Search

Shoaling behaviour is commonly displayed by fishes and is thought to reduce predation and increase foraging efficiency. Shoaling relies on coordination between individuals, with higher cohesion and alignment among individuals within a shoal providing greater net benefits of this behaviour. Whilst single species often shoal together in conspecific groups, mixed-species shoaling is frequently observed and has been identified as an important determinant of individual fitness for the multiple species involved. Despite their prevalence, the structure of mixed-species shoals and the mechanisms by which individuals gain protection from predators and enhance their foraging efficiency are not as well understood as for single-species shoals. In fact, mixed-species shoals may be less coordinated than single-species shoals, raising the intriguing question of why fishes form mixed-species shoals when this behaviour could be less beneficial than single-species shoaling. Here we used in situ stereo-video techniques to compare within and between shoal differences in cohesion and alignment, for mixed- and single-species shoals containing the tropical vagrant Indo pacific sergeant major damselfish, Abudefduf vaigiensis, in temperate waters. As expected, mixed-species shoals were less aligned than single-species shoals. However, within mixed-species shoals conspecifics were more cohesive and aligned than were heterospecifics, suggesting coordinated single-species subgroups formed within larger mixed-species shoals. The formation of subgroups may mitigate costs associated with differences between species, therefore enhancing benefits of mixed-species shoaling. As such, multiple levels of social structure may exist within mixed-species shoals that could facilitate growth and survival for vagrant A. vaigiensis in temperate regions. More broadly, this research highlights the importance of considering detailed internal structures of mixed-species shoals when trying to understand cost–benef

Shoaling behaviour is commonly displayed by fishes and is thought to reduce predation and increase foraging efficiency. Shoaling relies on coordination between individuals, with higher cohesion and alignment among individuals within a shoal providing greater net benefits of this behaviour. Whilst single species often shoal together in conspecific groups, mixed-species shoaling is frequently observed and has been identified as an important determinant of individual fitness for the multiple species involved. Despite their prevalence, the structure of mixed-species shoals and the mechanisms by which individuals gain protection from predators and enhance their foraging efficiency are not as well understood as for single-species shoals. In fact, mixed-species shoals may be less coordinated than single-species shoals, raising the intriguing question of why fishes form mixed-species shoals when this behaviour could be less beneficial than single-species shoaling. Here we used in situ stereo-video techniques to compare within and between shoal differences in cohesion and alignment, for mixed- and single-species shoals containing the tropical vagrant Indo pacific sergeant major damselfish, Abudefduf vaigiensis, in temperate waters. As expected, mixed-species shoals were less aligned than single-species shoals. However, within mixed-species shoals conspecifics were more cohesive and aligned than were heterospecifics, suggesting coordinated single-species subgroups formed within larger mixed-species shoals. The formation of subgroups may mitigate costs associated with differences between species, therefore enhancing benefits of mixed-species shoaling. As such, multiple levels of social structure may exist within mixed-species shoals that could facilitate growth and survival for vagrant A. vaigiensis in temperate regions. More broadly, this research highlights the importance of considering detailed internal structures of mixed-species shoals when trying to understand cost–benef

OBJECTIVE - Cardiovascular fitness (VO2max) and physical activity arc both related to risk of Metabolic disease. It is unclear, however, whether the metabolic effects of sedentary living are the same in fit and unfit individuals. The purpose of this study was, therefore, to describe the association between physical activity and the metabolic syndrome and to test whether fitness level modifies this relationship. RESEARCH DESIGN AND METHODS - physical activity Was measured objectively using individually calibrated heart rate against energy expenditure. VO2max was predicted front a submaximal exercise stress test. Fat mass and fat-free mass (FFM) were calculated using impedance biometry. A metabolic syndrome score was computed by summing the standardized values for obesity, hypertension, hyperglycemia, insulin resistance, hypertriglyceridemia, and the inverse level of HDL cholesterol and was expressed as a continuously distributed Outcome. To correct for exposure measurement cri-or, a random subsample (22\% of cohort) re-attended for three repeat measurements in the year following the first assessment. RESULTS - The relationship of VO2max (ml O-2 (.) kg(FFM)(-1) (.) min(-1)) and the metabolic syndrome score was of borderline significance after adjusting for age, sex, physical activity, and measurement error (beta = -0.58, P = 0.06). The magnitude of the association between physical activity (kJ (.) d(-1) (.) kg(FFM)(-1)) and the metabolic syndrome was more than three tunes greater than for VO(2ma)x (standardized beta = - 1,83, P = 0.0042). VO2max however, modified the relationship between physical activity energy expenditure and metabolic syndrome (P = 0 036). CONCLUSIONS - This study demonstrates a Strong inverse association between physical activity and metabolic syndrome, an association that is much steeper in unfit individuals. Thus, prevention of metabolic disease may be most effective In the subset of unfit inactive people.

The design of studies aimed at identifying the interaction between genetic and environmental determinants in disease risk is attracting increased attention. In this paper, we study the effect of errors on measuring exposures and the effect of assessing genotype at one locus on the association of a continuous outcome measure with continuous exposures and genotype. The estimation of misclassification errors in assessing genotypes from a separate study is proposed. If the exposure measurement error is substantial, then even relatively small errors in genotyping within limits that are often quoted can have an appreciable effect on interaction estimates. We, thus, consider a method for correcting the measurement errors when the interaction between the exposures and the genetic factor is significant. Finally, we present an epidemiological example to demonstrate the importance of correcting measurement errors. Copyright (C) 2004 John Wiley Sons, Ltd.

Background In nutritional epidemiology, it is common to fit models in which several dietary variables are included. However, with standard instruments for dietary assessment, not only are the intakes of many nutrients often highly correlated, but the errors in the estimation of the intake of different nutrients are also correlated. The effect of this error correlation on the results of observational studies has been little investigated. This paper describes the effect on multivariate regression coefficients of different levels of correlation, both between the variables themselves and between the errors of estimation of these variables. Methods Using a simple model for the multivariate error structure, we examine the effect on the estimates of bivariate linear regression coefficients of (1) differential precision of measurement of the two independent variables, (2) differing levels of correlation between the true values of the two variables, and (3) differing levels of correlation between the errors of measurement of the two variables. As an example, the prediction of plasma vitamin C levels by dietary intake variables is considered, using data from the European Prospective Investigation of Cancer (EPIC) Norfolk study in which dietary intake was estimated using both a food frequency questionaire (FFQ) and a 7-day diary (7DD). The dietary variables considered are vitamin C, fat, and energy, with different approaches taken to energy adjustment. Results When the error correlation is zero, the estimates of the bivariate regression coefficients reflect the precision of measurement of the two variables and mutual confounding. The sum of the observed regression coefficients is biased towards the null as in univariate regression. When the error correlation is non-zero but below about 0.7, the effect is minor. However, as the error correlation increases beyond 0.8 the effect becomes large and highly dependent on the relative precision with which the two variables are measured

The combination of heart rate (HR) monitoring and movement registration may improve measurement precision of physical activity energy expenditure (PAEE). Previous attempts have used either regression methods, which do not take full advantage of synchronized data, or have not used movement data quantitatively. The objective of the study was to assess the precision of branched model estimates of PAEE by utilizing either individual calibration (IC) of HR and accelerometry or corresponding mean group calibration (GC) equations. In 12 men (20.6 - 25.2 kg/m(2)), IC and GC equations for physical activity intensity (PAI) were derived during treadmill walking and running for both HR ( Polar) and hip-acceleration [ Computer Science and Applications (CSA)]. HR and CSA were recorded minute by minute during 22 h of whole body calorimetry and converted into PAI in four different weightings (P1-4) of the HR vs. the CSA (1- P1-4) relationships: if CSA > x, we used the P1 weighting if HR > y, otherwise P-2. Similarly, if CSA less than or equal to x, we used P-3 if HR > z, otherwise P-4. PAEE was calculated for a 12.5-h nonsleeping period as the time integral of PAI. A priori, we assumed P-1 = 1, P-2 = P-3 = 0.5, P-4 = 0, x = 5 counts/min, y = walking/ running transition HR, and z = flex HR. These parameters were also estimated post hoc. Means +/- SD estimation errors of a priori models were - 4.4 +/- 29 and 3.5 +/- 20\% for IC and GC, respectively. Corresponding post hoc model errors were - 1.5 +/- 13 and 0.1 +/- 9.8\%, respectively. All branched models had lower errors ( P less than or equal to 0.035) than single-measure estimates of CSA ( less than or equal to - 45\%) and HR ( greater than or equal to 39\%), as well as their nonbranched combination ( greater than or equal to 25.7\%). In conclusion, combining HR and CSA by branched modeling improves estimates of PAEE. IC may be less crucial with this modeling technique.

OBJECTIVE - Cardiovascular fitness (VO2max) and physical activity arc both related to risk of Metabolic disease. It is unclear, however, whether the metabolic effects of sedentary living are the same in fit and unfit individuals. The purpose of this study was, therefore, to describe the association between physical activity and the metabolic syndrome and to test whether fitness level modifies this relationship. RESEARCH DESIGN AND METHODS - physical activity Was measured objectively using individually calibrated heart rate against energy expenditure. VO2max was predicted front a submaximal exercise stress test. Fat mass and fat-free mass (FFM) were calculated using impedance biometry. A metabolic syndrome score was computed by summing the standardized values for obesity, hypertension, hyperglycemia, insulin resistance, hypertriglyceridemia, and the inverse level of HDL cholesterol and was expressed as a continuously distributed Outcome. To correct for exposure measurement cri-or, a random subsample (22\% of cohort) re-attended for three repeat measurements in the year following the first assessment. RESULTS - The relationship of VO2max (ml O-2 (.) kg(FFM)(-1) (.) min(-1)) and the metabolic syndrome score was of borderline significance after adjusting for age, sex, physical activity, and measurement error (beta = -0.58, P = 0.06). The magnitude of the association between physical activity (kJ (.) d(-1) (.) kg(FFM)(-1)) and the metabolic syndrome was more than three tunes greater than for VO(2ma)x (standardized beta = - 1,83, P = 0.0042). VO2max however, modified the relationship between physical activity energy expenditure and metabolic syndrome (P = 0 036). CONCLUSIONS - This study demonstrates a Strong inverse association between physical activity and metabolic syndrome, an association that is much steeper in unfit individuals. Thus, prevention of metabolic disease may be most effective In the subset of unfit inactive people.

The combination of heart rate (HR) monitoring and movement registration may improve measurement precision of physical activity energy expenditure (PAEE). Previous attempts have used either regression methods, which do not take full advantage of synchronized data, or have not used movement data quantitatively. The objective of the study was to assess the precision of branched model estimates of PAEE by utilizing either individual calibration (IC) of HR and accelerometry or corresponding mean group calibration (GC) equations. In 12 men (20.6 - 25.2 kg/m(2)), IC and GC equations for physical activity intensity (PAI) were derived during treadmill walking and running for both HR ( Polar) and hip-acceleration [ Computer Science and Applications (CSA)]. HR and CSA were recorded minute by minute during 22 h of whole body calorimetry and converted into PAI in four different weightings (P1-4) of the HR vs. the CSA (1- P1-4) relationships: if CSA > x, we used the P1 weighting if HR > y, otherwise P-2. Similarly, if CSA less than or equal to x, we used P-3 if HR > z, otherwise P-4. PAEE was calculated for a 12.5-h nonsleeping period as the time integral of PAI. A priori, we assumed P-1 = 1, P-2 = P-3 = 0.5, P-4 = 0, x = 5 counts/min, y = walking/ running transition HR, and z = flex HR. These parameters were also estimated post hoc. Means +/- SD estimation errors of a priori models were - 4.4 +/- 29 and 3.5 +/- 20\% for IC and GC, respectively. Corresponding post hoc model errors were - 1.5 +/- 13 and 0.1 +/- 9.8\%, respectively. All branched models had lower errors ( P less than or equal to 0.035) than single-measure estimates of CSA ( less than or equal to - 45\%) and HR ( greater than or equal to 39\%), as well as their nonbranched combination ( greater than or equal to 25.7\%). In conclusion, combining HR and CSA by branched modeling improves estimates of PAEE. IC may be less crucial with this modeling technique.

The design of studies aimed at identifying the interaction between genetic and environmental determinants in disease risk is attracting increased attention. In this paper, we study the effect of errors on measuring exposures and the effect of assessing genotype at one locus on the association of a continuous outcome measure with continuous exposures and genotype. The estimation of misclassification errors in assessing genotypes from a separate study is proposed. If the exposure measurement error is substantial, then even relatively small errors in genotyping within limits that are often quoted can have an appreciable effect on interaction estimates. We, thus, consider a method for correcting the measurement errors when the interaction between the exposures and the genetic factor is significant. Finally, we present an epidemiological example to demonstrate the importance of correcting measurement errors. Copyright (C) 2004 John Wiley Sons, Ltd.

Background In nutritional epidemiology, it is common to fit models in which several dietary variables are included. However, with standard instruments for dietary assessment, not only are the intakes of many nutrients often highly correlated, but the errors in the estimation of the intake of different nutrients are also correlated. The effect of this error correlation on the results of observational studies has been little investigated. This paper describes the effect on multivariate regression coefficients of different levels of correlation, both between the variables themselves and between the errors of estimation of these variables. Methods Using a simple model for the multivariate error structure, we examine the effect on the estimates of bivariate linear regression coefficients of (1) differential precision of measurement of the two independent variables, (2) differing levels of correlation between the true values of the two variables, and (3) differing levels of correlation between the errors of measurement of the two variables. As an example, the prediction of plasma vitamin C levels by dietary intake variables is considered, using data from the European Prospective Investigation of Cancer (EPIC) Norfolk study in which dietary intake was estimated using both a food frequency questionaire (FFQ) and a 7-day diary (7DD). The dietary variables considered are vitamin C, fat, and energy, with different approaches taken to energy adjustment. Results When the error correlation is zero, the estimates of the bivariate regression coefficients reflect the precision of measurement of the two variables and mutual confounding. The sum of the observed regression coefficients is biased towards the null as in univariate regression. When the error correlation is non-zero but below about 0.7, the effect is minor. However, as the error correlation increases beyond 0.8 the effect becomes large and highly dependent on the relative precision with which the two variables are measured

OBJECTIVE - Cardiovascular fitness (VO2max) and physical activity arc both related to risk of Metabolic disease. It is unclear, however, whether the metabolic effects of sedentary living are the same in fit and unfit individuals. The purpose of this study was, therefore, to describe the association between physical activity and the metabolic syndrome and to test whether fitness level modifies this relationship. RESEARCH DESIGN AND METHODS - physical activity Was measured objectively using individually calibrated heart rate against energy expenditure. VO2max was predicted front a submaximal exercise stress test. Fat mass and fat-free mass (FFM) were calculated using impedance biometry. A metabolic syndrome score was computed by summing the standardized values for obesity, hypertension, hyperglycemia, insulin resistance, hypertriglyceridemia, and the inverse level of HDL cholesterol and was expressed as a continuously distributed Outcome. To correct for exposure measurement cri-or, a random subsample (22\% of cohort) re-attended for three repeat measurements in the year following the first assessment. RESULTS - The relationship of VO2max (ml O-2 (.) kg(FFM)(-1) (.) min(-1)) and the metabolic syndrome score was of borderline significance after adjusting for age, sex, physical activity, and measurement error (beta = -0.58, P = 0.06). The magnitude of the association between physical activity (kJ (.) d(-1) (.) kg(FFM)(-1)) and the metabolic syndrome was more than three tunes greater than for VO(2ma)x (standardized beta = - 1,83, P = 0.0042). VO2max however, modified the relationship between physical activity energy expenditure and metabolic syndrome (P = 0 036). CONCLUSIONS - This study demonstrates a Strong inverse association between physical activity and metabolic syndrome, an association that is much steeper in unfit individuals. Thus, prevention of metabolic disease may be most effective In the subset of unfit inactive people.

The combination of heart rate (HR) monitoring and movement registration may improve measurement precision of physical activity energy expenditure (PAEE). Previous attempts have used either regression methods, which do not take full advantage of synchronized data, or have not used movement data quantitatively. The objective of the study was to assess the precision of branched model estimates of PAEE by utilizing either individual calibration (IC) of HR and accelerometry or corresponding mean group calibration (GC) equations. In 12 men (20.6 - 25.2 kg/m(2)), IC and GC equations for physical activity intensity (PAI) were derived during treadmill walking and running for both HR ( Polar) and hip-acceleration [ Computer Science and Applications (CSA)]. HR and CSA were recorded minute by minute during 22 h of whole body calorimetry and converted into PAI in four different weightings (P1-4) of the HR vs. the CSA (1- P1-4) relationships: if CSA > x, we used the P1 weighting if HR > y, otherwise P-2. Similarly, if CSA less than or equal to x, we used P-3 if HR > z, otherwise P-4. PAEE was calculated for a 12.5-h nonsleeping period as the time integral of PAI. A priori, we assumed P-1 = 1, P-2 = P-3 = 0.5, P-4 = 0, x = 5 counts/min, y = walking/ running transition HR, and z = flex HR. These parameters were also estimated post hoc. Means +/- SD estimation errors of a priori models were - 4.4 +/- 29 and 3.5 +/- 20\% for IC and GC, respectively. Corresponding post hoc model errors were - 1.5 +/- 13 and 0.1 +/- 9.8\%, respectively. All branched models had lower errors ( P less than or equal to 0.035) than single-measure estimates of CSA ( less than or equal to - 45\%) and HR ( greater than or equal to 39\%), as well as their nonbranched combination ( greater than or equal to 25.7\%). In conclusion, combining HR and CSA by branched modeling improves estimates of PAEE. IC may be less crucial with this modeling technique.

The design of studies aimed at identifying the interaction between genetic and environmental determinants in disease risk is attracting increased attention. In this paper, we study the effect of errors on measuring exposures and the effect of assessing genotype at one locus on the association of a continuous outcome measure with continuous exposures and genotype. The estimation of misclassification errors in assessing genotypes from a separate study is proposed. If the exposure measurement error is substantial, then even relatively small errors in genotyping within limits that are often quoted can have an appreciable effect on interaction estimates. We, thus, consider a method for correcting the measurement errors when the interaction between the exposures and the genetic factor is significant. Finally, we present an epidemiological example to demonstrate the importance of correcting measurement errors. Copyright (C) 2004 John Wiley Sons, Ltd.

Leptin is secreted by adipose tissue and acts upon receptors located in the hypothalamus to modify energy balance. Investigations of the relationship between leptin and physical activity energy expenditure (PAEE) at population level are scarce. The majority of studies addressing this topic are limited by their measurement of PAEE (i.e. questionnaires or ecological comparisons between rural and urban ethnic groups). To our knowledge, no studies have directly examined the relationship of objectively assessed PAEE and leptin in a large free-living population-based cohort. Therefore, we measured fasting plasma leptin and insulin concentrations, cardiorespiratory fitness ((V) over dot O-2max,O-pred), PAEE, and body composition in 758 Caucasian people (aged 40-65 yr). In sex-combined multiple regression analyses, leptin was significantly associated with PAEE (beta = -0.19, P = 0.0027), but not with (V) over dot O-2max,O-pred (beta = -0.0002, p = NS). The association between PAEE and leptin was significant in men when adjusted for percentage of body fat (beta = -0.28, P = 0.004) but not women (beta = -0.12, P = 0.18) but was significant in both men and women when adjusted for body mass index (men: beta = -0.28, P = 0.005; women: beta = -0.23, P = 0.01; combined: beta = -0.26, P = 0.00008). These data suggest the existence in this population of an independent inverse association between PAEE and fasting plasma leptin level.

Background The search for biologically relevant gene-environment interactions has been facilitated by technological advances in genotyping. The design of studies to detect interactions on continuous traits such as blood pressure and insulin sensitivity is attracting increasing attention. We have previously described power calculations for such studies, and this paper describes the extension of those calculations to take account of measurement error. Methods The model considered in this paper is a simple linear regression relating a continuous outcome to a continuously distributed exposure variable in which the ratio of slopes for each genotype is considered as the interaction parameter. The classical measurement error model is used to describe the uncertainty in measurement in the outcome and the exposure. The sample size to detect differing magnitudes of interaction With varying frequencies of the minor allele are calculated for a given main effect observed with error both in the exposure and the outcome. The sample size to detect a given interaction for, a given minor allele frequency is calculated for differing degrees of measurement error in the assessment of the exposure and,the outcome. Results The required sample size is dependent upon the magnitude of the interaction, the allele frequency and the strength of the association in those with the common allele. As an example, we take the situation in which the effect size in those with the common allele was a quarter of a standard deviation change in the outcome for a standard deviation change in the exposure. If a minor allele with a frequency of 20\% leads to a doubling of that effect size, then the sample size is highly dependent upon the precision with which the exposure and outcome are measured. rho(Tx) and rho(Ty) are the correlation between the measured exposure and outcome, respectively and the true value. if poor measures of the exposure and outcome are used, (e.g. rho(Tx) = 0.3, rho(Ty) = 0.4), then a s

Additive regression models have turned out to be useful statistical tools in the analysis of high-dimensional data. The attraction of such models is that the additive component can be estimated with the same optimal convergence rate as a one-dimensional nonparametric regression. However, this optimal property holds only when all the additive components have the same degree of "homogeneous" smoothness. In this paper, we propose a two-step wavelet thresholding estimation process in which the estimator is adaptive to different degrees of smoothness in different components and also adaptive to the "inhomogeneous" smoothness described by the Besov space. The estimator of an additive component constructed by the proposed procedure is shown to attain the one-dimensional optimal convergence rate even when the components have different degrees of "inhomogeneous" smoothness.

Leptin is secreted by adipose tissue and acts upon receptors located in the hypothalamus to modify energy balance. Investigations of the relationship between leptin and physical activity energy expenditure (PAEE) at population level are scarce. The majority of studies addressing this topic are limited by their measurement of PAEE (i.e. questionnaires or ecological comparisons between rural and urban ethnic groups). To our knowledge, no studies have directly examined the relationship of objectively assessed PAEE and leptin in a large free-living population-based cohort. Therefore, we measured fasting plasma leptin and insulin concentrations, cardiorespiratory fitness ((V) over dot O-2max,O-pred), PAEE, and body composition in 758 Caucasian people (aged 40-65 yr). In sex-combined multiple regression analyses, leptin was significantly associated with PAEE (beta = -0.19, P = 0.0027), but not with (V) over dot O-2max,O-pred (beta = -0.0002, p = NS). The association between PAEE and leptin was significant in men when adjusted for percentage of body fat (beta = -0.28, P = 0.004) but not women (beta = -0.12, P = 0.18) but was significant in both men and women when adjusted for body mass index (men: beta = -0.28, P = 0.005; women: beta = -0.23, P = 0.01; combined: beta = -0.26, P = 0.00008). These data suggest the existence in this population of an independent inverse association between PAEE and fasting plasma leptin level.

Additive regression models have turned out to be useful statistical tools in the analysis of high-dimensional data. The attraction of such models is that the additive component can be estimated with the same optimal convergence rate as a one-dimensional nonparametric regression. However, this optimal property holds only when all the additive components have the same degree of "homogeneous" smoothness. In this paper, we propose a two-step wavelet thresholding estimation process in which the estimator is adaptive to different degrees of smoothness in different components and also adaptive to the "inhomogeneous" smoothness described by the Besov space. The estimator of an additive component constructed by the proposed procedure is shown to attain the one-dimensional optimal convergence rate even when the components have different degrees of "inhomogeneous" smoothness.

Leptin is secreted by adipose tissue and acts upon receptors located in the hypothalamus to modify energy balance. Investigations of the relationship between leptin and physical activity energy expenditure (PAEE) at population level are scarce. The majority of studies addressing this topic are limited by their measurement of PAEE (i.e. questionnaires or ecological comparisons between rural and urban ethnic groups). To our knowledge, no studies have directly examined the relationship of objectively assessed PAEE and leptin in a large free-living population-based cohort. Therefore, we measured fasting plasma leptin and insulin concentrations, cardiorespiratory fitness ((V) over dot O-2max,O-pred), PAEE, and body composition in 758 Caucasian people (aged 40-65 yr). In sex-combined multiple regression analyses, leptin was significantly associated with PAEE (beta = -0.19, P = 0.0027), but not with (V) over dot O-2max,O-pred (beta = -0.0002, p = NS). The association between PAEE and leptin was significant in men when adjusted for percentage of body fat (beta = -0.28, P = 0.004) but not women (beta = -0.12, P = 0.18) but was significant in both men and women when adjusted for body mass index (men: beta = -0.28, P = 0.005; women: beta = -0.23, P = 0.01; combined: beta = -0.26, P = 0.00008). These data suggest the existence in this population of an independent inverse association between PAEE and fasting plasma leptin level.

Background The search for biologically relevant gene-environment interactions has been facilitated by technological advances in genotyping. The design of studies to detect interactions on continuous traits such as blood pressure and insulin sensitivity is attracting increasing attention. We have previously described power calculations for such studies, and this paper describes the extension of those calculations to take account of measurement error. Methods The model considered in this paper is a simple linear regression relating a continuous outcome to a continuously distributed exposure variable in which the ratio of slopes for each genotype is considered as the interaction parameter. The classical measurement error model is used to describe the uncertainty in measurement in the outcome and the exposure. The sample size to detect differing magnitudes of interaction With varying frequencies of the minor allele are calculated for a given main effect observed with error both in the exposure and the outcome. The sample size to detect a given interaction for, a given minor allele frequency is calculated for differing degrees of measurement error in the assessment of the exposure and,the outcome. Results The required sample size is dependent upon the magnitude of the interaction, the allele frequency and the strength of the association in those with the common allele. As an example, we take the situation in which the effect size in those with the common allele was a quarter of a standard deviation change in the outcome for a standard deviation change in the exposure. If a minor allele with a frequency of 20\% leads to a doubling of that effect size, then the sample size is highly dependent upon the precision with which the exposure and outcome are measured. rho(Tx) and rho(Ty) are the correlation between the measured exposure and outcome, respectively and the true value. if poor measures of the exposure and outcome are used, (e.g. rho(Tx) = 0.3, rho(Ty) = 0.4), then a s

Additive regression models have turned out to be useful statistical tools in the analysis of high-dimensional data. The attraction of such models is that the additive component can be estimated with the same optimal convergence rate as a one-dimensional nonparametric regression. However, this optimal property holds only when all the additive components have the same degree of "homogeneous" smoothness. In this paper, we propose a two-step wavelet thresholding estimation process in which the estimator is adaptive to different degrees of smoothness in different components and also adaptive to the "inhomogeneous" smoothness described by the Besov space. The estimator of an additive component constructed by the proposed procedure is shown to attain the one-dimensional optimal convergence rate even when the components have different degrees of "inhomogeneous" smoothness.

The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space B-p, q(s) is probed under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a Aide range of Besov scale is also constructed. (C) 2001 Elsevier Science.

The actual effect of ethylene on shoot gravitropic response has been controversial. To elucidate the role of ethylene in the modulation of shoot gravitropic response, Arabidopsis inflorescences and light-grown seedlings were pretreated with 0.1-10 muL L-1 of ethylene for either a long (12-48 h) or short term (0.5 h). When the gravicurvature was measured either in air or in ethylene, it was found that prolonged exposure to various levels of ethylene stimulated both inflorescence stem and hypocotyl gravicurvature in air, while the continued presence of ethylene immediately following reorientation of plant tissues inhibited gravicurvature of both tissues. Both stimulatory and inhibitory effects existed in inflorescence stems and hypocotyls when the plant tissues were exposed to a chosen concentration of ethylene. Stimulation by ethylene was stronger than its inhibition in inflorescence stems, while the reverse was true for the hypocotyls. Therefore, the continued presence of high levels of naturally produced ethylene in eto1-1 did not suppress the faster gravicurvature of inflorescence stems, whereas the removal of exogenously applied ethylene was necessary to observe faster gravicurvature of both the wild-type and eto1-1 hypocotyls. Both effects acted through the known ethylene receptor complex. These results strongly suggest that ethylene of a chosen concentration has opposing effects on the negative gravitropic responses of both inflorescence stems and hypocotyls. The ultimate negatively gravitropic behaviour of a plant tissue, when exposed to ethylene, depends on the dynamic interplay between these two opposing effects.

The fasting concentration of non-esterified fatty acids (NEFA) and the degree to which it declines during an oral glucose tolerance test are closely associated with insulin resistance and glucose intolerance. However, relatively few studies have described possible environmental determinants of NEFA concentrations. Physical activity is likely to be related to NEFA levels, but habitual activity level is difficult to quantify in epidemiological studies. In particular, it is unclear whether NEFA is more closely related to cardio-respiratory fitness or to habitual energy expenditure. In order to quantify these relationships, we analysed data from the Ely prospective population-based study in which 931 subjects underwent a glucose tolerance test with measurements of cardio-respiratory fitness and 4 d energy expenditure by heart-rate monitoring, a technique previously validated against whole-body calorimetry and doubly-labelled water. In order to estimate the latent variables of usual fitness and energy expenditure, a subset of 190 subjects underwent repeat testing on three further occasions over 1 year. In analyses adjusting only for age and sex, energy expenditure and cardio-respiratory fitness were both negatively correlated with the total area under the NEFA curve following the oral glucose load (standardised beta coefficients -0.030 and -0.039 respectively; both P<0.001) However, further adjustment for degree of obesity and bivariate measurement error suggested that the effect of energy expenditure was significantly greater than that for fitness (-0.047 and -0.005 respectively). These results suggest that the area under the NEFA curve in the oral glucose tolerance test, a measure of insulin sensitivity, is strongly associated with the habitual level of physical activity.

The actual effect of ethylene on shoot gravitropic response has been controversial. To elucidate the role of ethylene in the modulation of shoot gravitropic response, Arabidopsis inflorescences and light-grown seedlings were pretreated with 0.1-10 muL L-1 of ethylene for either a long (12-48 h) or short term (0.5 h). When the gravicurvature was measured either in air or in ethylene, it was found that prolonged exposure to various levels of ethylene stimulated both inflorescence stem and hypocotyl gravicurvature in air, while the continued presence of ethylene immediately following reorientation of plant tissues inhibited gravicurvature of both tissues. Both stimulatory and inhibitory effects existed in inflorescence stems and hypocotyls when the plant tissues were exposed to a chosen concentration of ethylene. Stimulation by ethylene was stronger than its inhibition in inflorescence stems, while the reverse was true for the hypocotyls. Therefore, the continued presence of high levels of naturally produced ethylene in eto1-1 did not suppress the faster gravicurvature of inflorescence stems, whereas the removal of exogenously applied ethylene was necessary to observe faster gravicurvature of both the wild-type and eto1-1 hypocotyls. Both effects acted through the known ethylene receptor complex. These results strongly suggest that ethylene of a chosen concentration has opposing effects on the negative gravitropic responses of both inflorescence stems and hypocotyls. The ultimate negatively gravitropic behaviour of a plant tissue, when exposed to ethylene, depends on the dynamic interplay between these two opposing effects.

The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space B-p, q(s) is probed under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a Aide range of Besov scale is also constructed. (C) 2001 Elsevier Science.

The fasting concentration of non-esterified fatty acids (NEFA) and the degree to which it declines during an oral glucose tolerance test are closely associated with insulin resistance and glucose intolerance. However, relatively few studies have described possible environmental determinants of NEFA concentrations. Physical activity is likely to be related to NEFA levels, but habitual activity level is difficult to quantify in epidemiological studies. In particular, it is unclear whether NEFA is more closely related to cardio-respiratory fitness or to habitual energy expenditure. In order to quantify these relationships, we analysed data from the Ely prospective population-based study in which 931 subjects underwent a glucose tolerance test with measurements of cardio-respiratory fitness and 4 d energy expenditure by heart-rate monitoring, a technique previously validated against whole-body calorimetry and doubly-labelled water. In order to estimate the latent variables of usual fitness and energy expenditure, a subset of 190 subjects underwent repeat testing on three further occasions over 1 year. In analyses adjusting only for age and sex, energy expenditure and cardio-respiratory fitness were both negatively correlated with the total area under the NEFA curve following the oral glucose load (standardised beta coefficients -0.030 and -0.039 respectively; both P<0.001) However, further adjustment for degree of obesity and bivariate measurement error suggested that the effect of energy expenditure was significantly greater than that for fitness (-0.047 and -0.005 respectively). These results suggest that the area under the NEFA curve in the oral glucose tolerance test, a measure of insulin sensitivity, is strongly associated with the habitual level of physical activity.

The actual effect of ethylene on shoot gravitropic response has been controversial. To elucidate the role of ethylene in the modulation of shoot gravitropic response, Arabidopsis inflorescences and light-grown seedlings were pretreated with 0.1-10 muL L-1 of ethylene for either a long (12-48 h) or short term (0.5 h). When the gravicurvature was measured either in air or in ethylene, it was found that prolonged exposure to various levels of ethylene stimulated both inflorescence stem and hypocotyl gravicurvature in air, while the continued presence of ethylene immediately following reorientation of plant tissues inhibited gravicurvature of both tissues. Both stimulatory and inhibitory effects existed in inflorescence stems and hypocotyls when the plant tissues were exposed to a chosen concentration of ethylene. Stimulation by ethylene was stronger than its inhibition in inflorescence stems, while the reverse was true for the hypocotyls. Therefore, the continued presence of high levels of naturally produced ethylene in eto1-1 did not suppress the faster gravicurvature of inflorescence stems, whereas the removal of exogenously applied ethylene was necessary to observe faster gravicurvature of both the wild-type and eto1-1 hypocotyls. Both effects acted through the known ethylene receptor complex. These results strongly suggest that ethylene of a chosen concentration has opposing effects on the negative gravitropic responses of both inflorescence stems and hypocotyls. The ultimate negatively gravitropic behaviour of a plant tissue, when exposed to ethylene, depends on the dynamic interplay between these two opposing effects.

The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space B-p, q(s) is probed under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a Aide range of Besov scale is also constructed. (C) 2001 Elsevier Science.

The fasting concentration of non-esterified fatty acids (NEFA) and the degree to which it declines during an oral glucose tolerance test are closely associated with insulin resistance and glucose intolerance. However, relatively few studies have described possible environmental determinants of NEFA concentrations. Physical activity is likely to be related to NEFA levels, but habitual activity level is difficult to quantify in epidemiological studies. In particular, it is unclear whether NEFA is more closely related to cardio-respiratory fitness or to habitual energy expenditure. In order to quantify these relationships, we analysed data from the Ely prospective population-based study in which 931 subjects underwent a glucose tolerance test with measurements of cardio-respiratory fitness and 4 d energy expenditure by heart-rate monitoring, a technique previously validated against whole-body calorimetry and doubly-labelled water. In order to estimate the latent variables of usual fitness and energy expenditure, a subset of 190 subjects underwent repeat testing on three further occasions over 1 year. In analyses adjusting only for age and sex, energy expenditure and cardio-respiratory fitness were both negatively correlated with the total area under the NEFA curve following the oral glucose load (standardised beta coefficients -0.030 and -0.039 respectively; both P<0.001) However, further adjustment for degree of obesity and bivariate measurement error suggested that the effect of energy expenditure was significantly greater than that for fitness (-0.047 and -0.005 respectively). These results suggest that the area under the NEFA curve in the oral glucose tolerance test, a measure of insulin sensitivity, is strongly associated with the habitual level of physical activity.

Background The search for interaction effects is common in epidemiological studies, but the power of such studies is a major concern. This is a practical issue as many future studies will wish to investigate potential gene-gene and gene-environment interactions and therefore need to be planned on the basis of appropriate sample size calculations. Methods and the Results The underlying model considered in this paper is a simple linear regression and relating a continuous outcome to a continuously distributed exposure variable. Results The slope of the regression line is taken to be dependent on genotype, and the ratio of the slopes for each genotype is considered as the interaction parameter. Sample size, is affected by the allele frequency and whether the genetic model is dominant or recessive. It is also critically dependent upon the size of the association between exposure and outcome, and the strength of the interaction term. The link between these determinants is graphically displayed to allow sample size and power to be estimated. An example of the analysis of the association between physical activity and glucose intolerance demonstrates how information from previous studies can be used to determine the sample size required to examine gene-environment interactions. Conclusions The formulae allowing the computation of the sample size required to study the interaction between a continuous environmental exposure and a genetic factor on a continuous outcome variable should have a practical utility in assisting the design of studies of appropriate power.

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation gamma between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of gamma is appreciably more powerful than that based on r(1), the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r(1). (C) 2001 Academic Press.

Background Validation studies of dietary instruments developed for epidemiological studies have typically used some form of diet record as the standard for comparison. Recent work suggests that comparison with diet record may overestimate the ability of the epidemiological instrument to measure habitual dietary intake, due to lack of independence of the measurement errors. The degree of regression dilution in estimating diet-disease association may therefore have been correspondingly underestimated. Use of biochemical measures of intake may mitigate the problem. In this paper, we report on the use of urinary measures of intakes of nitrogen, potassium and sodium to compare the performance of a semiquantitative food frequency questionnaire (FFQ) and a 7-day diet diary (7DD) to estimate average intake of these nutrients over one year. Methods In all, 179 individuals were asked to complete an FFQ and a 7DD on two occasions separated by approximately 12 months. The individuals were also asked to provide 24-hour urine samples on six occasions over a 6-9-month period, covering the time at which the record FFQ and 7DD were completed. The urine was assayed for nitrogen, potassium and sodium. The protocol was completed by 123 individuals. The data from these individuals were analysed to estimate the covariance structure of the measurement errors of the FFQ, the 7DD and a single 24-hour urine measurement, and to estimate the degree of regression dilution associated with the FFQ and 7DD. Results The results demonstrated that: (1) the error variances for each of the three nutrients was more than twice as great with the FFQ than the 7DD; (2) there was substantial correlation (0.46-0.58) between the error of both the FFQ and the 7DD completed on different occasions; (3) there was moderate correlation (0.24-0.29) between the error in the FFQ and the error in the 7DD for each nutrient; (4) the correlation between errors in different nutrients was higher for the FFQ (0.77-0.80) than

Several methods for testing the difference between two group means of k independent populations are compared. Simulation shows that the likelihood ratio test with the Bartlett correction factor and the t test with appropriate degrees of freedom perform better, particularly when the sample size is small. However, the latter is very good for all configurations.

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation gamma between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of gamma is appreciably more powerful than that based on r(1), the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r(1). (C) 2001 Academic Press.

Background Validation studies of dietary instruments developed for epidemiological studies have typically used some form of diet record as the standard for comparison. Recent work suggests that comparison with diet record may overestimate the ability of the epidemiological instrument to measure habitual dietary intake, due to lack of independence of the measurement errors. The degree of regression dilution in estimating diet-disease association may therefore have been correspondingly underestimated. Use of biochemical measures of intake may mitigate the problem. In this paper, we report on the use of urinary measures of intakes of nitrogen, potassium and sodium to compare the performance of a semiquantitative food frequency questionnaire (FFQ) and a 7-day diet diary (7DD) to estimate average intake of these nutrients over one year. Methods In all, 179 individuals were asked to complete an FFQ and a 7DD on two occasions separated by approximately 12 months. The individuals were also asked to provide 24-hour urine samples on six occasions over a 6-9-month period, covering the time at which the record FFQ and 7DD were completed. The urine was assayed for nitrogen, potassium and sodium. The protocol was completed by 123 individuals. The data from these individuals were analysed to estimate the covariance structure of the measurement errors of the FFQ, the 7DD and a single 24-hour urine measurement, and to estimate the degree of regression dilution associated with the FFQ and 7DD. Results The results demonstrated that: (1) the error variances for each of the three nutrients was more than twice as great with the FFQ than the 7DD; (2) there was substantial correlation (0.46-0.58) between the error of both the FFQ and the 7DD completed on different occasions; (3) there was moderate correlation (0.24-0.29) between the error in the FFQ and the error in the 7DD for each nutrient; (4) the correlation between errors in different nutrients was higher for the FFQ (0.77-0.80) than

Several methods for testing the difference between two group means of k independent populations are compared. Simulation shows that the likelihood ratio test with the Bartlett correction factor and the t test with appropriate degrees of freedom perform better, particularly when the sample size is small. However, the latter is very good for all configurations.

Background The search for interaction effects is common in epidemiological studies, but the power of such studies is a major concern. This is a practical issue as many future studies will wish to investigate potential gene-gene and gene-environment interactions and therefore need to be planned on the basis of appropriate sample size calculations. Methods and the Results The underlying model considered in this paper is a simple linear regression and relating a continuous outcome to a continuously distributed exposure variable. Results The slope of the regression line is taken to be dependent on genotype, and the ratio of the slopes for each genotype is considered as the interaction parameter. Sample size, is affected by the allele frequency and whether the genetic model is dominant or recessive. It is also critically dependent upon the size of the association between exposure and outcome, and the strength of the interaction term. The link between these determinants is graphically displayed to allow sample size and power to be estimated. An example of the analysis of the association between physical activity and glucose intolerance demonstrates how information from previous studies can be used to determine the sample size required to examine gene-environment interactions. Conclusions The formulae allowing the computation of the sample size required to study the interaction between a continuous environmental exposure and a genetic factor on a continuous outcome variable should have a practical utility in assisting the design of studies of appropriate power.

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation gamma between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of gamma is appreciably more powerful than that based on r(1), the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r(1). (C) 2001 Academic Press.

Background Validation studies of dietary instruments developed for epidemiological studies have typically used some form of diet record as the standard for comparison. Recent work suggests that comparison with diet record may overestimate the ability of the epidemiological instrument to measure habitual dietary intake, due to lack of independence of the measurement errors. The degree of regression dilution in estimating diet-disease association may therefore have been correspondingly underestimated. Use of biochemical measures of intake may mitigate the problem. In this paper, we report on the use of urinary measures of intakes of nitrogen, potassium and sodium to compare the performance of a semiquantitative food frequency questionnaire (FFQ) and a 7-day diet diary (7DD) to estimate average intake of these nutrients over one year. Methods In all, 179 individuals were asked to complete an FFQ and a 7DD on two occasions separated by approximately 12 months. The individuals were also asked to provide 24-hour urine samples on six occasions over a 6-9-month period, covering the time at which the record FFQ and 7DD were completed. The urine was assayed for nitrogen, potassium and sodium. The protocol was completed by 123 individuals. The data from these individuals were analysed to estimate the covariance structure of the measurement errors of the FFQ, the 7DD and a single 24-hour urine measurement, and to estimate the degree of regression dilution associated with the FFQ and 7DD. Results The results demonstrated that: (1) the error variances for each of the three nutrients was more than twice as great with the FFQ than the 7DD; (2) there was substantial correlation (0.46-0.58) between the error of both the FFQ and the 7DD completed on different occasions; (3) there was moderate correlation (0.24-0.29) between the error in the FFQ and the error in the 7DD for each nutrient; (4) the correlation between errors in different nutrients was higher for the FFQ (0.77-0.80) than

Several methods for testing the difference between two group means of k independent populations are compared. Simulation shows that the likelihood ratio test with the Bartlett correction factor and the t test with appropriate degrees of freedom perform better, particularly when the sample size is small. However, the latter is very good for all configurations.

Background The search for interaction effects is common in epidemiological studies, but the power of such studies is a major concern. This is a practical issue as many future studies will wish to investigate potential gene-gene and gene-environment interactions and therefore need to be planned on the basis of appropriate sample size calculations. Methods and the Results The underlying model considered in this paper is a simple linear regression and relating a continuous outcome to a continuously distributed exposure variable. Results The slope of the regression line is taken to be dependent on genotype, and the ratio of the slopes for each genotype is considered as the interaction parameter. Sample size, is affected by the allele frequency and whether the genetic model is dominant or recessive. It is also critically dependent upon the size of the association between exposure and outcome, and the strength of the interaction term. The link between these determinants is graphically displayed to allow sample size and power to be estimated. An example of the analysis of the association between physical activity and glucose intolerance demonstrates how information from previous studies can be used to determine the sample size required to examine gene-environment interactions. Conclusions The formulae allowing the computation of the sample size required to study the interaction between a continuous environmental exposure and a genetic factor on a continuous outcome variable should have a practical utility in assisting the design of studies of appropriate power.

Background Previous studies have demonstrated an association between physical inactivity and hypertension, but the methods used to assess activity have been subjective and imprecise. Recently methods have become available allowing measurement of energy expenditure in free-living populations. Our aim was to employ these methods to assess the independent association between energy expenditure, cardio-respiratory fitness and blood pressure. Methods In a cross-sectional study of 775 people (45-70 years) participating in a continuing population-based cohort study, energy expenditure was assessed by 4 days of heart rate monitoring with individual calibration of the relationship between heart rate and energy expenditure, a method validated against doubly-labelled water and whole body calorimetry. Cardio-respiratory fitness was assessed in a sub-maximal test. To adjust for measurement error in the assessment of usual energy expenditure and fitness, 190 subjects repeated both tests on three further occasions at 4-monthly intervals. Results A highly significant linear trend in blood pressure was found across quintiles of the physical activity level, the ratio of total energy expenditure to basal metabolic rate. The differences in the mean systolic/diastolic blood pressure between the top and bottom quintile was 6.3/4.4 mmHg in men and 10.7/5.9 mmHg in women. These effects were independent of obesity and cardio-respiratory fitness. Correction for measurement error suggests that the true underlying relationship between usual energy expenditure and blood pressure is stronger still. Conclusions These findings are compatible with a strong association between usual energy expenditure and blood pressure and support public health strategies aimed at increasing overall energy expenditure.

Glucose intolerance and diabetes mellitus are associated with physical inactivity, but it is unclear whether preventive interventions should aim at increasing overall energy expenditure or increasing participation in vigorous, fitness-enhancing activities. Studies aimed at separating and quantifying the effects of these two dimensions of physical activity should use well-validated measurement instruments and employ a study design in which the bivariate error structure of these instruments is determined. In the Isle of Ely Study (Cambridgeshire, United Kingdom), 775 individuals aged 45-70 years in 1994-1997 completed a glucose tolerance test and assessment of 4-day physical activity level (total energy expenditure/basal metabolic rate) by heart rate monitoring, a technique that has been validated against doubly labeled water and whole-body calorimetry. Cardiorespiratory fitness (maximum oxygen uptake (VO2max) per kg)) was measured in a submaximal test. To correct for measurement error, the authors had 190 individuals repeat both tests on three occasions at 4-month intervals. Two-hour glucose level was negatively correlated with physical activity level (men: r = -0.22, p < 0.001; women: r = -0.11, p < 0.05) and VO2max per kg (men: r = -0.18, p < 0.01; women: r = -0.19, p < 0.001) and was positively correlated with age and obesity. The model incorporating bivariate adjustment for measurement error showed that energy expenditure had a major effect on glucose tolerance, but there was less of an effect for cardiorespiratory fitness. These data provide support for public health strategies aimed at increasing overall energy expenditure.

Glucose intolerance and diabetes mellitus are associated with physical inactivity, but it is unclear whether preventive interventions should aim at increasing overall energy expenditure or increasing participation in vigorous, fitness-enhancing activities. Studies aimed at separating and quantifying the effects of these two dimensions of physical activity should use well-validated measurement instruments and employ a study design in which the bivariate error structure of these instruments is determined. In the Isle of Ely Study (Cambridgeshire, United Kingdom), 775 individuals aged 45-70 years in 1994-1997 completed a glucose tolerance test and assessment of 4-day physical activity level (total energy expenditure/basal metabolic rate) by heart rate monitoring, a technique that has been validated against doubly labeled water and whole-body calorimetry. Cardiorespiratory fitness (maximum oxygen uptake (VO2max) per kg)) was measured in a submaximal test. To correct for measurement error, the authors had 190 individuals repeat both tests on three occasions at 4-month intervals. Two-hour glucose level was negatively correlated with physical activity level (men: r = -0.22, p < 0.001; women: r = -0.11, p < 0.05) and VO2max per kg (men: r = -0.18, p < 0.01; women: r = -0.19, p < 0.001) and was positively correlated with age and obesity. The model incorporating bivariate adjustment for measurement error showed that energy expenditure had a major effect on glucose tolerance, but there was less of an effect for cardiorespiratory fitness. These data provide support for public health strategies aimed at increasing overall energy expenditure.

Background Previous studies have demonstrated an association between physical inactivity and hypertension, but the methods used to assess activity have been subjective and imprecise. Recently methods have become available allowing measurement of energy expenditure in free-living populations. Our aim was to employ these methods to assess the independent association between energy expenditure, cardio-respiratory fitness and blood pressure. Methods In a cross-sectional study of 775 people (45-70 years) participating in a continuing population-based cohort study, energy expenditure was assessed by 4 days of heart rate monitoring with individual calibration of the relationship between heart rate and energy expenditure, a method validated against doubly-labelled water and whole body calorimetry. Cardio-respiratory fitness was assessed in a sub-maximal test. To adjust for measurement error in the assessment of usual energy expenditure and fitness, 190 subjects repeated both tests on three further occasions at 4-monthly intervals. Results A highly significant linear trend in blood pressure was found across quintiles of the physical activity level, the ratio of total energy expenditure to basal metabolic rate. The differences in the mean systolic/diastolic blood pressure between the top and bottom quintile was 6.3/4.4 mmHg in men and 10.7/5.9 mmHg in women. These effects were independent of obesity and cardio-respiratory fitness. Correction for measurement error suggests that the true underlying relationship between usual energy expenditure and blood pressure is stronger still. Conclusions These findings are compatible with a strong association between usual energy expenditure and blood pressure and support public health strategies aimed at increasing overall energy expenditure.

Background Previous studies have demonstrated an association between physical inactivity and hypertension, but the methods used to assess activity have been subjective and imprecise. Recently methods have become available allowing measurement of energy expenditure in free-living populations. Our aim was to employ these methods to assess the independent association between energy expenditure, cardio-respiratory fitness and blood pressure. Methods In a cross-sectional study of 775 people (45-70 years) participating in a continuing population-based cohort study, energy expenditure was assessed by 4 days of heart rate monitoring with individual calibration of the relationship between heart rate and energy expenditure, a method validated against doubly-labelled water and whole body calorimetry. Cardio-respiratory fitness was assessed in a sub-maximal test. To adjust for measurement error in the assessment of usual energy expenditure and fitness, 190 subjects repeated both tests on three further occasions at 4-monthly intervals. Results A highly significant linear trend in blood pressure was found across quintiles of the physical activity level, the ratio of total energy expenditure to basal metabolic rate. The differences in the mean systolic/diastolic blood pressure between the top and bottom quintile was 6.3/4.4 mmHg in men and 10.7/5.9 mmHg in women. These effects were independent of obesity and cardio-respiratory fitness. Correction for measurement error suggests that the true underlying relationship between usual energy expenditure and blood pressure is stronger still. Conclusions These findings are compatible with a strong association between usual energy expenditure and blood pressure and support public health strategies aimed at increasing overall energy expenditure.

Glucose intolerance and diabetes mellitus are associated with physical inactivity, but it is unclear whether preventive interventions should aim at increasing overall energy expenditure or increasing participation in vigorous, fitness-enhancing activities. Studies aimed at separating and quantifying the effects of these two dimensions of physical activity should use well-validated measurement instruments and employ a study design in which the bivariate error structure of these instruments is determined. In the Isle of Ely Study (Cambridgeshire, United Kingdom), 775 individuals aged 45-70 years in 1994-1997 completed a glucose tolerance test and assessment of 4-day physical activity level (total energy expenditure/basal metabolic rate) by heart rate monitoring, a technique that has been validated against doubly labeled water and whole-body calorimetry. Cardiorespiratory fitness (maximum oxygen uptake (VO2max) per kg)) was measured in a submaximal test. To correct for measurement error, the authors had 190 individuals repeat both tests on three occasions at 4-month intervals. Two-hour glucose level was negatively correlated with physical activity level (men: r = -0.22, p < 0.001; women: r = -0.11, p < 0.05) and VO2max per kg (men: r = -0.18, p < 0.01; women: r = -0.19, p < 0.001) and was positively correlated with age and obesity. The model incorporating bivariate adjustment for measurement error showed that energy expenditure had a major effect on glucose tolerance, but there was less of an effect for cardiorespiratory fitness. These data provide support for public health strategies aimed at increasing overall energy expenditure.

It is becoming standard practice in epidemiology to adjust relative risk estimates to remove the bias caused by non-differential errors in the exposure measurement. Estimation of the correction factor is often based on a validation study incorporating repeated measures of exposure, which are assumed to be independent. This assumption is difficult to verify and often likely to be false. We examine the effect of departures from this assumption on the correction factor estimate, and explore the design of validation studies using two or even three different types of measurement of exposure, where assumption of independence between the measures may be more realistic. The value of good biomarker measures of exposure is demonstrated even if they are feasible to use only in a validation study. Copyright (C) 1999 John Wiley & Sons, Ltd.

The bias in relative risk estimates caused by errors in measurement of the relevant exposure is being increasingly recognized in epidemiology. Estimation of the necessary correction factor to remove this bias for univariate exposure has been considered in an earlier paper. We consider here the multivariate situation in which non-differential errors in measurement can lead to incorrect identification of the variable most closely associated with disease. Estimation of the necessary correction factor when the true exposure is unobservable necessarily requires assumptions. We explore the robustness of the estimation to departures from a range of assumptions. The value of good biomarkers is demonstrated. We present a bivariate example in which failure to take account of measurement error leads to the incorrect exposure being identified as the important determinant of disease risk. Copyright (C) 1999 John Wiley & Sons, Ltd.