Adjustment For Measurement Error Research Articles

Sweep programs and optimal monetary aggregation

This paper examines the admissibility of monetary aggregate groupings for the US over 1993–2001, based upon weak separability. We investigate the impact of retail and commercial demand deposit sweep programs on the separability of monetary asset groupings. Weak separability is tested using the Swofford–Whitney and Fleissig–Whitney tests. We use Varian's measurement error adjustment procedure to eliminate violations of the Generalized Axiom of Revealed Preference (GARP). When funds from both retail and commercial demand deposit sweep programs are placed within checkable deposits, all groupings, narrow and broad, pass GARP and weak separability. For groupings based on conventional money measures, tests tend to favor broad aggregates.

PHYSICAL ACTIVITY AND RISK OF CORONARY HEART DISEASE AND STROKE

Many studies have examined the relationship between levels of physical activity (PA) and risk of developing coronary heart disease (CHD) and stroke. Public health recommendations indicate that at least 30 minutes of moderate-intensity PA on most days of the week is required for health benefits. However, the risk reduction associated with activity at this specific level has not been assessed. PURPOSE To undertake a meta-analysis to evaluate the risk of CHD and ischaemic stroke (istroke) due to physical inactivity relative to public health recommendations of at least 30 minutes of moderate—intensity PA on most days of the week. METHODS Literature searches (since 1980) revealed 43 articles on CHD and 30 on istroke. Of these 20 studies on CHD and eight on istroke met the defined inclusion criteria. Only data from studies using a measure of PA along with the health outcomes of mortality and morbidity due to CHD and istroke were included. Studies with measures of physical fitness were excluded. Studies generally assessed participation in discretionary time PA, walking and stair climbing. Several studies assessed ‘all physical activity’, sports participation, or occupational activity. To address concerns regarding error associated with variability in the instruments used to measure PA, an adjustment factor was incorporated into the meta-analysis. Log relative risk estimates were combined using an inverse-variance weighting scheme to derive summary estimates of relative risk in the inactive group for each health outcome. RESULTS For both conditions, the physically inactive group had a significantly higher risk of disease-related morbidity and mortality than the group active at recommended levels. The relative risk (and 95% CI) of the independent effect of inactivity on CHD (i.e. with adjustment for confounding effects and intermediate variables) was estimated to be 1.38 (1.30, 1.47). Relative risks computed with the adjustment for measurement error were 1.71 (1.58, 1.85) for CHD and 1.53 (1.31, 1.79) for istroke. CONCLUSIONS PA at recommended levels provides protection against CHD and istroke.

The performance of methods for correcting measurement error in case-control studies.

It is generally agreed that adjustment for measurement error (when feasible) can substantially increase the validity of epidemiologic analyses. Although a broad variety of methods for measurement error correction has been developed, application in practice is rare. One reason may be that little is known about the robustness of these methods against violations of their restrictive assumptions. We carried out a simulation study to assess the performance of two error correction methods (a regression calibration method and a semiparametric approach) as compared with standard analyses without measurement error correction in case-control studies with internal validation data. Performance was assessed over a wide range of model parameters including varying degrees of violations of assumptions. In nearly all the settings assessed, the semiparametric estimate performed better than all alternatives under investigation. The regression calibration method is sensitive to violations of the assumptions of nondifferential error and small error variance. The semiparametric method is a very robust method to correct for measurement error in case-control studies, but lack of functional software hinders widespread use. If the assumptions for the regression calibration method are fulfilled, application of this method, originally developed for cohort studies, in case-control studies may be a useful alternative that is easy to implement.

Covariate measurement error adjustment for matched case-control studies.

We propose a conditional scores procedure for obtaining bias-corrected estimates of log odds ratios from matched case-control data in which one or more covariates are subject to measurement error. The approach involves conditioning on sufficient statistics for the unobservable true covariates that are treated as fixed unknown parameters. For the case of Gaussian nondifferential measurement error, we derive a set of unbiased score equations that can then be solved to estimate the log odds ratio parameters of interest. The procedure successfully removes the bias in naive estimates, and standard error estimates are obtained by resampling methods. We present an example of the procedure applied to data from a matched case-control study of prostate cancer and serum hormone levels, and we compare its performance to that of regression calibration procedures.

Genetic and environmental contributions to educational attainment in Australia

The genetic and environmental contributions to educational attainment in Australia are examined using a multiple regression model drawn from the medical research literature. Data from a large sample of Australian twins are analysed. The findings indicate that at least as much as 50 percent and perhaps as much as 65 percent of the variance in educational attainments can be attributed to genetic endowments. It is suggested that only around 25 percent of the variance in educational attainments may be due to environmental factors, though this contribution is shown to be around 40 percent when adjustments for measurement error and assortative mating are made. The high fraction of the observed variation in educational attainments due to genetic differences is consistent with results reported by Heath et al. (Heath, A.C., Berg, K., Eaves, L.J., Solaas, M.H., Corey, L.A., Sundet, J., Magnus, P., Nance, W.E., 1985. Education policy and the heritability of educational attainment. Nature 314(6013), 734–736.), Tambs et al. (Tambs, K., Sundet, J.M., Magnus, P., Berg, K., 1989. Genetic and environmental contributions to the covariance between occupational status, educational attainment and IQ: a study of twins. Behavior Genetics 19(2), 209–222.), Vogler and Fulker (Vogler, G.P., Fulker, D.W., 1983. Familial resemblance for educational attainment. Behavior Genetics 13(4), 341–354.) and Behrman and Taubman (Behrman, J., Taubman, P., 1989. Is schooling mostly in the genes? Nature-nurture decomposition using data on relatives. Journal of Political Economy 97(6), 1425–1446.), suggesting that the finding is robust.

Simulating the impact of policy upon chronic and transitory poverty in rural Pakistan

Anti‐poverty programmes often seek to improve their impact by targeting households for assistance according to welfare measures in a single time period. However, a growing literature shows the importance to poor households of fluctuations in their welfare from month to month and year to year. This study uses a five‐year panel of 686 households from rural Pakistan to investigate the magnitude of chronic or transitory poverty making an explicit adjustment for measurement error. The impact of two types of policies (those designed to ‘smooth’ incomes and those designed to promote income growth) on the severity of chronic and transitory poverty is examined. Since the largest part of the squared poverty gap in our sample is transitory, large reductions in poverty can be achieved by interventions designed to ‘smooth’ incomes, but reducing chronic poverty in the long‐term requires large and sustained growth in household incomes. The level and variability of incomes is then modelled as a function of household characteristics, education and assets. The resulting model of the income generation process is used to simulate the impact that a range of transfer and investment policies would have upon chronic and transitory poverty.

Glucose intolerance and physical inactivity: the relative importance of low habitual energy expenditure and cardiorespiratory fitness.

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.

Estimating short-term PM effects accounting for surrogate exposure measurements from ambient monitors

We propose a framework for modeling short-term pollutant exposure effects of ambient source personal exposures using ambient monitoring data. We begin by outlining a model for the health effects of air pollutants on individuals given true pollutant exposure. This is aggregated to form a group-level model of pollutant effects. The aggregation preserves the individual-level interpretation of the exposure effect. However, only surrogate exposure data are available from ambient monitors. We therefore also consider the exposure distribution and measurement characteristics of the pollutant data. We combine these with the disease model of interest and discuss estimation of the exposure effect in the presence of the additional modeling. While the framework includes spatial variation of exposure, we simplify the implementation to ignore the spatial component. We examine the approach in simulations and apply it to asthma hospital admissions and particulate matter data from greater Seattle. The results indicate that adjustment for measurement error alone, without inclusion of spatial variation in ambient PM or fraction of ambient air exposure, does not alter the conclusions from the simpler ecologic time series regression analyses typically reported in the literature. Copyright © 2000 John Wiley & Sons, Ltd.

On measurement error adjustment methods in Poisson regression

This paper echoes the familiar warning that additive measurement error and multicollinearity in the explanatory variables can mislead investigators in multiple Poisson regression analysis. Often, a causal variable measured with error may be overlooked and its significance transferred to another covariate. Two measurement error adjustment methods were applied and compared in terms of mean squared error of the regression estimates as well as confidence interval coverage of the parameters. Computer simulation was used to evaluate these methods when the explanatory variables are subject to both classical and Berkson error. Results showed that the regression calibration method (RCAL) performed the best in all situations considered, except in the presence of Berkson error when the predictor variables are highly correlated. Copyright © 1999 John Wiley & Sons, Ltd.

Some useful statistical methods for model validation.

Although formal hypothesis tests provide a convenient framework for displaying the statistical results of empirical comparisons, standard tests should not be used without consideration of underlying measurement error structure. As part of the validation process, predictions of individual blood lead concentrations from models with site-specific input parameters are often compared with blood lead concentrations measured in field studies that also report lead concentrations in environmental media (soil, dust, water, paint) as surrogates for exposure. Measurements of these environmental media are subject to several sources of variability, including temporal and spatial sampling, sample preparation and chemical analysis, and data entry or recording. Adjustments for measurement error must be made before statistical tests can be used to empirically compare environmental data with model predictions. This report illustrates the effect of measurement error correction using a real dataset of child blood lead concentrations for an undisclosed midwestern community. We illustrate both the apparent failure of some standard regression tests and the success of adjustment of such tests for measurement error using the SIMEX (simulation-extrapolation) procedure. This procedure adds simulated measurement error to model predictions and then subtracts the total measurement error, analogous to the method of standard additions used by analytical chemists.

Determinants of bone and blood lead levels among community-exposed middle-aged to elderly men. The normative aging study.

Levels of lead in bone serve as a dosimeter for cumulative exposure to lead; moreover, lead in bone may serve as an internal source of circulating lead many years after environmental exposure has ceased. The authors measured lead in blood and used a K-x-ray fluorescence instrument to measure lead in the tibia (cortical) and patella (trabecular) bones in a cross-sectional survey of 719 middle-aged to elderly male participants in the Normative Aging Study who were without unusual occupational exposures to lead and who were healthy when enrolled in 1962-1965. Blood lead levels ranged from < 1 to 27.9 micrograms/dl, with a geometric mean of 5.7 micrograms/dl. Tibia and patella lead level ranges (geometric means) were < 1-51 (20.8) micrograms/g and 3-77 (29.8) micrograms/g, respectively. In backwards elimination multivariate regression models that considered age, race, education, retirement status, measures of both current and cumulative smoking, and alcohol consumption, the factors that remained significantly related to higher levels of both tibia and patella lead were higher age and measures of cumulative smoking, and lower levels of education. In the final model predicting blood lead that began with these same covariates and also included tibia and patella lead, the factor that accounted for the dominant portion of the variance in blood lead was patella lead. After adjustment for measurement error, a rise in patella lead from the median of the lowest to the median of the highest quintiles (13-56 micrograms/g) corresponded to a rise in blood lead of 4.3 micrograms/dl. The authors conclude that bone lead levels are substantial and comprise the major source of circulating lead in these men.

Effect of reduced dietary sodium on blood pressure: a meta-analysis of randomized controlled trials.

- To ascertain whether restriction of dietary sodium lowers blood pressure in hypertensive and normotensive individuals. - An English-language computerized literature search, restricted to human studies with Medical Subject Heading terms, "hypertension," "blood pressure," "vascular resistance," "sodium and dietary," "diet and sodium restricted," "sodium chloride," "clinical trial," "randomized controlled trial," and "prospective studies," was conducted. Bibliographies of review articles and personal files were also searched. - Trials that had randomized allocation to control and dietary sodium intervention groups, monitored by timed sodium excretion, with outcome measures of both systolic and diastolic blood pressure were selected by blinded review of the methods section. - Two observers extracted data independently, using purpose-designed forms, and discrepancies were resolved by discussion. - The 56 trials that met our inclusion criteria showed significant heterogeneity. Publication bias was also evident. The mean reduction (95% confidence interval) in daily urinary sodium excretion, a proxy measure of dietary sodium intake, was 95 mmol/d (71-119 mmol/d) in 28 trials with 1131 hypertensive subjects and 125 mmol/d (95-156 mmol/d) in 28 trials with 2374 normotensive subjects. After adjustment for measurement error of urinary sodium excretion, the decrease in blood pressure for a 100-mmol/d reduction in daily sodium excretion was 3.7 mm Hg (2.35-5.05 mm Hg) for systolic (P<.001) and 0.9 mm Hg (-0.13 to 1.85 mm Hg) for diastolic (P=.09) in the hypertensive trials, and 1.0 mm Hg (0.51-1.56 mm Hg) for systolic (P<.001) and 0.1 mm Hg (-0.32 to 0.51 mm Hg) for diastolic (P=.64) in the normotensive trials. Decreases in blood pressure were larger in trials of older hypertensive individuals and small and nonsignificant in trials of normotensive individuals whose meals were prepared and who lived outside the institutional setting. - Dietary sodium restriction for older hypertensive individuals might be considered, but the evidence in the normotensive population does not support current recommendations for universal dietary sodium restriction.

Association of serum total cholesterol with coronary disease and all-cause mortality: multivariate correction for bias due to measurement error.

Measurement error in the exposure under investigation is an important but often ignored source of bias in observational studies. The authors examined the impact of measurement error in the association between total serum cholesterol and 16-year coronary heart disease and all-cause mortality in a cohort of 6,137 middle-aged men of Japanese descent in the Honolulu Heart Program (1973-1988). A Cox regression model that enables modeling of survival time with correction for measurement errors in multiple covariates was employed. After controlling for age, body mass index, systolic blood pressure, smoking status, alcohol consumption, dietary cholesterol, and total calorie intake, a difference of one standard deviation (38 mg/dL) in total cholesterol was associated with a significant increase in the risk of coronary disease death (uncorrected hazard ratio = 1.35). After correction for measurement errors in total cholesterol and covariates (except smoking and age), the estimated hazard ratio increased to 1.65 (a 22% increase). A U-shaped relation was observed between total cholesterol levels and the risk of all-cause mortality. This association was then examined with a quadratic model and with a two-slope or V-shaped regression model. In the quadratic fit, the magnitude of the quadratic total cholesterol term increased threefold after the adjustment for measurement error. In the V fit, the hazard ratio of all-cause death corresponding to a change in one standard deviation above 214 mg/dL (the nadir of the V) was 1.15, and increased to 1.49 (by 29%) after the correction. The corresponding hazard ratio of a change in one standard deviation below 214 mg/dL was 1.11, and increased to 1.37 (by 23%) after the correction. The authors conclude that the impact of elevated total cholesterol on the risk of coronary disease and all-cause mortality may be greater than previously estimated with standard methods of analysis. In addition, the correction for measurement error in total cholesterol and covariates did not explain the excess mortality associated with low total cholesterol. More research is needed to elucidate the fundamental issues underlying the U-shaped association, i.e., confounding versus causal implications.

Individual Income, Incomplete Information, and Aggregate Consumption

Individual income is much more variable than aggregate per capita income. I argue that aggregate information is therefore not very important for individual consumption decisions and study models of life-cycle consumption in which individuals react optimally to their own income process but have incomplete or no information on economy-wide variables. Since individual income is less persistent than aggregate income consumers will react too little to aggregate income variation. Aggregate consumption will be excessively smooth. Since aggregate information is slowly incorporated into consumption, aggregate consumption will be autocorrelated and correlated with lagged income. On the other hand, the model has the same prediction for micro data as the standard permanent income model. The second part of the paper provides empirical evidence on individual and aggregate income processes. Different models for individual income are fit to quarterly data from the Survey of Income and Program Participation making various adjustments for measurement error. Calibrating the consumption model using the estimated parameters for the income process yields predictions which qualitatively correspond to the empirical findings for aggregate consumption but do not match them well in magnitude.

Modelling the female-to-male per-act HIV transmission probability in an emerging epidemic in Asia.

The per-sexual-act probability of transmission of the human immunodeficiency virus type 1 (HIV) from an infected person to a susceptible sex partner can be determined from a simple model if the number of contacts each study participant has with infected partners is known. The unusual epidemiologic situation in the emerging HIV epidemic in Thailand allowed this quantity to be estimated from a cross-sectional study of young men conscripted into the Thai military in 1991. Although the simple model does not fit the data, an errors-in-variables approach provides a model with adequate fit. Other sources of lack of fit, including heterogeneity of the transmission probability, are discussed. With adjustment for measurement error, the per-act probability is estimated to be 0.056, an order of magnitude higher than similar estimates in North America. Because data indicate that recently infected persons may be more infectious, and because extensive HIV transmission in Thailand began in 1988, this difference may be due, in part, to a higher proportion of recently infected individuals in the emerging Thai epidemic from 1988 to 1991.

Measurement error adjustment in statistical control

Measurement error adjustment in statistical control