Improved Tolerance Factors for Multivariate Normal Distributions

Distribution-free hyperrectangular tolerance regions for setting multivariate reference regions in laboratory medicine

Reference regions are important in laboratory medicine to interpret the test results of patients, and usually given by tolerance regions. Tolerance regions ofp   ( ≥ 2 ) $$ p\;\left(\ge 2\right) $$ dimensions are highly desirable when the test results containsp $$ p $$ outcome measures. Nonparametric hyperrectangular tolerance regions are attractive in real problems due to their robustness with respect to the underlying distribution of the measurements and ease of intepretation, and methods to construct them have been recently provided by Young and Mathew [Stat Methods Med Res. 2020;29:3569-3585]. However, their validity is supported by a simulation study only. In this paper, nonparametric hyperrectangular tolerance regions are constructed by using Tukey's [Ann Math Stat. 1947;18:529-539; Ann Math Stat. 1948;19:30-39] elegant results of equivalence blocks. The validity of these new tolerance regions is proven mathematically in [Ann Math Stat. 1947;18:529-539; Ann Math Stat. 1948;19:30-39] under the only assumption that the underlying distribution of the measurements is continuous. The methodology is applied to analyze the kidney function problem considered in Young and Mathew [Stat Methods Med Res. 2020;29:3569-3585].

Multivariate reference and tolerance regions based on conditional transformation models: Application to glycemic markers

The reference interval is the most widely used medical decision-making, constituting a central tool in determining whether an individual is healthy or not. When the results of several continuous diagnostic tests are available for the same patient, their clinical interpretation is more reliable if a multivariate reference region (MVR) is available rather than multiple univariate reference intervals. MVRs, defined as regions containing 95% of the results of healthy subjects, extend the concept of the reference interval to the multivariate setting. However, they are rarely used in clinical practice owing to difficulties associated with their interpretability and the restrictions inherent to the assumption of a Gaussian distribution. Further statistical research is thus needed to make MVRs more applicable and easier for physicians to interpret. Since the joint distribution of diagnostic test results may well change with patient characteristics independent of disease status, MVRs adjusted for covariates are desirable. The present work introduces a novel formulation for MVRs based on multivariate conditional transformation models (MCTMs). Additionally, we take into account the estimation uncertainty of such MVRs by means of tolerance regions. These conditional MVRs imply no parametric restriction on the response, and potentially nonlinear continuous covariate effects can be estimated. MCTMs allow the estimation of the effects of covariates on the joint distribution of multivariate response variables and on these variables' marginal distributions, via the use of most likely transformation estimation. Our contributions proved reliable when tested with simulated data and for a real data application with two glycemic markers.

Combined statistical decision limits based on two GH-2000 scores for the detection of growth hormone misuse

The growth hormone-2000 biomarker method, based on the measurements of insulin-like growth factor-I and the amino-terminal pro-peptide of type III collagen, has been developed as a powerful technique for the detection of growth hormone misuse by athletes. Insulin-like growth factor-I and amino-terminal pro-peptide of type III collagen are combined in gender-specific formulas to create the growth hormone-2000 score, which is used to determine whether growth hormone has been administered. To comply with World Anti-Doping Agency regulations, each analyte must be measured by two methods. Insulin-like growth factor-I and amino-terminal pro-peptide of type III collagen can be measured by a number of approved methods, each leading to its own growth hormone-2000 score. Single decision limits for each growth hormone-2000 score have been introduced and developed by Bassett, Erotokritou-Mulligan, Holt, Böhning and their co-authors in a series of papers. These have been incorporated into the guidelines of the World Anti-Doping Agency. A joint decision limit was constructed based on the sample correlation between the two growth hormone-2000 scores generated from an available sample to increase the sensitivity of the biomarker method. This paper takes this idea further into a fully developed statistical approach. It constructs combined decision limits when two growth hormone-2000 scores from different assay combinations are used to decide whether an athlete has been misusing growth hormone. The combined decision limits are directly related to tolerance regions and constructed using a Bayesian approach. It is also shown to have highly satisfactory frequentist properties. The new approach meets the required false-positive rate with a pre-specified level of certainty.

Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration

Statistical tolerance intervals are commonly employed in biomedical and pharmaceutical research, such as in lifetime analysis, the assessment of biosimilarity of branded and generic versions of biopharmaceutical drugs, and in quality control of drug products to ensure that a specified proportion of the products are covered within established acceptance limits. Exact two-sided parametric tolerance intervals are only available for the normal distribution, while exact one-sided parametric tolerance limits are available for a limited number of distributions. Approximations to two-sided parametric tolerance intervals often use the Bonferroni correction on the one-sided tolerance interval calculation; however, this often incurs a higher coverage probability than the nominal level. Recently, the usage of a bootstrap calibration has been demonstrated as a way to improve coverage probabilities of tolerance intervals for very specific and complex distributional settings. We present a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals. Simulation results clearly demonstrate the improved coverage probabilities towards the nominal level over the uncalibrated setting. Applications to medical data for various parametric distributions also highlight the utility of constructing these calibrated tolerance intervals.

A geometric approach for computing tolerance bounds for elastic functional data

We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. This work is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Similarly, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.

An anthropometric study of Serbian metal industry workers

BACKGROUND

There are recent studies using new industrial workers' anthropometric data in different countries, but for Serbia such data are not available.

OBJECTIVE

This study is the first anthropometric study of Serbian metal industry workers in the country, whose labor force is increasingly employed both on local and international markets. The metal industry is one of Serbia's most important economic sectors.

METHODS

To this end, we collected the basic static anthropometric dimensions of 122 industrial workers and used principal components analysis (PCA) to obtain multivariate anthropometric models. To confirm the results, the dimensions of an additional 50 workers were collected. The PCA methodology was also compared with the percentile method.

RESULTS

Comparing both data samples, we found that 96% of the participants are within the tolerance ellipsoid. According to this study, multivariate modeling covers a larger extent of the intended population proportion compared to percentiles.

CONCLUSIONS

The results of this research are useful for the designers of metal industry workstations. This information can be used in dimensioning the workplace, thus increasing job satisfaction, reducing the risk of injuries and fatalities, and consequently increasing productivity and safety.