On easily interpretable multivariate reference regions of rectangular shape

Till now, multivariate reference regions have played only a marginal role in the practice of clinical chemistry and laboratory medicine. The major reason for this fact is that such regions are traditionally determined by means of concentration ellipsoids of multidimensional Gaussian distributions yielding reference limits which do not allow statements about possible outlyingness of measurements taken in specific diagnostic tests from a given patient or subject. As a promising way around this difficulty we propose to construct multivariate reference regions as p-dimensional rectangles or (in the one-sided case) rectangular half-spaces whose edges determine univariate percentile ranges of the same probability content in each marginal distribution. In a first step, the corresponding notion of a quantile of a p-dimensional probability distribution of any type and shape is made mathematically precise. Subsequently, both parametric and nonparametric procedures of estimating such a quantile are described. Furthermore, results on sample-size calculation for reference-centile studies based on the proposed definition of multivariate quantiles are presented generalizing the approach of Jennen-Steinmetz and Wellek.     

Computation of model-dependent tolerance bands for ambulatorily monitored blood pressure

The construction of time-specified reference limits requires systematic sampling in clinical health, particularly for those variables characterized by a circadian rhythm of large amplitude, as it is the case for blood pressure (BP). For the detection of false negatives, tolerance intervals (limits that will include at least a specified proportion of the population with a stated confidence) are important and should substitute when possible for prediction limits. We have previously described a nonparametric method for the computation of model-independent tolerance intervals that are constructed by first dividing the sampling range in several time spans in which no appreciable changes in population characteristics (namely, mean and variance) take place. The tolerance interval is then computed for each of the time spans. The limits thus computed, as well as results of any comparison of a given individual's profile against such tolerance intervals, are highly dependent on the sampling scheme of both the reference individuals and the test subject. To avoid this problem, we have developed an alternative method that allows the computation of model-dependent tolerance bands for hybrid time series. Assuming that a set X of longitudinal series monitored from a given group of reference individuals can be fitted with the same individual model, a population model C(X,t) can be also determined, as well as the deviation S(X,t) of each individual curve from the population model. The tolerance band will then have the form C(X,t) ± kS(X,t), where k is here estimated following a nonparametric approach based on bootstrap techniques. Alternatively, two different values of k can be estimated (for the lower and upper limits of the tolerance interval, respectively) in cases for which we cannot assume symmetry. The method is generally applicable for any population model describing the reference population (including the fit of multiple significant components, nonsinusoidal waveforms, and/or trends). The method was used to establish time-specified tolerance bands for time series of blood pressure monitored automatically in healthy individuals of both genders. Model-dependent intervals are preferred to the model-independent limits when reliance on a specified sampling rate needs to be avoided. These limits may serve for an objective and positive definition of health, for the screening and diagnosis of disease, and for gauging the subject's response to treatment. (Chronobiology International, 17(4), 567-582, 2000)     

Computation of Time-Specified Tolerance Intervals for Hybrid Time Series with Nonequidistant Sampling,Illustrated for Plasma Growth Hormone

The ideal reference interval for a variable of clinical interest would be specific for all deterministic factors affecting that variable, including the time of sampling in relation to biological rhythms. In particular, growth hormone is characterized in children by circadian and ultradian variability, with high peaks of secretion occurring mainly during sleep. For clinical applications, the use of tolerance intervals has been recommended, and they should substitute, whenever possible, for prediction limits. In the case of hybrid data (time series of data collected from a group of subjects), such a tolerance interval could be very difficult to determine following a parametric approach similar to the procedure used for the computation of prediction intervals, especially when consideration of both within-subjects and among-subjects variances is wanted. Accordingly, we have developed a nonparametric method for the computation of such tolerance intervals. Because the method is based on bootstrap techniques, it does not require the assumption of normality or symmetry in the data and is also more appropriate when dealing with small samples. The method was used to establish time-qualified reference limits for a series of growth hormone sampled around the clock in groups of prepubertal children differentiated according to stature. The use of these tolerance intervals may eliminate many false-positive and false-negative diagnoses that might be obtained when relying on time-unspecified single samples. The provision of such tolerance limits introduces time-specification and time-structure evaluation into prevention, diagnosis, and treatment of growth disorders. (Chronobiology International, 14(4), 409–425, 1997)     

Scale-independent non-parametric multivariate tolerance regions and their application in medicine

Based on the principles introduced by TUKEY and FRASER , a method is proposed to construct non-parametric multivariate tolerance regions of irregular multiplanar shape. Contrary to the regions of corresponding shape as constructed by Tukey and Fraser, the tolerance regions constructed according to the proposed method can be shown to be invariant to linear scale transformations. In medical applications, where the concept of multivariate tolerance regions can be used to define “normal” regions for p ≦ 2 variables with measuring units generally differing from each other, the quality of scale-independency of the regions is essential. With reference to the method proposed, sample size determination and some important aspects of the use of multivariate tolerance regions are discussed.     

COMPUTATION OF MODEL-DEPENDENT TOLERANCE BANDS FOR AMBULATORILY MONITORED BLOOD PRESSURE

The construction of time-specified reference limits requires systematic sampling in clinical health, particularly for those variables characterized by a circadian rhythm of large amplitude, as it is the case for blood pressure (BP). For the detection of false negatives, tolerance intervals (limits that will include at least a specified proportion of the population with a stated confidence) are important and should substitute when possible for prediction limits. We have previously described a nonparametric method for the computation of model-independent tolerance intervals that are constructed by first dividing the sampling range in several time spans in which no appreciable changes in population characteristics (namely, mean and variance) take place. The tolerance interval is then computed for each of the time spans. The limits thus computed, as well as results of any comparison of a given individual's profile against such tolerance intervals, are highly dependent on the sampling scheme of both the reference individuals and the test subject. To avoid this problem, we have developed an alternative method that allows the computation of model-dependent tolerance bands for hybrid time series. Assuming that a set X of longitudinal series monitored from a given group of reference individuals can be fitted with the same individual model, a population model C(X,t) can be also determined, as well as the deviation S(X,t) of each individual curve from the population model. The tolerance band will then have the form C(X,t) ± kS(X,t), where k is here estimated following a nonparametric approach based on bootstrap techniques. Alternatively, two different values of k can be estimated (for the lower and upper limits of the tolerance interval, respectively) in cases for which we cannot assume symmetry. The method is generally applicable for any population model describing the reference population (including the fit of multiple significant components, nonsinusoidal waveforms, and/or trends). The method was used to establish time-specified tolerance bands for time series of blood pressure monitored automatically in healthy individuals of both genders. Model-dependent intervals are preferred to the model-independent limits when reliance on a specified sampling rate needs to be avoided. These limits may serve for an objective and positive definition of health, for the screening and diagnosis of disease, and for gauging the subject's response to treatment. (Chronobiology International, 17(4), 567–582, 2000)     

Haematological and biochemical reference intervals for farmed channel catfish

The reference intervals for biochemical variables and red blood cell indices of healthy intensively bred channel catfish Ictalurus punctatus were determined. The blood variables were determined using standardized clinical methods. The reference intervals (25th and 75th percentiles) were established using a non-parametric method. Reference intervals for plasma glucose, serum total protein, sodium, potassium, calcium, magnesium, chloride concentration, primary and secondary red blood cell indices were established. The haematological and biochemical reference intervals established may allow important clinical decisions about channel catfish.     

Mapping of chromosome regions conferring boron toxicity tolerance in barley (Hordeum vulgare L.)

 Boron toxicity has been recognised as an important problem limiting production in the low-rainfall regions of southern Australia, West Asia and North Africa. Genetic variation for boron toxicity tolerance in barley has been characterised but the mode of inheritance and the location of genes controlling tolerance were not previously known. A population of 150 doubled-haploid lines from a cross between a boron toxicity tolerant Algerian landrace, Sahara 3771, and the intolerant Australian cultivar Clipper was screened in four tolerance assays. An RFLP linkage map of the Clipper×Sahara population was used to identify chromosomal regions associated with boron tolerance in barley. Interval regression-mapping allowed the detection of four chromosomal regions involved in the boron tolerance traits measured. A region on chromosome 2H was associated with leaf-symptom expression, a region on chromosome 3H was associated with a reduction of the affect of boron toxicity on root growth suppression, a region on chromosome 6H was associated with reduced boron uptake, and a region on chromosome 4H was also associated with the control of boron uptake as well as being associated with root-length response, dry matter production and symptom expression. The benefits and potential of marker-assisted selection for boron toxicity tolerance are discussed. Received: 18 December 1997 / Accepted: 28 November 1998     

Multivariate Non-parametric Tolerance Regions: A New Construction Technique

In continuation of the work by Abt (1977, 1982) and Ackermann (1980) a new construction technique is proposed to construct multivariate non-parametric tolerance regions based on the higher-dimensional correlations among the N variables under consideration. The scale-independency of the method is shown and a decision function is described to decide whether a given point lies within such a tolerance region or not. The method is discussed using the data of a clinical example.     

Mapping and validation of chromosome regions conferring boron toxicity tolerance in wheat (Triticum aestivum)

Boron is an essential plant micro-nutrient which can be phytotoxic to plants if present in soils in high concentration. Boron toxicity has been recognised as an important problem limiting production in the low rainfall areas of southern Australia, West Asia and North Africa. Genetic variation for boron toxicity tolerance in wheat has been well-characterised. The efficiency of breeding for boron toxicity tolerance could be greatly enhanced by the development of molecular markers associated with QTLs for tolerance in wheat. A population of 161 doubled haploids from a cross between the tolerant cultivar Halberd and the moderately sensitive cultivar Cranbrook was used to identify chromosomal regions involved in boron tolerance. A combined RFLP and AFLP linkage map of the Cranbrook x Halberd population was used to identify chromosomal regions involved in the boron tolerance traits measured. Regions on chromosome 7B and 7D were associated with leaf symptom expression. The region on chromosome 7B was also associated with the control of boron uptake and with a reduction in the effect of boron toxicity on root-growth suppression. RFLP markers at the chromosome 7B and 7D loci were shown to be effective in selecting for improved boron tolerance in an alternative genetic background. Halberd alleles at the chromosome 7B locus were associated with the concentration of boron in whole shoots and grain. The concentration of boron in whole shoots and in grain were both related to grain yield in a field trial conducted on soil containing toxic levels of boron. Implications relating to marker-assisted selection for boron toxicity tolerance in wheat are discussed. Received: 3 September 1999 / Accepted: 12 February 2000     

Biomarkers of human gastrointestinal tract regions

Dysregulation of intestinal epithelial cell performance is associated with an array of pathologies whose onset mechanisms are incompletely understood. While whole-genomics approaches have been valuable for studying the molecular basis of several intestinal diseases, a thorough analysis of gene expression along the healthy gastrointestinal tract is still lacking. The aim of this study was to map gene expression in gastrointestinal regions of healthy human adults and to implement a procedure for microarray data analysis that would allow its use as a reference when screening for pathological deviations. We analyzed the gene expression signature of antrum, duodenum, jejunum, ileum, and transverse colon biopsies using a biostatistical method based on a multivariate and univariate approach to identify region-selective genes. One hundred sixty-six genes were found responsible for distinguishing the five regions considered. Nineteen had never been described in the GI tract, including a semaphorin probably implicated in pathogen invasion and six novel genes. Moreover, by crossing these genes with those retrieved from an existing data set of gene expression in the intestine of ulcerative colitis and Crohn’s disease patients, we identified genes that might be biomarkers of Crohn’s and/or ulcerative colitis in ileum and/or colon. These include CLCA4 and SLC26A2, both implicated in ion transport. This study furnishes the first map of gene expression along the healthy human gastrointestinal tract. Furthermore, the approach implemented here, and validated by retrieving known gene profiles, allowed the identification of promising new leads in both healthy and disease states.     

Ecological assessment of vegetation from a nature reserve using regional reference data and indicator scores

A method is presented for ecological assessment of botanical sample data from a nature reserve network. The approach uses regional floristic survey data for a specific biotope as a context for spatial and temporal comparison. Assessments are based upon floristic similarity to reference vegetation types and indicator scores that summarise multivariate plant species data in relation to important environmental gradients. The approach was implemented as a software tool using floristic survey data for soligenous mires in a UK region. Plant community monitoring data were assessed against reference communities from this regional baseline to illustrate the potential advantages of the method. These include; (a) allowing links to be made between multivariate plant species data and measurements of environmental drivers, (b) providing realistic assessments of spatial and temporal differences because comparisons are against typical values of indicator scores for the region, (c) providing the scope for setting realistic criteria for vegetation monitoring.     

Prerequisites for use of common reference intervals

The theory of reference values was developed more than 30 years ago, but its application in most clinical laboratories is still incomplete today. This is for several reasons, the most relevant ones being the lack of standardisation of the analytical methods, resulting in method-dependent values, and the difficulty in recruiting the proper number of reference subjects for establishment of reference intervals. With the recent progress in method standardisation the first problem is reducing while the second can be addressed optimally via multicentre collaborative studies that aim to establish common reference intervals. To be effective this approach requires the following prerequisites: 1) the existence of a reference measurement system for the analyte; 2) field methods producing results traceable to the reference system; and 3) a carefully planned multicentre reference interval study. Such a procedure will produce results traceable to the reference measurement system for a large number of reference subjects, under controlled pre-analytical conditions. It will also enable a better understanding of the various sources of population variability, if there is the need for partitioning of a reference interval or if there are any limitations to adopting the established reference intervals on a national or global scale. Once reference intervals are determined, clinical laboratories can adopt a common reference interval provided: 1) the population that the laboratory services is similar to the one studied; 2) methods producing traceable results are used; and 3) analytical quality is within defined targets of precision and bias. Moreover, some validation of the interval using a small sample of reference individuals from the laboratory's population is advisable.     

Age-specific reference intervals for routine biochemical parameters in healthy neonates,infants, and young children in Iran

Age and sex need to be considered in the establishment of reference intervals (RIs), especially in early life when there are dynamic physiological changes. Since data for important biomarkers in healthy neonates and infants are limited, particularly in Iranian populations, we have determined age-specific RIs for 7 laboratory biochemical parameters. This cross-sectional study comprised a total of 344 paediatric participants (males: 158, females: 186) between the ages of 3 days and 30 months (mean age: 12.91 ± 7.15 months). Serum levels of creatinine, urea, uric acid, calcium, phosphate, vitamin D and high-sensitivity C-reactive protein (hs-CRP) were measured using an Alpha classic-AT plus auto-analyser. We determined age-specific RIs using CLSI Ep28-A3 and C28-A3 guidelines. No sex partitioning was required for any of the biomarkers. Age partitioning was required for kidney function tests and phosphate. The serum concentration of urea and creatinine increased with age, while phosphate and uric acid decreased with age. Age partitioning was not required for serum calcium, vitamin D, and hs-CRP, which remained relatively constant throughout the age range. Age-specific RIs for 7 routine biochemical markers were determined to address critical gaps in RIs in early life to help improve clinical interpretation of blood test results in young children, including neonates. Established age partitions demonstrate the biochemical changes that take place during child growth and development. These novel data will ultimately better disease management in the Iranian paediatric population and can be of value to clinical and hospital laboratories with similar populations.     

Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points

The inverse problem of electrocardiography, the computation of epicardial potentials from body surface potentials, is influenced by the desired resolution on the epicardium, the number of recording points on the body surface, and the method of limiting the inversion process. To examine the role of these variables in the computation of the inverse transform, Tikhonov's zero-order regularization and singular value decomposition (SVD) have been used to invert the forward transfer matrix. The inverses have been compared in a data-independent manner using the resolution and the noise amplification as endpoints. Sets of 32, 50, 192, and 384 leads were chosen as sets of body surface data, and 26, 50, 74, and 98 regions were chosen to represent the epicardium.The resolution and noise were both improved by using a greater number of electrodes on the body surface. When 60% of the singular values are retained, the results show a trade-off between noise and resolution, with typical maximal epicardial noise levels of less than 0.5% of maximum epicardial potentials for 26 epicardial regions, 2.5% for 50 epicardial regions, 7.5% for 74 epicardial regions, and 50% for 98 epicardial regions. As the number of epicardial regions is increased, the regularization technique effectively fixes the noise amplification but markedly decreases the resolution, whereas SVD results in an increase in noise and a moderate decrease in resolution. Overall the regularization technique performs slightly better than SVD in the noise-resolution relationship.There is a region at the posterior of the heart that was poorly resolved regardless of the number of regions chosen. The variance of the resolution was such as to suggest the use of variable-size epicardial regions based on the resolution.     

Generalized Confidence Intervals for Ratios of Regression Coefficients with Applications to Bioassays

The problem of constructing a confidence interval for the ratio of two regression coefficients is addressed in the context of multiple regression. The concept of a Generalized Confidence Interval is used, and the resulting confidence interval is shown to perform well in terms of coverage probability. The proposed methodology always results in an interval, unlike the confidence region generated from Fieller's theorem. The procedure can easily be implemented for parallel‐line assays, slope‐ratio assays, and quantal assays under a probit model. Furthermore, this approach can also be extended to compute confidence intervals based on data from multiple bioassays. The results are illustrated using several examples.     

Establishing reference intervals for von Willebrand factor multimers

Backgroundvon Willebrand factor (VWF) multimers (VWF:MM) methodologies are technically difficult, laborious, time consuming, non-standardized and results vary between laboratories. A new semi automated VWF:MM assay is available for routine use (Sebia). Due to lack of reference values for VWF:MM fractions, results interpretation can be challenging in some cases. The aim of this study was to determine reference intervals for low molecular weight (LMWM), intermediate molecular weight (IMWM) and high molecular weight (HMWM) multimers.MethodsBy the international cooperation initiated between 4 countries (Estonia, Latvia, France, and USA) 131 samples of relatively healthy individuals were analyzed for VWF:MM (in total 51 males and 80 non-pregnant females aged 17-69 years). Reference intervals were calculated according to CLSI C28-A3 standard.ResultsThe proposed reference intervals for VWF:MM were calculated for LMWM 10.4-22.5%, IMWM 22.6-37.6%, HMWM 45.6-66.6%. Age related differences were seen in IMWM and HMWM (p<0.001 and 0.038). There was no gender related difference observed. Geographically LMWM results of France were different from the other regions (p<0.05).ConclusionsQuantification of VWF:MM fractions, in addition to qualitative assessment of VWF:MM patterns, has the potential to aid in differential diagnosis of von Willebrand disease (VWD) subtypes. The reference values calculated in this study can be used in future research to establish clinical decision limits.     

Some important physiological selection criteria for salt tolerance in plants

Undoubtedly, plant breeders have made a significant achievement in the past few years, improving salinity tolerance in a number of potential crops using artificial selection and conventional breeding approaches, although molecular biology approaches are currently being intensively pursued for achieving this goal. However, most of the selection procedures used so far, were based merely on differences in agronomic characters. Agronomic characters represent the combined genetic and environmental effects on plant growth, and include the integration of the physiological phenomena conferring salinity tolerance. In fact, physiological criteria are able to supply more reliable information than agronomic characters. Although there are large numbers of reports in the literature mainly dealing with water relations, photosynthesis, and accumulation of various inorganic ions and organic metabolites in individual crops, there is little information available on the use of these attributes as selection criteria for improving salt tolerance through selection and breeding programs. In this review, the major adaptive components of salt tolerance such as osmotic adjustment, photosynthesis, water relations and ion relations are reviewed. In view of the complexity of salt tolerance and its great variation at intra-specific and inter-specific levels, it is difficult to identify single criteria, which could be used as effective selection targets. Rather it is most meaningful if physiological and biochemical indicators for individual species are determined rather than generic indicators.