Logistic regression with correlated measurement error and misclassification in covariates.

Many areas of research, such as nutritional epidemiology, may encounter measurement errors of continuous covariates and misclassification of categorical variables when modeling. It is well known that ignoring measurement errors or misclassification can lead to biased results. But most research has focused on solving these two problems separately. Addressing both measurement error and misclassification simultaneously in a single analysis is less actively studied. In this article, we propose a new correction method for a logistic regression to handle correlated error variables involved in multivariate continuous covariates and misclassification in a categorical variable simultaneously. It is not computationally intensive since a closed-form of the approximate likelihood function conditional on observed covariates is derived. The asymptotic normality of this proposed estimator is established under regularity conditions and its finite-sample performance is empirically examined by simulation studies. We apply this new estimation method to handle measurement error in some nutrients of interest and misclassification of a categorical variable named physical activity in the European Prospective Investigation into Cancer and Nutrition-InterAct Study data. Analyses show that fruit is negatively associated with type 2 diabetes for a group of women doing active physical activity, protein has positive association with type 2 diabetes for the group of less active physical activity, and actual physical activity has a greater effect on reducing the risk of type 2 diabetes than observed physical activity.

Approximate profile likelihood estimation for Cox regression with covariate measurement error.

In nutritional epidemiology, measurement error in covariates is a well-known problem since dietary intakes are usually assessed through self-reporting. In this article, we consider an additive error model in which error variables are highly correlated, and propose a new method called approximate profile likelihood estimation (APLE) for covariates measured with error in the Cox regression. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to examine the finite sample performance of the proposed estimator empirically. Moreover, the popular correction method called regression calibration is shown to be a special case of APLE. We then apply APLE to deal with measurement error in some nutrients of interest in the EPIC-InterAct Study under a sensitivity analysis framework.

Moment estimation method of parameters in additive measurement error model.

BACKGROUND: In nutritional epidemiology, covariates in some studies such as the EPIC are prone to measurement error. Estimation of unknown parameters in most measurement error models for food frequency questionnaire (FFQ) and nutrient biomarkers requires replicated measurements. But, the EPIC-InterAct Study did not collect replicated measurements for FFQ or 24-hour dietary recalls (24HR). The method of correcting measurement error in this case is worth studying. METHODS: A moment method is applied to estimate unknown parameters of the proposed error model with correlated errors between biased measurements of FFQ and 24HR. Then, correction factor and reliability ratio of each error-prone nutrient can be obtained correspondingly. Afterwards, regression calibration (RC) under a Cox model is used to correct measurement error of nutrients of interest in the EPIC-InterAct data. RESULTS: Compared to the naive estimation, estimation results for dietary intakes could be very different when we take measurement error into consideration. Using RC as the correction method, hazard ratios (HR) of vegetable plus fruit, fat and energy for males become 1.01 (95% CI 0.75-1.35), 1.30 (95% CI 1.12-1.51) and 1.16 (95% CI 1.04-1.28), respectively, and HR of energy for females becomes 0.99 (95% CI 0.91-1.08). These HRs are greatly different from those by naive estimation. CONCLUSIONS: Although there is no repeated measurement for FFQ and 24HR, we can still estimate all unknown parameters in our proposed error model under four assumptions and then correct measurement error in nutrients of interest in EPIC-InterAct Study by RC for avoiding some misleading results from naive estimation.

Approximate maximum likelihood estimation for logistic regression with covariate measurement error.

In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)-InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC-InterAct Study under a sensitivity analysis framework.

Effects of health-related quality of life on health service utilisation in patients with colorectal neoplasms.

This study was to assess the impact of HRQOL on health service utilisation using four different count data models. The HRQOL was measured using the Short-Form Six-Dimension instrument and the functional assessment of cancer therapy-colorectal whereas health service utilisation was measured by the number of monthly clinical consultations and the number of monthly hospitalisation. Different count data models (Poisson's regression, negative binomial regression, zero-inflated Poisson's regression and zero-inflated negative binomial regression) were used to assess the association between HRQOL and health service utilisation. A performance comparison was made between the models. Goodness-of-fit statistics (the Pearson's chi-squared test statistic, the Akaike and Bayesian information criteria) were used to determine the best-fitting model. The negative binomial model performed the best in assessing the association between HRQOL measures and health service utilisation in patients with colorectal neoplasm and thus recommended. Physical well-being of patients was negatively and significantly associated with the monthly rate of health service utilisation after controlling for patient demographics. Both physical and function well-beings of patients were negatively and significantly associated with the number of monthly hospitalisations. If the data for the condition-specific FACT-C are not available, SF-6D showed a very strong negative relationship with health service utilisation. Such models can be used to guide the allocation of clinical resources and funding for the care of colorectal cancer patients.

Tests for detecting overdispersion in models with measurement error in covariates.

Measurement error in covariates can affect the accuracy in count data modeling and analysis. In overdispersion identification, the true mean-variance relationship can be obscured under the influence of measurement error in covariates. In this paper, we propose three tests for detecting overdispersion when covariates are measured with error: a modified score test and two score tests based on the proposed approximate likelihood and quasi-likelihood, respectively. The proposed approximate likelihood is derived under the classical measurement error model, and the resulting approximate maximum likelihood estimator is shown to have superior efficiency. Simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi-likelihood and other alternatives in terms of empirical power. By analyzing a real dataset containing the health-related quality-of-life measurements of a particular group of patients, we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results.

Comparison of two bupivacaine delivery methods to control postoperative pain after enucleation in dogs.

OBJECTIVE: To compare the efficacy of a preoperative retrobulbar injection of bupivacaine to an intraoperative splash block of bupivacaine in controlling postoperative pain following enucleation in dogs. ANIMALS STUDIED: Prospective, randomized, double-masked clinical study of 31 client owned dogs with end-stage ophthalmic disease requiring enucleation. PROCEDURES: Dogs admitted for unilateral enucleation were randomly assigned to receive bupivacaine 0.5% (1 mL/kg) into the retrobulbar space either via an inferior-temporal palpebral (ITP) injection preoperatively or an intraoperative splash block. Pain was assessed prior to pre-anesthetic sedation and at 0, 0.25, 0.5, 1, 2, 4 6, 8, and 24 hours (H) after extubation by masked observers using a previously described subjective pain scoring system. Rescue analgesia was initiated if overall pain score was >9 or if the score in any category at any time point was >3. RESULTS: There were no adverse reactions. One of 15 dogs that received bupivacaine via a preoperative retrobulbar ITP injection required rescue analgesia. There was no significant difference between groups with regard to the need for rescue analgesia or pain scores at any time point or overall. CONCLUSIONS AND CLINICAL RELEVANCE: Pain control using an intraoperative orbital splash administration of bupivacaine is not significantly different to a preoperative retrobulbar injection of bupivacaine.

Small for gestational age and age at puberty: evidence from Hong Kong's "Children of 1997" birth cohort.

The predictive-adaptive response paradigm postulates that slow fetal growth advances puberty as a life-history strategy for reproductive success, when constraints on postnatal growth are minimal. The authors examined the association of birth weight for gestational age and small for gestational age (SGA) status (birth weight for gestational age <10th percentile, 6.9%) with clinically assessed age at onset of Tanner stage II in a non-Western developed population using interval-censored regression in 7,366 children (89% follow-up) from a population-representative Chinese birth cohort, "Children of 1997" in Hong Kong. Neither SGA status nor birth weight z score for gestational age was associated with age at onset of puberty, adjusted for sex, mother's place of birth, parental height, income, and parental education. Greater childhood height and linear growth were associated with younger age at onset of puberty. SGA status was associated with earlier puberty after adjustment for childhood height (time ratio = 0.984, 95% confidence interval: 0.972, 0.995) but later puberty after adjustment for linear growth (time ratio = 1.017, 95% confidence interval: 1.005, 1.030). In this developed city of China, SGA status was not associated with timing of puberty. However, the observation may be contextually specific depending on how other attributes, such as childhood growth, differ between SGA and other children.

Infant growth and onset of puberty: prospective observations from Hong Kong's "Children of 1997" birth cohort.

PURPOSE: Infant growth and early puberty are associated with the risk of cardiovascular disease. It is unclear whether pubertal timing has an independent etiologic role or is a marker of preceding growth. We examined whether infant growth was associated with age at pubertal onset and whether any associations were mediated by childhood height or body mass index. METHODS: We used multivariable interval-censored proportional hazards regression in 6873 term births (87% follow-up, 53% male) from a population-representative Hong Kong Chinese birth cohort, "Children of 1997." We examined the adjusted associations of sex-specific infant growth trajectories, derived from latent class analyses by the use of, on average, 4.2 measurements per child, with clinically assessed age at pubertal onset (Tanner stage II). We used Sobel tests to assess mediation. RESULTS: Compared with children of average birth weight whose weight followed the same centile curve, a faster weight growth trajectory from birth to 12 months was associated with earlier pubertal onset (time ratio, 0.979; 95% confidence interval, 0.965-0.993) among boys, whereas girls born light with slow infant growth had later puberty (time ratio 1.020, 95% confidence interval 1.006-1.034). These associations were mediated by both height and body mass index among girls but only by height in boys. CONCLUSIONS: Infant weight growth may be associated with earlier pubertal onset, particularly in boys, at least in part because it is associated with more linear growth in childhood. Earlier pubertal onset may be an indicator of up-regulation of growth axes related to the risk of cardiovascular disease.

Soy intake is associated with lower lung cancer risk: results from a meta-analysis of epidemiologic studies.

BACKGROUND: Although several in vitro and animal in vivo studies have suggested that soy or soy isoflavones may exert inhibitory effects on lung carcinogenesis, epidemiologic studies have reported inconclusive results on the association between soy intake and lung cancer. OBJECTIVE: The aim of this meta-analysis was to investigate whether an association exists between soy and lung cancer in epidemiologic studies. DESIGN: We searched PubMed, EMBASE, and the Cochrane Library from their inception to February 2011 for both case-control and cohort studies that assessed soy consumption and lung cancer risk. Study-specific risk estimates were combined by using fixed-effect or random-effect models. RESULTS: A total of 11 epidemiologic studies that consisted of 8 case-control and 3 prospective cohort studies were included. A significantly inverse association was shown between soy intake and lung cancer with an overall RR of 0.77 (95% CI: 0.65, 0.92). Findings were slightly different when analyses were restricted to 5 high-quality studies (RR: 0.70; 95% CI: 0.45, 0.99). In a subgroup meta-analysis, a statistically significant protective effect of soy consumption was observed in women (RR: 0.79; 95% CI: 0.67, 0.93), never smokers (RR: 0.62; 95% CI: 0.51, 0.76), and Asian populations (RR: 0.86; 95% CI: 0.74, 0.98). CONCLUSIONS: Our findings indicate that the consumption of soy food is associated with lower lung cancer risk. Because of different methods used to assess soy consumption across studies, more well-designed cohort studies or intervention studies that use unified measures of soy intake are needed to fully characterize such an association.

An ensemble learning approach jointly modeling main and interaction effects in genetic association studies.

Complex diseases are presumed to be the results of interactions of several genes and environmental factors, with each gene only having a small effect on the disease. Thus, the methods that can account for gene-gene interactions to search for a set of marker loci in different genes or across genome and to analyze these loci jointly are critical. In this article, we propose an ensemble learning approach (ELA) to detect a set of loci whose main and interaction effects jointly have a significant association with the trait. In the ELA, we first search for "base learners" and then combine the effects of the base learners by a linear model. Each base learner represents a main effect or an interaction effect. The result of the ELA is easy to interpret. When the ELA is applied to analyze a data set, we can get a final model, an overall P-value of the association test between the set of loci involved in the final model and the trait, and an importance measure for each base learner and each marker involved in the final model. The final model is a linear combination of some base learners. We know which base learner represents a main effect and which one represents an interaction effect. The importance measure of each base learner or marker can tell us the relative importance of the base learner or marker in the final model. We used intensive simulation studies as well as a real data set to evaluate the performance of the ELA. Our simulation studies demonstrated that the ELA is more powerful than the single-marker test in all the simulation scenarios. The ELA also outperformed the other three existing multi-locus methods in almost all cases. In an application to a large-scale case-control study for Type 2 diabetes, the ELA identified 11 single nucleotide polymorphisms that have a significant multi-locus effect (P-value=0.01), while none of the single nucleotide polymorphisms showed significant marginal effects and none of the two-locus combinations showed significant two-locus interaction effects.

Physical activity energy expenditure predicts changes in body composition in middle-aged healthy whites: effect modification by age.

BACKGROUND: It is unclear whether physical activity energy expenditure (PAEE) predicts changes in body composition. OBJECTIVE: The objective was to describe the independent associations between PAEE and changes in body composition in a population-based cohort. DESIGN: This was a prospective population-based study conducted in 739 (311 men and 428 women) healthy middle-aged (median age: 53.8 y) whites. The median follow-up was 5.6 y. PAEE (MJ/d) was assessed by heart rate monitoring, individually calibrated by using the FLEX heart rate method. Fat mass (FM) and fat-free mass (FFM) were assessed by bioimpedance. RESULTS: Body weight (BW) at follow-up was significantly related to baseline PAEE (P < 0.05) after adjustment for sex, baseline age, FM, FFM, and follow-up time. A significant interaction between PAEE and age (P = 0.023) was observed. After the subjects were stratified (above and below the median for age), BW increased by a mean (+/-SD) of 1.7 +/- 5.9 kg (P < 0.0001) in the younger cohort. In this group, follow-up FM was significantly associated with baseline PAEE (P = 0.036) after adjustment for confounders. In the older cohort, BW did not change between baseline and follow-up. In this group, in contrast with the younger population, follow-up BW, FM, and FFM were all significantly and positively associated with baseline PAEE (P < 0.01 for all). CONCLUSIONS: Baseline PAEE predicts a change in FM in younger adults, who as a group gained weight in this study. In contrast, baseline PAEE in older adults--who were on average weight stable--is associated with a gain in BW, which was explained by an increase in FM and FFM.

Does the association of habitual physical activity with the metabolic syndrome differ by level of cardiorespiratory fitness?

OBJECTIVE: Cardiovascular fitness (VO(2max)) and physical activity are 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. VO(2max) was predicted from 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 error, a random subsample (22% of cohort) re-attended for three repeat measurements in the year following the first assessment. RESULTS: The relationship of VO(2max) (ml O2.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 times greater than for VO(2max) (standardized beta = -1.83, P = 0.0042). VO(2max), 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.

Branched equation modeling of simultaneous accelerometry and heart rate monitoring improves estimate of directly measured physical activity energy expenditure.

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/m2), IC and GC equations for physical activity intensity (PAI) were derived during treadmill walking and running for both HR (Polar) and hipacceleration [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 P2. Similarly, if CSA < or = x, we used P3 if HR > z, otherwise P4. PAEE was calculated for a 12.5-h nonsleeping period as the time integral of PAI. A priori, we assumed P1 = 1, P2 = P3 = 0.5, P4 = 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 < or = 0.035) than single-measure estimates of CSA (less than or equal to -45%) and HR (> or =39%), as well as their nonbranched combination (> or =25.7%). In conclusion, combining HR and CSA by branched modeling improves estimates of PAEE. IC may be less crucial with this modeling technique.

Does physical activity energy expenditure explain the between-individual variation in plasma leptin concentrations after adjusting for differences in body composition?

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 (O(2max.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 O(2max.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.

Non-esterified fatty acid levels and physical inactivity: the relative importance of low habitual energy expenditure and cardio-respiratory fitness.

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.

Prolonged exposure to ethylene stimulates the negative gravitropic responses of Arabidopsis inflorescence stems and hypocotyls.

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 -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.