Within-individual Variance Research Articles

Using the overdispersed exponential family to estimate the distribution of usual daily intakes of people aged between 18 and 28 in Taiwan.

Assessment of usual dietary intake of a population is essential to understand the nutrition status of the population. Methods like 24-hour dietary recall and food records are commonly used for this task. However, within-individual variation exists in the food record data. Methods considering measurement errors have been used to evaluate the association between nutrient intakes and diseases. Few have been devoted to estimating the distribution of usual daily intakes. This paper proposes applying the formulation of the overdispersed exponential family to estimate the distribution of usual nutrient intake and applies the adjustments developed by Liu to reduce the variance of the distribution. The proposed method has the advantages of working on the original scale of data and implementation convenience. The adjustment of the variance is carried out by dividing the variance into within-individual variance and among-individual variance. The adjusted variance, then, is used to estimate the distribution of the usual daily intake. Sampling weights are considered in all the steps, except the estimation of the ratio of within to among variance. The data for this study are from the Nutritional and Health Survey in Taiwan conducted between 1993 and 1996 (NAHSIT, 1993-1996). An independent external set of data for people aged between 18 and 28 years (49 males and 20 females) is used to estimate the ratio of within to among individual variance. Due to the availability of data in estimating the ratio of within to among individual variance, 430 males and 422 females in the NAHSIT sample are used to estimate the distribution of usual daily intakes for people aged between 18 and 28 in Taiwan. The distribution also allows us to estimate the proportion of people who do not meet the recommended daily nutrient allowance (RDNA). The results show that the intakes of calcium and vitamin E of this group of people fall far below RDNA.

Motor Patterns of Herbivorous Feeding: Electromyographic Analysis of Biting in the Parrotfishes Cetoscarus bicolor and Scarus iseri

The motor patterns of the herbivorous feeding bite were investigated in two species of parrotfish (Cetoscarus bicolor and Scarus iseri) with functionally distinct biting modes using electromyographic recordings. Behavioral data revealed that S. iseri utilized faster bites, took more bites per feeding bout, and bit at a higher frequency than did C. bicolor. EMGs recorded from the epaxialis (EP), levator operculi (LOP), 3 subdivisions of the adductor mandibulae (A1–A3), and the sternohyoideus (SH) muscles displayed a high degree of within-individual variance. Duration of muscle activity and onset time relative to LOP were shorter in S. iseri than in C. bicolor and S. iseri displayed a greater EMG amplitude in the LOP and SH muscles than did C. bicolor. We calculated the duty factors of the muscles as the relative timing of EMG variables divided by the total feeding cycle time. Patterns of duty factors of the feeding muscles were similar in both species, though muscles were active for a longer portion of the total bite cycle in S. iseri. In addition to its typical bite, S. iseri employed additional motor patterns when taking particularly hard bites. A multivariate comparison of EMGs from biting and suction feeding taxa revealed that the biting motor pattern was significantly different from suction feeding, although there was a high degree of overlap among all feeding strikes. The activity of the sternohyoideus muscle was significantly different between suction feeders and biters. Despite strong similarities of the general motor pattern in a wide range of teleost fishes, components of this pattern are shown to be evolutionarily plastic.

Food diversity and validity of semiquantitative food frequency questionnaire.

We hypothesized that validity of semiquantitative food frequency questionnaire would be affected by food diversity (variety of foods consumed), because greater food diversity may be related to greater within-individual variation of nutrient intake, which can attenuate the correlation coefficient measuring validity of the questionnaire. We obtained 12 one-day diet records over one year and responses to a semiquantitative food frequency questionnaire from 37 subjects. The food diversity score for each subject was determined by the total number of different foods consumed during the 12 days for the diet records, and the subjects were divided into two groups according to the score. The within-individual variances were similar in those with higher and lower food diversity scores. We never observed a significantly lower correlation coefficient for any nutrient in those with higher food diversity scores. The observed and corrected correlations for most of the micronutrients were higher in those with higher food diversity scores, and the differences were statistically significant for crude fiber, vitamin C, iron, and potassium. The validity of the semiquantitative food frequency questionnaire did not appear to be lowered greatly by greater food diversity.

A Semiparametric Transformation Approach to Estimating Usual Daily Intake Distributions

Abstract The distribution of usual intakes of dietary components is important to individuals formulating food policy and to persons designing nutrition education programs. The usual intake of a dietary component for a person is the long-run average of daily intakes of that component for that person. Because it is impossible to directly observe usual intake for an individual, it is necessary to develop an estimator of the distribution of usual intakes based on a sample of individuals with a small number of daily observations on a subsample of the individuals. Daily intake data for individuals are nonnegative and often very skewed. Also, there is large day-to-day variation relative to the individual-to-individual variation, and the within-individual variance is correlated with the individual means. We suggest a methodology for estimating usual intake distributions that allows for varying degrees of departure from normality and recognizes the measurement error associated with one-day dietary intakes. The est...

A Semiparametric Transformation Approach to Estimating Usual Daily Intake Distributions

Abstract The distribution of usual intakes of dietary components is important to individuals formulating food policy and to persons designing nutrition education programs. The usual intake of a dietary component for a person is the long-run average of daily intakes of that component for that person. Because it is impossible to directly observe usual intake for an individual, it is necessary to develop an estimator of the distribution of usual intakes based on a sample of individuals with a small number of daily observations on a subsample of the individuals. Daily intake data for individuals are nonnegative and often very skewed. Also, there is large day-to-day variation relative to the individual-to-individual variation, and the within-individual variance is correlated with the individual means. We suggest a methodology for estimating usual intake distributions that allows for varying degrees of departure from normality and recognizes the measurement error associated with one-day dietary intakes. The estimation method contains four steps. First, the original data are standardized by adjusting for nuisance effects, such as day-of-week and interview sequence. Second, the daily intake data are transformed to normality using a combination of power and grafted polynomial transformations. Third, using a normal components-of-variance model, the distribution of usual intakes is constructed for the transformed data. Finally, a transformation of the normal usual intake distribution to the original scale is defined. The approach is applied to data from the 1985 Continuing Survey of Food Intakes by Individuals and works well for a set of dietary components that are consumed nearly daily and exhibit varying distributional shapes.

Inter- and Intraspecific Variation in Fruit Traits in Co-Occurring Vertebrate-Dispersed Plants

A quantitative analysis of the patterns of intra- and interspecific variance of fleshy fruit traits (length, width, pulp mass, seed mass, percent pulp mass) in eight species of southeastern Spanish vertebrate-dispersed plants, Berberis hispanica, Crataegus monogyna, Daphne laureola, Hedera helix, Juniperus communis, Juniperus phoenicea, Juniperus sabina, and Rosa canina, shows a statistically significant individual variability in the five fruit traits considered. Individual variability tended to be largest for pulp mass and seed mass (coefficient of variation of individual means between 20% and 30%) and smallest for fruit width and length and for proportion of pulp (CV of 5%-12%). Most variance in fruit traits (67%-88%) was accounted for by taxonomic affiliation, while the remainder of the variance was partitioned in roughly similar proportions among and within plants of individual species. There were some differences between fruit traits in the relative proportion of variance contributed by within and among individual variation, but all fruits traits in all species consistently exhibited a remarkably high proportion of within-individual variance, roughly comparable to the variance among individuals. The potential ecological and evolutionary implications of observed patterns of fruit variability are discussed in relation to the foraging behavior of seed-dispersing frugivores.

Design and analysis of studies of the health effects of ozone.

The design and analysis of studies that investigate the effect of exposure to ozone on health outcomes need to define carefully the methods for the assessment of the exposure and to determine precisely which is the outcome of biological relevance. The estimation of sample size for longitudinal studies requires the expected rates of change among the exposed and unexposed, the variance of the outcome, and the correlation of measurements taken within an individual. Methods of analysis whose primary interest is in the combination of cross-sectional studies for the determination of the marginal distribution of the outcome are particularly appropriate for biological processes where the effect of exposure is acute. Conditional models are particularly useful for investigating the effect of changes in exposure on changes in outcome at the individual level. In addition, conditional models incorporate a dampening effect of exposure that may provide a reasonable agreement with several biological mechanisms. The identification of susceptible individuals and the description of the behavior of their outcomes over time may be better accomplished by using the within-individual variance as the outcome of interest. Discrepancies of the within- and between-individual regressions may be suggestive of chronic effects, and methodological research in this area is needed. Studies of the health effects of ozone exposure need to address the incorporation of missing data, measurement error, and the combination of complementary studies.

Value of early weight measurements as predictors of body weight at later ages in reindeer

Phenotypic variances in live weight in a reindeer population and repeatabilities of the weights were estimated. The population consisted of 1847 and 1878 unselected male and female calves respectively, for which data from weighings at 2 and 7 months of age were available. All individuals in a selected population, consisting of 469 of the heaviest females, were weighed at 2, 7 and 19 months of age. The data were colleted during four successive years, 1986 - 1989. An indirect selection model for improving female weight at 19 months of age was proposed. Variance in the unselected population was higher between animals than within animals. Repeatability was estimated to be 0.636 for the male calves and 0.609 for the female calves. In the selected population, within-individual variance was higher than between-animal variance. Repeatabilities were, after correction for the effect of selection, 0.316 (between 2 and 19 months) and 0.548 (between 7 and 19 months). The aim of the selection model was to increase the average weight in the primiparous group to improve their calf production ability. Using the model, the number of animals weighing equal to or more than a certain threshold weight and the number needed for recruitment at 19 months of age could be determined.

Does it all go together when it goes? The Nineteenth Bartlett Memorial Lecture.

As groups of people age, the differences in the cognitive abilities of the most and least able become more extreme. This increase in between-individual variance is accompanied by an increase in within-individual variance: the difference between individuals' levels of performance on their best and least well retained skills. The implications of increasing between-individual variance are discussed in terms of the range of different factors that may affect cognitive ageing. Increases in within-individual variance are discussed in terms of differences between "fluid" and "crystallized" abilities. The usefulness of this distinction and its functional implications are questioned. The hypothesis that age-related declines in "fluid" abilities are best modelled in terms of declines in a single factor is evaluated. Evidence is presented of disparate rates of decline, even of "fluid" cognitive abilities, such as performance on IQ tests, ability on information-processing tasks, and efficiency on memory tasks. Data from large-scale cross-sectional studies suggests that cognitive skills do not "all go together when they go," but that there may rather, be characteristic patterns, or syndromes, of cognitive ageing.

Estimating an Individual's True Cholesterol Level and Response to Intervention

An individual's blood cholesterol measurement may differ from the true level because of short-term biological and technical measurement variability. Using data on the within-individual and population variance of serum cholesterol, we addressed the following clinical concerns: Given a cholesterol measurement, what is the individual's likely true level? The confidence interval for the true level is wide and asymmetrical around extreme measurements because of regression to the mean. Of particular concern is the misclassification of people with a screening measurement below 5.2 mmol/L who may be advised that their cholesterol level is "desirable" when their true level warrants further action To what extent does blood cholesterol change in response to an intervention? In general, confidence intervals are too wide to allow decision making and patient feedback about an individual's cholesterol response to a dietary intervention, even with multiple measurements. If no change is observed in an individual's cholesterol value based on three measurements before and three after dietary intervention, the 80% confidence interval ranges from a true increase of 4% to a true decrease of 9%.

The glycemic index: variation between subjects and predictive difference.

It is not known whether the variability of the glycemic index (GI) in different subjects is due to within- or between-individual variation. In addition, it is not known how large a difference in GI between different meals is clinically important for individuals with diabetes. Therefore, insulin-dependent (IDDM) and non-insulin-dependent (NIDDM) diabetic subjects tested four foods, with each food taken by each subject on two separate occasions. For each food, most of the variation of absolute glycemic responses was due to differences between the subjects. However, when the results were expressed as the GI, there were no significant differences between the subjects, and most of the variation was due to within-individual variation. Using the within-individual variance, we estimated the so-called "predictive difference" of GI values. Its reliability was assessed by consideration of published data from eight studies where different mixed meals were taken by the same group of subjects. There were 37 cases where the difference between the GI of any two meals was greater than the predictive difference. Of these 37 pairs of meals, the GI correctly ranked the glycemic responses in 36 (97%). We conclude that GI values for the same food do not vary significantly between different individuals. For a subject with NIDDM a difference in GI of 34 will predict the ranking of glycemic responses of two meals with 95% probability. The corresponding value for a subject with IDDM is 50.

Variability of urine albumin excretion in normal and diabetic children.

The variability of urine albumin excretion (UAE) was studied in normal and diabetic children and, in addition, the best method of expressing the data was investigated. In 39 timed overnight urine samples from diabetic children, the urine albumin creatinine clearance ratio (CA/CC) was compared with the urine albumin creatinine concentration ratio (UA/UC), the urine albumin excretion rate (UAER) and the urine albumin concentration (UA). UA/UC predicted CA/CC (r = 0.95) better than either UAER (r = 0.83, P less than 0.02) or UA (r = 0.90), 0.1 greater than P greater than 0.05). The within-individual and the between-individual variability in overnight UA/UC in 171 urine samples from 73 normal children was compared with that of 406 urine samples from 119 diabetic children, using a "random effects type 2 nested analysis of variance" model. Geometric mean (range) UA/UC (mg/mmol) in diabetic children, 0.55 (0.04-6.90), was greater than in normal children, 0.33 (0.05-2.10, P less than 0.01), and 18% of diabetics had a value of UA/UC above the normal range. Within-individual variance was the same in normals (0.12) and diabetics (0.12), but between-individual variance in diabetics (0.18) was much greater than in normals (0.03). These data show that within-individual observations for both normals and diabetics are highly but equally variable. Furthermore, from these data, it is possible to infer that a minimum of five estimations are necessary per individual to estimate the true mean value of urine albumin excretion with reasonable confidence.

Correcting for selection bias in estimation of within-individual variance.

Consider a variable whose expected value distributes among individuals in a population, and which also has an important component of within-individual variance. In a screening study that involves repeated observations only for those individuals whose initial observation exceeds an arbitrary cutoff point, the usual estimator of within-individual variance is biased. Assuming normality and independence, this note gives the derivation of the expected value of the estimator and uses it to obtain an unbiased estimator. The results generalize to the bivariate case that involves selection on only one variable of the pair. A companion paper provides an example with use of blood pressure.

The B-Chromosome System of Myrmeleotettix maculatus (Thunb). IV. The Dynamics

A necessary first step in the analysis oJ the population genetics of a given species is the adequate description, both in space and in time, of the genetic variation present in different populations of that species. Such variation may be studied in terms of two principal differences. First, allelic variation at individual loci, and second. variation in the structure and/or the number of chromosomes. Both, in fact, frequently lead to the development of polymorphic facies. Those associated with allelic variation are now relatively well understood for they have pronounced, often dramatic, effects on the exophenotype, effects which greatly facilitate an analysis of their adaptive roles. Thus allelic polymorphism is associated with mimicry in butterflies, with camouflage in moths and snails, with resistance to malarial parasites in man, and with floral biology in primroses (Sheppard, 1967). By contrast, most of the known chromosome polymorphisms are exophenotypically cryptic in character. It is often assumed that such polymorphisms are concerned, in some undefined way, with biochemical effects (see for example Wallace, 196,8), but the balance of evidence to date is that chromosome polymorphisms are expressed initially in the endophenotype rather than the exophenotype (John and Lewis, 1966). Coupled with this, the endophenotypic effects they promote can be either supplemented or counteracted by other components of the genetic system. Their study and their analysis is thus both more complex and more exacting than that of the conventional allelic nolvmornhisms. It comes as no surprise, therefore, to find that in very few instances have we any real appreciation of the factors which govern the presence or the frequency of particular chromosome polymorphisms in particular populations. British populations of the mottled or club-horned grasshopper, Myrmeleotettix maculatus, are polymorphic with respect to the presence of supernumerary or Bchromosomes (Barker, 1960; John and Hewitt, 1965a, b). These extra elements have no obvious immediate effect on exophenotype, as has been demonstrated by a study of five populations with from 10% to 40% B-chromosomes, in which five morphological characters were scored for each individual. The characters were (1) the number of stridulatory pegs per hind leg, (2) average length of tibiae (3) average length of femurs, (4) average length of wings, and (5) number of segments per antenna. These particular characters were chosen since they are important in a range of functions, from courtship and species recognition to movement and dispersal, and are probably influenced by a variety of developmental pathways. Table 1 contains a brief summary of the results from these five populations, all of which occur in a parkland about 3 miles across. There is no consistent picture with regard to differences between non-B and B-containing individuals within or between populations. The reason for considering the between-individual and within-individual variances, is because of the established effect of B-chromosomes on the chiasma frequency. Individuals with such supernumeraries have higher mean cell chiasma