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 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)     

Circadian Time-Qualified Tolerance Intervals for Ambulatory Blood Pressure Monitoring in the Diagnosis of Hypertension

The large-amplitude circadian pattern in blood pressure of healthy subjects of both genders suggests that the constant threshold currently used to diagnose hypertension should be replaced by a time-specified reference limit reflecting the mostly predictable blood pressure variability during the 24 h. Accordingly, we derived circadian time-specified reference standards for blood pressure as a function of gender. We studied 743 normotensive Caucasian volunteers (400 men and 343 women), 45.7 ± 16.5 (mean ± SD) years of age. Blood pressure was measured by ambulatory monitoring at 20-min intervals during the day and at 30-min intervals at night for 48 consecutive hours. Data from each blood pressure series were synchronized according to the rest-activity cycle of each individual in order to avoid differences among subjects in actual times of daily activity. Data were then used to compute 90% circadian tolerance intervals for each gender separately. The method, derived on the basis of bootstrap techniques, does not need to assume normality or symmetry in the data and, therefore, it is highly appropriate to describe the circadian pattern of blood pressure variability. Results reflect expected changes in the tolerance limits as a function of gender and circadian sampling time, as well as upper blood pressure limits below the thresholds currently used for diagnosing hypertension, especially for women. The use of these time-dependent tolerance limits for the computation of a hyperbaric index as a measure of blood pressure excess has already been shown to provide a reproducible and high-sensitivity test for the diagnosis of hypertension, which can also be used to evaluate treatment efficacy.     

Circadian time-qualified tolerance intervals for ambulatory blood pressure monitoring in the diagnosis of hypertension

The large-amplitude circadian pattern in blood pressure of healthy subjects of both genders suggests that the constant threshold currently used to diagnose hypertension should be replaced by a time-specified reference limit reflecting the mostly predictable blood pressure variability during the 24 h. Accordingly, we derived circadian time-specified reference standards for blood pressure as a function of gender. We studied 743 normotensive Caucasian volunteers (400 men and 343 women), 45.7 ± 16.5 (mean ± SD) years of age. Blood pressure was measured by ambulatory monitoring at 20-min intervals during the day and at 30-min intervals at night for 48 consecutive hours. Data from each blood pressure series were synchronized according to the rest-activity cycle of each individual in order to avoid differences among subjects in actual times of daily activity. Data were then used to compute 90% circadian tolerance intervals for each gender separately. The method, derived on the basis of bootstrap techniques, does not need to assume normality or symmetry in the data and, therefore, it is highly appropriate to describe the circadian pattern of blood pressure variability. Results reflect expected changes in the tolerance limits as a function of gender and circadian sampling time, as well as upper blood pressure limits below the thresholds currently used for diagnosing hypertension, especially for women. The use of these time-dependent tolerance limits for the computation of a hyperbaric index as a measure of blood pressure excess has already been shown to provide a reproducible and high-sensitivity test for the diagnosis of hypertension, which can also be used to evaluate treatment efficacy.     

The tolerance-hyperbaric test: a chronobiologic approach for improved diagnosis of hypertension

Blood pressure (BP) displays predictable large-amplitude circadian variability. Thus, the identification and the proper definition of hypertension are highly ambiguous when based on single time-unspecified measurements. One way to deal with such variability in the diagnosis of hypertension is to replace the commonly used constant limits of BP by a time-specified reference interval based on the normal circadian BP rhythm assessed by ambulatory BP monitoring (ABPM). A proper reference limit can be constructed, for instance, as a tolerance interval computed for every specific time interval throughout the 24 h. Once such a threshold (given by the upper limit of the tolerance interval) is constructed, a hyperbaric index (HBI) can be computed by numerical integration of the total area of any given patient's BP profile above threshold. The HBI plus the duration of excess within the 24h day serves as nonparametric endpoints for assessing hypertension. Both retrospective and prospective evaluation of this tolerance-hyperbaric test validate its high sensitivity and specificity in the diagnosis of hypertension. We describe the theory of the HBI as well as a newly created dedicated software program that automatically derives the tolerance intervals from a reference database of normotensive subjects and calculates the HBI and other potentially valuable parameters based on data obtained by ABPM. The establishment of time-qualified tolerance limits and the assessment of the extent and timing of BP elevation represents a valuable tool for the more accurate diagnosis of hypertension as well as means of gauging response to treatment.     

Rectangular tolerance regions and multivariate normal reference regions in laboratory medicine

Reference intervals are widely used in the interpretation of results of biochemical and physiological tests of patients. When there are multiple biochemical analytes measured from each subject, a multivariate reference region is needed. Because of their greater specificity against false positives, such reference regions are more desirable than separate univariate reference intervals that disregard the cross-correlations between variables. Traditionally, under multivariate normality, reference regions have been constructed as ellipsoidal regions. This approach suffers from a major drawback: it cannot detect component-wise extreme observations. In the present work, procedures are developed to construct rectangular reference regions in the multivariate normal setup. The construction is based on the criteria for tolerance intervals. The problems addressed include the computation of a rectangular tolerance region and simultaneous tolerance intervals. Also addressed is the computation of mixed reference intervals that include both two-sided and one-sided limits, simultaneously. A parametric bootstrap approach is used in the computations, and the accuracy of the proposed methodology is assessed using estimated coverage probabilities. The problem of sample size determination is also addressed, and the results are illustrated using examples that call for the computation of reference regions.     

THE TOLERANCE-HYPERBARIC TEST: A CHRONOBIOLOGIC APPROACH FOR IMPROVED DIAGNOSIS OF HYPERTENSION

Blood pressure (BP) displays predictable large-amplitude circadian variability. Thus, the identification and the proper definition of hypertension are highly ambiguous when based on single time-unspecified measurements. One way to deal with such variability in the diagnosis of hypertension is to replace the commonly used constant limits of BP by a time-specified reference interval based on the normal circadian BP rhythm assessed by ambulatory BP monitoring (ABPM). A proper reference limit can be constructed, for instance, as a tolerance interval computed for every specific time interval throughout the 24 h. Once such a threshold (given by the upper limit of the tolerance interval) is constructed, a hyperbaric index (HBI) can be computed by numerical integration of the total area of any given patient's BP profile above threshold. The HBI plus the duration of excess within the 24h day serves as nonparametric endpoints for assessing hypertension. Both retrospective and prospective evaluation of this tolerance-hyperbaric test validate its high sensitivity and specificity in the diagnosis of hypertension. We describe the theory of the HBI as well as a newly created dedicated software program that automatically derives the tolerance intervals from a reference database of normotensive subjects and calculates the HBI and other potentially valuable parameters based on data obtained by ABPM. The establishment of time-qualified tolerance limits and the assessment of the extent and timing of BP elevation represents a valuable tool for the more accurate diagnosis of hypertension as well as means of gauging response to treatment.     

Closing the Gaps in Paediatric Reference Intervals: The CALIPER Initiative

Screening, diagnosis and monitoring of paediatric diseases relies on the measurement of a spectrum of disease biomarkers in clinical laboratories to guide important clinical decisions. Physicians rely on the availability of suitable and reliable reference intervals to accurately interpret laboratory test results with data collected during medical history and physical examination. However, critical gaps currently exist in accurate and up-to-date reference intervals (normal values) for accurate interpretation of laboratory tests performed in children and adolescents. These gaps in the available paediatric laboratory reference intervals have the clear potential of contributing to erroneous diagnosis or misdiagnosis of many diseases of childhood and adolescence. Most of the available reference intervals for laboratory tests were determined over two decades ago on older instruments and technologies, and are no longer relevant considering the current testing technology used by clinical laboratories. It is thus critical and of utmost urgency that a more acceptable and comprehensive database be established. There are however many challenges when attempting to establish paediatric reference intervals. Paediatric specimen collection is a major concern for health care providers as it is frequently difficult to obtain sufficient volumes of blood or urine from paediatric patients. Common reference intervals have not been widely implemented due to lack of harmonisation of methods and differences in patient populations. Consequently, clinical laboratory accreditation organisations and licensing agencies require that each laboratory verify or establish reference intervals for each method. To provide such reference intervals requires selection criteria for suitable reference individuals, defined conditions for specimen collection and analysis, method selection to determine reference limits and validation of the reference interval. The current review will provide a brief introduction to the current approach to establishment of reference intervals, will highlight the current gaps in data available in paediatric populations, and review a recent Canadian initiative, CALIPER (Canadian Laboratory Initiative on Paediatric Reference Intervals), to establish a comprehensive database for both traditional and emerging biomarkers of paediatric disease.     

Calculating confidence intervals for prediction error in microarray classification using resampling

Cross-validation based point estimates of prediction accuracy are frequently reported in microarray class prediction problems. However these point estimates can be highly variable, particularly for small sample numbers, and it would be useful to provide confidence intervals of prediction accuracy. We performed an extensive study of existing confidence interval methods and compared their performance in terms of empirical coverage and width. We developed a bootstrap case cross-validation (BCCV) resampling scheme and defined several confidence interval methods using BCCV with and without bias-correction. The widely used approach of basing confidence intervals on an independent binomial assumption of the leave-one-out cross-validation errors results in serious under-coverage of the true prediction error. Two split-sample based methods previously proposed in the literature tend to give overly conservative confidence intervals. Using BCCV resampling, the percentile confidence interval method was also found to be overly conservative without bias-correction, while the bias corrected accelerated (BCa) interval method of Efron returns substantially anti-conservative confidence intervals. We propose a simple bias reduction on the BCCV percentile interval. The method provides mildly conservative inference under all circumstances studied and outperforms the other methods in microarray applications with small to moderate sample sizes.     

Physiology and its Importance for Reference Intervals

Reference intervals are ideally defined on apparently healthy individuals and should be distinguished from clinical decision limits that are derived from known diseased patients. Knowledge of physiological changes is a prerequisite for understanding and developing reference intervals. Reference intervals may differ for various subpopulations because of differences in their physiology, most obviously between men and women, but also in childhood, pregnancy and the elderly. Changes in laboratory measurements may be due to various physiological factors starting at birth including weaning, the active toddler, immunological learning, puberty, pregnancy, menopause and ageing. The need to partition reference intervals is required when there are significant physiological changes that need to be recognised. It is important that laboratorians are aware of these changes otherwise reference intervals that attempt to cover a widened inter-individual variability may lose their usefulness. It is virtually impossible for any laboratory to directly develop reference intervals for each of the physiological changes that are currently known, however indirect techniques can be used to develop or validate reference intervals in some difficult situations such as those for children. Physiology describes our life’s journey, and it is only when we are familiar with that journey that we can appreciate a pathological departure.     

Reference intervals

Recommended elements of a process for establishing a reference interval: Define the analyte (measurand) for which the reference interval is being established, the clinical utility, biological variation and major variations in form. Define the method used, the accuracy base, and analytical specificity. Define important pre-analytical considerations together with any actions in response to the interference. Define the principle behind the reference interval (i.e. central 95% etc.). Describe the data source(s), including: number of subjects, nature of subjects, exclusions, pre-analytical factors, statistical measures, outliers excluded and analytical method. Define considerations of partitioning based on age, sex etc. Define the number of significant figures, i.e. the degree of rounding. Define the clinical relevance of the reference limits. Consider the use of common reference intervals. Decision and implementation.     

温室甜瓜营养生长期日蒸腾量估算模型

建立了基于温室环境参数、甜瓜生长发育参数和土壤水分参数的温室甜瓜日蒸腾量估算模型,以研究温室条件下甜瓜蒸腾量的估算方法.根据温室内特定环境对Penman-Monteith方程中空气动力项进行修正,推导出了适于计算温室条件下参考作物蒸腾量的温室环境因子子模型;以甜瓜叶面积指数为自变量构建了作物因子子模型,模型形式为线性函数;以土壤相对有效含水量为自变量构建了土壤水分因子子模型,模型形式为对数函数.采用分期播种法,根据周年不同播期实测数据对模型参数进行估计和分析.采用土壤相对含水量分别为80%、70%、60%的实测蒸腾数据,对模型在充分灌溉和节水灌溉条件下的预测精度进行了检验,模拟值的平均相对误差分别为11.5%、16.2%、16.9%.所建蒸腾模型是对Penman-Monteith公式在温室环境和节水灌溉条件下的有益探索,具有重要推广应用价值.     

Birth interval, mortality and growth of children in a rural area in Kenya

The impact of the length of birth intervals on mortality and growth of children from the perinatal period to 2 years in the Northern Division of Machakos District, Eastern Province, Kenya, were analyzed. There are 2 types of birth intervals: 1) the prospective birth interval--between the birth concerned (the 1st birth of the interval pair) and the subsequent birth; and 2) the retrospective birth interval--between the birth considered (the 2nd of the interval pair) and the preceeding birth. This study includes 3019 women who had at least 1 live birth between April, 1974 and April, 1981. They gave birth to 6778 children (including stillbirths). Births occurring in 1974 are excluded in the analysis because of considerable underregistration. 102 stillbirths and 213 deaths in the 1st 2 years are analyzed. They have been grouped into deaths during the perimatal period; the 1st year after the 1st week of life (infant period); and the 2nd year of life. The most convient method of analysis of the relation between retrospective birth interval and mortality is multivariate analysis, as the intermedicate biological and behavioral factors through which birth intervals can affect health are simultaneously influenced by other variables like maternal age and birth order; the log linear model is applied here. The probability of dying is the dependent variable. The impact of short prospective intervals are closely associated. Only infant and child deaths occurring after the conception of the next child are included. The size of cohorts in which these deaths occur can be calculated with a life table approach. The mortality probability between 5 and 12 months for children with short prospective intervals is .034. This is higher than the corresponding rate for all children in the area (P0.05). It is shown that children with short retrospective or prospective birth intervals do not run a greater risk of mortality or growth retardation than children with longer intervals, neither during the perinatal period nor during the 1st 2 years of life.     

Growth hormone and tumour recurrence.

OBJECTIVE--To determine whether using growth hormone to treat radiation induced growth hormone deficiency causes tumour recurrence. DESIGN--Comparison of tumour recurrence rates in children treated with growth hormone for radiation induced deficiency and an untreated population. Computed tomograms from children with brain tumours were reviewed when starting growth hormone and subsequently. SETTING--North West region. PATIENTS--207 children treated for brain tumour, 47 of whom received growth hormone and 161 children with acute lymphoblastic leukaemia 15 of whom received growth hormone. MAIN OUTCOME MEASURES--Tumour recurrence and changes in appearances on computed tomography. RESULTS--Among children with brain tumour, five (11%) who received growth hormone had recurrences compared with 42 (26%) who did not receive growth hormone. Also adjusting for other variables that might affect tumour recurrence the estimated relative risk of recurrence was 0.82 (95% confidence interval 0.28 to 2.37). The only child with acute lymphoblastic leukaemia who relapsed while taking growth hormone had relapsed previously before starting treatment. Two of the five children with brain tumours who relapsed had abnormal appearances on computed tomography when growth hormone was started. 14 other children who remained relapse free and had follow up computed tomography showed no deterioration in radiological appearance during treatment. CONCLUSIONS--In this population growth hormone did not increase the risk of tumour recurrence but continued surveillance is essential. Abnormal results on computed tomography are not a contraindication to treatment with growth hormone.     

Estimation of Sample Size for Reference Interval Studies

The currently used criterion for sample size calculation in a reference interval study is not well stated and leads to imprecise control of the ratio in question. We propose a generalization of the criterion used to determine sufficient sample size in reference interval studies. The generalization allows better estimation of the required sample size when the reference interval estimation will be using a power transformation or is nonparametric. Bootstrap methods are presented to estimate sample sizes required by the generalized criterion. Simulation of several distributions both symmetric and positively skewed is presented to compare the sample size estimators. The new method is illustrated on a data set of plasma glucose values from a 50‐g oral glucose tolerance test. It is seen that the sample sizes calculated from the generalized criterion leads to more reliable control of the desired ratio.     

Likelihood-Weighted Confidence Intervals for the Difference of Two Binomial Proportions

Two new methods for computing confidence intervals for the difference δ = p₁ — p₂ between two binomial proportions (p₁, p₂) are proposed. Both the Mid-P and Max-P likelihood weighted intervals are constructed by mapping the tail probabilities from the two-dimensional (p₁, p₂)-space into a one-dimensional function of δ based on the likelihood weights. This procedure may be regarded as a natural extension of the CLOPPER-PEARSON (1934) interval to the two-sample case where the weighted tail probability is α/2 at each end on the δ scale. The probability computation is based on the exact distribution rather than a large sample approximation. Extensive computation was carried out to evaluate the coverage probability and expected width of the likelihood-weighted intervals, and of several other methods. The likelihood-weighted intervals compare very favorably with the standard asymptotic interval and with intervals proposed by HAUCK and ANDERSON (1986), COX and SNELL (1989), SANTNER and SNELL (1980), SANTNER and YAMAGAMI (1993), and PESKUN (1993). In particular, the Mid-P likelihood-weighted interval provides a good balance between accurate coverage probability and short interval width in both small and large samples. The Mid-P interval is also comparable to COE and TAMHANE'S (1993) interval, which has the best performance in small samples.     

Hypothesis Testing of Inclusion of the Tolerance Interval for the Assessment of Food Safety

In the testing of food quality and safety, we contrast the contents of the newly proposed food (genetically modified food) against those of conventional foods. Because the contents vary largely between crop varieties and production environments, we propose a two-sample test of substantial equivalence that examines the inclusion of the tolerance intervals of the two populations, the population of the contents of the proposed food, which we call the target population, and the population of the contents of the conventional food, which we call the reference population. Rejection of the test hypothesis guarantees that the contents of the proposed foods essentially do not include outliers in the population of the contents of the conventional food. The existing tolerance interval (TI₀) is constructed to have at least a pre-specified level of the coverage probability. Here, we newly introduce the complementary tolerance interval (TI₁) that is guaranteed to have at most a pre-specified level of the coverage probability. By applying TI₀ and TI₁ to the samples from the target population and the reference population respectively, we construct a test statistic for testing inclusion of the two tolerance intervals. To examine the performance of the testing procedure, we conducted a simulation that reflects the effects of gene and environment, and residual from a crop experiment. As a case study, we applied the hypothesis testing to test if the distribution of the protein content of rice in Kyushu area is included in the distribution of the protein content in the other areas in Japan.     

Shape analysis of two sympatric coral species: Implications for taxonomy and evolution

Fourier shape analysis of Pleurodictyum americanum and P. dividua , favositid tabulate corals, from the Middle Devonian Hamilton Group of New York State, indicates that colony growth form is variable within species between environments, but that the range of variability in growth form is static through time. Pleurpdictyum dividua displays a columnar morphotype; however, P. dividua and P. americanum cannot be discriminated from one another based on colony shape alone. A major prediction of the punctuated equilibrium model of evolution is morphological stasis throughout the duration of a species. Harmonic means of assemblages of P. americanum show no persistent temporal trends. The range of harmonic means present among the oldest assemblages (Centerfield Limestone) are comparable to those among the youngest assemblages (Windom Shale) and to those in the intervening intervals. Character stasis in colony growth form lasted throughout a 2.5-3.5 my interval. In tabulate corals, where reproductive modes such as fragmentation have not been demonstrated, growth form may be useful in interpreting ancient environments. In addition, the tempo of evolution of growth form can be analyzed when sufficient morphological data are available from a wide distribution of environments. Thus, Fourier shape analysis of growth form provides a powerful tool for paleontologists to interpret the ecology and evolution of colonial marine animals.