 X. hortorum pv. carotae-positive seeds were detected (34.4%). Rates of X. hortorum pv. carotae detection on individual seed in seed lots ranged from 0% (not detected) to 97.9%, and the mean and median X. hortorum pv. carotae population on an individual seed was 8.3 × 104 and 6.3 × 101 CFU/seed, respectively. Among individual seeds, X. hortorum pv. carotae populations ranged from 2 (the limit of detection of the assay) to 3.6 × 107 CFU/seed. CFU data for 23 of the 24 seed lots were nonnormal and the Log-Logistic (3P) distribution best described populations of X. hortorum pv. carotae recovered from individual carrot seeds. The influence and impact of nonnormal distributions of X. hortorum pv. carotae in commercial carrot seed lots on seed health tests, seedborne transmission, and bacterial blight epidemiology requires further study.

Is It Time to Rethink “Normal” in Population Health Research?

The normal distribution has been useful to the field of population health—appropriately describing the distribution of many outcomes and serving as a foundation for powerful statistical analyses. But not all outcomes are normally distributed, and this chapter reminds readers of the importance of recognizing, empirically testing for this case, and using appropriate distributional functions to characterize outcomes or as the foundation for statistical and other models. The chapter begins by briefly highlighting several common examples in which nonnormal distributions are used in population health research and then describes two examples in more detail where tremendous meaning is found in recognizing nonnormality. The first is focused on “spectral effects,” variables that contextualize—or change—the relationship between predictor variables and outcomes. These relationships are only illuminated when subpopulations are disaggregated. The second example describes power law distributions and the phenomena that generate them—long recognized but understudied in population health.

A Comparison of Different Nonnormal Distributions in Growth Mixture Models

The purpose of the present study is to compare nonnormal distributions (i.e., t, skew-normal, skew- t with equal skew and skew- t with unequal skew) in growth mixture models (GMMs) based on diverse conditions of a number of time points, sample sizes, and skewness for intercepts. To carry out this research, two simulation studies were conducted with two different models: an unconditional GMM and a GMM with a continuous distal outcome variable. For the simulation, data were generated under the conditions of a different number of time points (4, 8), sample size (300, 800, 1,500), and skewness for intercept (1.2, 2, 4). Results demonstrate that it is not appropriate to fit nonnormal data to normal, t, or skew-normal distributions other than the skew- t distribution. It was also found that if there is skewness over time, it is necessary to model skewness in the slope as well.

Data Analyses When Sample Sizes Are Small: Modern Advances for Dealing With Outliers, Skewed Distributions, and Heteroscedasticity

The paper reviews advances and insights relevant to comparing groups when the sample sizes are small. There are conditions under which conventional, routinely used techniques are satisfactory. But major insights regarding outliers, skewed distributions, and unequal variances (heteroscedasticity) make it clear that under general conditions they provide poor control over the type I error probability and can have relatively poor power. In practical terms, important differences among groups can be missed and poorly characterized. Many new and improved methods have been derived that are aimed at dealing with the shortcomings of classic methods. To provide a conceptual basis for understanding the practical importance of modern methods, the paper reviews some modern insights related to why methods based on means can perform poorly. Then some strategies for dealing with nonnormal distributions and unequal variances are described. For brevity, the focus is on comparing 2 independent groups or 2 dependent groups based on the usual difference scores. The paper concludes with comments on issues to consider when choosing from among the methods reviewed in the paper.