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The effects of measurement errors on relative risk regressions.

This paper concerns the effects of random error in numerical measurements of risk factors (covariates) in relative risk regressions. When not dependent on outcome (nondifferential), such error usually attenuates relative risk estimates (shifts them toward one) and leads to spuriously narrow confidence intervals. The presence of measurement error also reduces precision of estimates and power of significance tests. However, significance levels obtained by using the approximate measurements are usually valid and as powerful as possible given the measurement error. The attenuation in risk estimate depends not only on the size (variance) of the measurement error, but also on its distributional form, on whether it is dependent on the true level of the risk factor (whether it is of "Berkson" type), on the variance and distributional form of true levels of the risk factor, on the functional form of the regression (exponential or linear), and on the confounding variables included in the model. Error in measuring confounding variables leads to loss of control of confounding, leaving residual bias. Uncomplicated techniques of correcting the effects of measurement error in simple models in which distributions are assumed normal are available in the statistical literature. For these corrections, information on measurement error variance is required. Some approaches appropriate for more general models have been proposed, but these appear to be insufficiently developed for routine application.

Bias↗

Axial characteristics of circular external skeletal fixator single ring constructs.

OBJECTIVE: Evaluate the effects of varying ring diameter, wire tension, and wire-divergence angle on the axial stiffness characteristics of circular external skeletal fixator single-ring constructs. Study Design-Biomechanical evaluation using circular fixator components and a Delrin cylinder bone model. METHODS: Single ring constructs using two 1.6 mm diameter Kirschner wires to secure a 19 mm Delrin cylinder centered within the ring were examined. Component variables evaluated were ring diameter (50 mm, 66 mm, 84 mm, and 118 mm), wire-divergence angle (30 degrees, 60 degrees, and 90 degrees ), and wire tension (0 kg, 30 kg, 60 kg, and 90 kg). A total of 48 constructs were examined. Rings were rigidly mounted on a universal testing system and the cylinder loaded in axial compression (7.4 N/s) to 220 N. Load/displacement curves were analyzed to determine the following: the displacement (mm) that occurred before the slope of each load/displacement curve became linear, the stiffness (N/mm) of the linear portion of each load/deformation curve, and the total displacement (mm) produced at maximal load. Least-squares linear regression was used to model response variables as linear functions of ring diameter, wire divergence angle, and wire tension. Three-way interactions and 2-way interactions among independent component variables were evaluated first in the modeling process and included in a best model if response variables were found to have statistically significant regression coefficients. The regression coefficients and corresponding standard errors and covariances were used to estimate the maximal effect and standard error attributable to wire divergency angle (change from 30 degrees to 90 degrees ) and wire tension (change from 0 to 90 kg) for each ring diameter. RESULTS: All load/deformation curves had an initial exponential increase in stiffness, with the slope becoming linear at higher loads. The exponential phase was more pronounced in larger-diameter ring constructs and was mitigated by tensioning the wires. Ring diameter had the greatest influence on displacement that occurred before the curve became linear (semipartial r(2) [sp-r2] = .89), stiffness (sp-r2 = .94), and total displacement (sp-r2 = .93). Wire tension exerted a smaller influence on displacement that occurred before the curve became linear (sp-r2 =.06), stiffness (sp-r2 = .03), and total displacement (sp-r2 = .05). Wire divergence angle had a nominal effect on displacement that occurred before the curve became linear (sp-r2 = .0001), on stiffness (sp-r2 = .004), and on total displacement (sp-r2 =.003). CONCLUSIONS: Ring diameter had a profound effect on the axial stiffness characteristic of single ring constructs. Tensioning of the fixation wires can improve the axial stiffness characteristics of these constructs, particularly in larger diameter ring constructs, by mitigating the initial exponential phase of the load/deformation curve. Wire divergence angle had only a nominal differential effect on axial stability. CLINICAL RELEVANCE: Understanding how individual component variables and their interactions influence bone segment stability should help surgeons to optimize interfragmentary strain. Tensioning fixation wires is probably unnecessary in 50 mm diameter ring constructs, but assumes greater importance as ring diameter increases.

Animals↗

The performance of random coefficient regression in accounting for residual confounding.

Greenland (2000, Biometrics 56, 915-921) describes the use of random coefficient regression to adjust for residual confounding in a particular setting. We examine this setting further, giving theoretical and empirical results concerning the frequentist and Bayesian performance of random coefficient regression. Particularly, we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding. This devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model. The approach described by Gustafson (2005, Statistical Science 20, 111-140) is used to quantify the performance of a Bayesian estimator arising from a nonidentified model. From both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints. In terms of point-estimator bias this superiority arises when the extent of residual confounding is substantial, but the advantage is much broader in terms of interval estimation. The benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality, for the standard identifying constraints are equivalent to priors that typically correspond much worse.

Bayes Theorem↗

Comparison of possible covariates for use in a random regression model for analyses of test day yields.

Random regression models have been proposed for the genetic evaluation of dairy cattle using test day records. Random regression models contain linear functions of fixed and random coefficients and a set of covariates to describe the shapes of lactation curves for groups of cows and for individual cows. Previous work has used a linear function of five covariates to describe lactation shape. This study compared the function of five covariates with a function of only three covariates in three random regression models. Comparisons of estimates of components of variances and covariances, as well as comparisons of EBV and their prediction errors for milk yield, were made among models. Small practical differences existed between models in all respects. The model using regressions with five covariates had a slight advantage for comparison of prediction error variances of daily yields.

Animals↗

Hierarchical modeling of the relation between sequence variants and a quantitative trait: addressing multiple comparison and population stratification issues.

When analyzing the relation between genetic sequence information and disease traits, false-positive associations can arise due to multiple comparisons and population stratification. In an attempt to address these issues, we incorporate into a conventional analytic model higher-level--or "prior"--models that use additional information to improve estimates while allowing for differing population structures. We apply this hierarchical model to simulated data from the Genetic Analysis Workshop 12. We focus on the effects of common candidate gene sequence variants on quantitative risk factor 5 (Q5) levels. In particular, we compare the regression coefficients (and 95% confidence intervals) obtained from conventional (one-stage) analyses versus the corresponding results from the hierarchical analyses. When examining either the marry-ins or all subjects in the general and isolate populations, the conventional model detected numerous sites in candidate genes 1-5 and 7 that had statistically significant regression coefficients (alpha level = 0.05). In contrast, our hierarchical model primarily only detected associations for variants in candidate gene 2, which is the casual gene for Q5.

Chromosome Mapping↗

An annotated bibliography of methods for analysing correlated categorical data.

This paper provides an annotated bibliography of over 100 articles concerning methods for analysing correlated categorical response data. Most of the papers listed here concern categorical regression models and estimation, with particular emphasis on binary responses. The papers are classified by several characteristics which group them according to common themes. The bibliography serves as a reference of methods for analysts of correlated categorical data, as well as for persons interested in methodologic work in this active area of statistical research.

Clinical Trials as Topic↗

Prediction of maintenance warfarin dosage from initial patient response.

This study was conducted to determine the reliability of two methods of predicting maintenance warfarin dosage. Fifty-nine patients were studied using Method 1 and 44 using Method 2. Both methods produced a statistically significant correlation between predicted and actual dose for the two populations. However, actual vs. predicted doses for individual patients were significantly different. Method 1 predicted a dose within +/- 2.5 mg/d of actual dose in only 40.7 percent of patients. With Method 2, the corresponding value was 56.8 percent. Although the linear regression was statistically significant in our population, many patients would have excessive or subtherapeutic dosage predictions.

Adult↗

Linearity Versus nonlinearity of offspring-parent regression: an experimental study of Drosophila melanogaster.

An experiment was conducted to investigate the offspring-parent regression for three quantitative traits (weight, abdominal bristles and wing length) in Drosophila melanogaster. Linear and polynomial models were fitted for the regressions of a character in offspring on both parents. It is demonstrated that responses by the characters to selection predicted by the nonlinear regressions may differ substantially from those predicted by the linear regressions. This is true even, and especially, if selection is weak. The realized heritability for a character under selection is shown to be determined not only by the offspring-parent regression but also by the distribution of the character and by the form and strength of selection.

Analysis of Variance↗

Approximate hierarchical modelling of discrete data in epidemiology.

Hierarchical models are used in epidemiology to estimate and analyse multiple, related relative risks. Examples include meta-analyses of series of 2 x 2 tables and mapping of spatially correlated disease rates. Empirical transform and penalized quasilikelihood procedures, both of which may be implemented using standard programs for mixed model analysis, provide satisfactory approximate inferences for these problems when cell frequencies are large. Simulation studies show that, in certain situations involving small cell frequencies, penalized quasilikelihood provides satisfactory estimates of variance components and regression coefficients whereas the empirical transform approach does not.

BCG Vaccine↗

Uncertainty and sensitivity analysis of spatial predictions of heavy metals in wheat.

Heavy metals seriously threaten the health of human beings when they enter the food chain. Therefore, policymakers require precise predictions of heavy metal concentrations in agricultural crops. In this paper we quantify the uncertainty of regression predictions of Cd and Pb in wheat (Triticum aestivum L.) and the contributions to the uncertainties in these predictions associated with inputs to the regression model. For each node of the 500- x 500-m grid covering the arable soils in The Netherlands, a latin hypercube sample size of 1000 is constructed from the uncertainty distributions of the explanatory variables (pH, soil organic matter [SOM], and heavy metal concentration in soil), the regression coefficients, and the random term of the regression model. This sample is used as input for the regression model to obtain 1000 values from the uncertainty distributions of the log(Cd) and log(Pb) concentration in wheat. There were no nodes where the recent EU quality standards for Cd and Pb (0.2 mg kg(-1) fresh wt.) in wheat were almost certain to be exceeded. For most nodes with clay soils, the quality standard for Cd in wheat almost certainly will not be exceeded; for Pb this is much less certain. The uncertainty in the Cd concentration in soil contributes most to the uncertainty in the predicted Cd concentrations in wheat (36% on the average), followed by the random term of the regression model (23%). For Pb the contribution of the random term is by far the largest (52%).

Agriculture↗

Impact of tumor size on the long-term survival of patients with early stage renal cell cancer.

As the biological behaviour of even early stage renal cell cancer (RCC) strongly correlates with tumor size, it has been argued that the inclusion of RCC up to a maximum diameter of 7 cm into a common subgroup classified as T1 according to the 5th edition of the TNM system would not adequately represent the different biological aggressiveness of these malignancies. Taking this into account, the TNM classification, which now categorizes T1 RCC as T1a and T1b according to a cutoff size of 4 cm, was recently modified. However, only a few larger investigations, mainly based on univariate statistical analyses, that support the suitability of this cutoff are at present available from the literature. Therefore, it was the aim of the present investigation to determine the tumor size that best separates patients with low responses from those with high risk for tumor progression by univariate (log rank test) and multivariate (Cox regression model) statistical analyses. Between 1981 and 2000, 652 patients (443 males and 209 females) underwent tumor nephrectomy in our clinic for the diagnosis of RCC. Of these, 243 patients revealed primary tumors with a local growth not extending beyond the renal capsula at the time of surgery. For the different cutoff levels (starting from 2 cm in increments of 1 cm up to 8 cm) that were selected to subdivide the patients into groups according to the maximum tumor diameter, the correlation between tumor size and overall survival was determined by univariate and multivariate statistical analyses. It became evident that although during univariate analysis the prognostic value of a cutoff size of 4 cm was confirmed, multivariate analysis identified the highest relative risk for cause-specific death (2.93) for patients having tumors larger than 5 cm in maximum diameter. Therefore, the 5 cm cutoff seems to best determine the clinical prognosis of patients undergoing tumor nephrectomy for early stage RCC. The present study demonstrates the need for multivariate statistical approaches when the latest modification of the TNM classification system is critically evaluated.

Adult↗

Relationships between the orientation and moment arms of the human jaw muscles and normal craniofacial morphology.

It has been suggested that subjects with increased vertical craniofacial dimensions have relatively oblique orientated jaw muscles with a reduced possibility to restrain the vertical component of craniofacial growth. To test this hypothesis, relationships were investigated between the spatial orientation of the jaw muscles and the craniofacial morphology. Computer reconstructions of the external shape of the jaw muscles of 30 adult males with a normal skull were made with the use of serial magnetic resonance imaging (MRI) scans. The orientation of the jaw muscles was defined by a regression line through the centroids of the serial cross-sections. Sagittal and frontal projections of the moment arms of the muscles were measured with respect to the centre of the ipsilateral condyle. Craniofacial morphology was analysed three-dimensionally using lateral head films and coronal MRI scans. The cephalometric data were analysed statistically using regression and factor analyses. Six cephalometric factors with Eigen values higher than 1 were correlated with jaw muscle orientation and moment arm data, using a multiple regression analysis. The anterior face height factor was significantly correlated with the orientation of the jaw opening muscles in the sagittal plane but was not significantly correlated with the orientation of the mandibular elevators. The sagittal moment arms of the mandibular elevators showed significant correlations with the factors describing the gonial angle and the posterior face height. It was concluded that the variation of spatial orientation of the human jaw closing muscles is predominantly associated with the variation of mandibular morphology (expressed by the gonial angle) and the posterior face height. The orientation of the jaw opening muscles shows significant relationships with anterior vertical craniofacial dimensions. The hypothesis that persons with an increased anterior face height have relatively oblique orientated jaw elevators was rejected.

Adult↗

Relation between increased numbers of safe playing areas and decreased vehicle related child mortality rates in Japan from 1970 to 1985: a trend analysis.

OBJECTIVES: To examine vehicle related mortality trends of children in Japan; and to investigate how environmental modifications such as the installation of public parks and pavements are associated with these trends. DESIGN: Poisson regression was used for trend analysis, and multiple regression modelling was used to investigate the associations between trends in environmental modifications and trends in motor vehicle related child mortality rates. SETTING: Mortality data of Japan from 1970 to 1994, defined as E-code 810-23 from 1970 to 1978 and E810-25 from 1979 to 1994, were obtained from vital statistics. Multiple regression modelling was confined to the 1970-1985 data. Data concerning public parks and other facilities were obtained from the Ministry of Land, Infrastructure, and Transport. SUBJECTS: Children aged 0-14 years old were examined in this study and divided into two groups: 0-4 and 5-14 years. MAIN RESULTS: An increased number of public parks was associated with decreased vehicle related mortality rates among children aged 0-4 years, but not among children aged 5-14. In contrast, there was no association between trends in pavements and mortality rates. CONCLUSIONS: An increased number of public parks might reduce vehicle related preschooler deaths, in particular those involving pedestrians. Safe play areas in residential areas might reduce the risk of vehicle related child death by lessening the journey both to and from such areas as well as reducing the number of children playing on the street. However, such measures might not be effective in reducing the vehicle related mortalities of school age children who have an expanded range of activities and walk longer distances.

Accidents, Traffic↗

Regression-adjusted small area estimates of functional dependency in the noninstitutionalized American population age 65 and over.

Health planning efforts for the population age 65 and over have been hampered continually by the lack of reliable estimates of the noninstitutionalized long-term care population. Until recently national estimates were virtually nonexistent, and reliable small area estimates remain unavailable. However, with the recent publication of several national surveys and the 1990 Census, synthetic estimates can be made for states and counties by using multivariate methods to model functional dependency at the national level, and then applying the predicted probabilities to corresponding state and county data. Using the 1984 National Health Interview Survey's Supplement on Aging and the 1986 Area Health Resources File System, we have produced log-linear regression models that include demographic and contextual variables as predictors of functional dependency among the noninstitutionalized population age 65 and over. Age, sex, race, and the percent of the 65 and over population who reside in poverty were found to be significant predictors of functional dependency. Applying these models to 1986 Medicare Enrollment Statistics, regression-adjusted synthetic estimates of two levels of functional dependency were produced for all states and--as examples of how the rates can be used to produce additional synthetic estimates--the largest county in each state. We also produced point estimates and standard errors for the national prevalence of functional dependency among the noninstitutionalized population age 65 and over.

Activities of Daily Living↗

Robust regression of scattered data with adaptive spline-wavelets.

A coarse-to-fine data fitting algorithm for irregularly spaced data based on boundary-adapted adaptive tensor-product semi-orthogonal spline-wavelets has been proposed in Castaño and Kunoth, 2003. This method has been extended in Castaño and Kunoth, 2005 to include regularization in terms of Sobolev and Besov norms. In this paper, we develop within this least-squares approach some statistical robust estimators to handle outliers in the data. Our wavelet scheme yields a numerically fast and reliable way to detect outliers.

Algorithms↗

Prognostic value of the Island sign for hematoma expansion and functional outcome after intracerebral hemorrhage: a systematic review and meta-analysis.

PURPOSE: The Island Sign (IS) is a radiological finding observed in patients with intracerebral hemorrhage (ICH). This meta-analysis aimed to evaluate the association between IS and both hematoma expansion (HE) and functional outcomes by comparing ICH patients with and without IS. METHODS: We searched PubMed, Embase and Cochrane Library for studies of intracerebral hemorrhage reporting the IS. The primary outcomes were functional status and hematoma expansion, secondary outcome was mortality. Statistical analysis was performed using RStudio, effect sizes were calculated as odds ratios (ORs) with 95% confidence interval (95% CIs), and heterogeneity was assessed with I2 statistics. In addition, meta-regression and sensitivity analyses were performed, and publication bias was assessed through funnel plots and Egger's regression test. RESULTS: We included 21 observational studies with a total of 9,459 patients with spontaneous ICH, 1,769 of them had IS, while 7,690 did not. The mean age was 63.5&#xa0;&#xb1;&#xa0;13.2 and 5,835 (61.7%) were male. Poor functional outcomes (OR 2.77, 95% CI: 2.14-3.58, p&#xa0;<&#xa0;0.0001, I2&#xa0;=&#xa0;4.9%) and hematoma expansion (OR 2.75, 95% CI: 1.87-4.03, p&#xa0;<&#xa0;0.0001, I2&#xa0;=&#xa0;77.4%) were substantially higher in patients with IS, as well as the overall mortality rate (OR 2.54, 95% CI: 1.55-4.17, p&#xa0;=&#xa0;0.0002, I2&#xa0;=&#xa0;0%). Meta-regression analysis showed no statistically significant association between imaging-related timing variables and hematoma expansion. Furthermore, the leave-one-out sensitivity analyses showed that no single study exerted a disproportionate influence on the overall effect for the examined outcomes, and Egger's linear regression tests were not statistically significant for both outcomes. CONCLUSION: Patients with the Island Sign are associated with higher rates of poor functional outcomes and hematoma expansion. Thus, IS is a relevant radiological finding with potential to support early risk stratification and optimize patient management and treatment selection.

Humans↗

Marginalized transition models and likelihood inference for longitudinal categorical data.

Marginal generalized linear models are now frequently used for the analysis of longitudinal data. Semiparametric inference for marginal models was introduced by Liang and Zeger (1986, Biometrics 73, 13-22). This article develops a general parametric class of serial dependence models that permits likelihood-based marginal regression analysis of binary response data. The methods naturally extend the first-order Markov models of Azzalini (1994, Biometrika 81, 767-775) and prove computationally feasible for long series.

Biometry↗

Efficient regression analysis with ranked-set sampling.

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.

Biometry↗