Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Non-invasive quantitative estimation of bone density in rats throughout the life cycle and in arthritic osteopenia: preliminary results

A longitudinal bone survey was conducted in 86 female Wistar rats in order to assess mineral density kinetics from young age (5 weeks: 115 g) till late adulthood (64 weeks: 586 g). In vivo quantitative radiographic scanning was performed on the caudal vertebrae, taking trabecular mass as the parameter. Measurements were expressed as Relative Optical Density (ROD) units by means of a high resolution densitometric device. Results showed a progressive increase in mineral density throughout the life cycle, with a tendency to level in the higher weight range, indicating that progressive mineral aposition occurs in rats in dependency of age. This phenomenon, however, should be always considered within the context of continuous skeletal growth and related changes typical of this species. Twelve different animals were also examined following induction of articular inflammation with Freund's adjuvant in six of them. Bone survey conducted 12 to 18 days after inoculation revealed a significant (P less than 0.01) reduction in trabecular bone mass of scanned vertebrae in comparison with the weight-matched untreated controls. It is concluded that the in vivo quantitative assessment of bone density illustrated in this report represents a sensitive and useful tool for the long-term survey of naturally occurring or experimentally induced bone changes. Scanning of the same part of the skeleton can be repeated, thereby avoiding sacrifice of the animal and time-consuming preparation of post-mortem material.

Climate spectrum estimation in the presence of timescale errors

We introduce an algorithm (called REDFITmc2) for spectrum estimation in the presence of timescale errors. It is based on the Lomb-Scargle periodogram for unevenly spaced time series, in combination with the Welch's Overlapped Segment Averaging procedure, bootstrap bias correction and persistence estimation. The timescale errors are modelled parametrically and included in the simulations for determining (1) the upper levels of the spectrum of the red-noise AR(1) alternative and (2) the uncertainty of the frequency of a spectral peak. Application of REDFITmc2 to ice core and stalagmite records of palaeoclimate allowed a more realistic evaluation of spectral peaks than when ignoring this source of uncertainty. The results support qualitatively the intuition that stronger effects on the spectrum estimate (decreased detectability and increased frequency uncertainty) occur for higher frequencies. The surplus information brought by algorithm REDFITmc2 is that those effects are quantified. Regarding timescale construction, not only the fixpoints, dating errors and the functional form of the age-depth model play a role. Also the joint distribution of all time points (serial correlation, stratigraphic order) determines spectrum estimation.

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Individual risk factors for Mycoplasma hyopneumoniae infections in suckling pigs at the age of weaning.

BACKGROUND In recent years, the occurrence and the relevance of Mycoplasma hyopneumoniae infections in suckling pigs has been examined in several studies. Whereas most of these studies were focused on sole prevalence estimation within different age groups, follow-up of infected piglets or assessment of pathological findings, none of the studies included a detailed analysis of individual and environmental risk factors. Therefore, the aim of the present study was to investigate the frequency of M. hyopneumoniae infections in suckling pigs of endemically infected herds and to identify individual risk factors potentially influencing the infection status of suckling pigs at the age of weaning. RESULTS The animal level prevalence of M. hyopneumoniae infections in suckling pigs examined in three conventional pig breeding herds was 3.6% (41/1127) at the time of weaning. A prevalence of 1.2% was found in the same pigs at the end of their nursery period. In a multivariable Poisson regression model it was found that incidence rate ratios (IRR) for suckling pigs are significantly lower than 1 when teeth grinding was conducted (IRR: 0.10). Moreover, high temperatures in the piglet nest during the first two weeks of life (occasionally >40°C) were associated with a decrease of the probability of an infection (IRR: 0.23-0.40). Contrary, the application of PCV2 vaccines to piglets was associated with an increased infection risk (IRR: 9.72). CONCLUSIONS Since single infected piglets are supposed to act as initiators for the transmission of this pathogen in nursery and fattening pigs, the elimination of the risk factors described in this study should help to reduce the incidence rate of M. hyopneumoniae infections and thereby might contribute to a reduced probability of high prevalences in older pigs.

Factors influencing the accuracy of fetal weight estimation with a focus on preterm birth at the limit of viability: a systematic literature review

BACKGROUND Fetal weight estimation (FWE) is an important factor for clinical management decisions, especially in imminent preterm birth at the limit of viability between 23(0/7) and 26(0/7) weeks of gestation. It is crucial to detect and eliminate factors that have a negative impact on the accuracy of FWE. DATA SOURCES In this systematic literature review, we investigated 14 factors that may influence the accuracy of FWE, in particular in preterm neonates born at the limit of viability. RESULTS We found that gestational age, maternal body mass index, amniotic fluid index and ruptured membranes, presentation of the fetus, location of the placenta and the presence of multiple fetuses do not seem to have an impact on FWE accuracy. The influence of the examiner's grade of experience and that of fetal gender were discussed controversially. Fetal weight, time interval between estimation and delivery and the use of different formulas seem to have an evident effect on FWE accuracy. No results were obtained on the impact of active labor. DISCUSSION This review reveals that only few studies investigated factors possibly influencing the accuracy of FWE in preterm neonates at the limit of viability. Further research in this specific age group on potential confounding factors is needed.

P-T-t estimation of syn-kinematic strain in low-grade quartz-feldspar bearing rocks using thermodynamic modeling and 40Ar/39Ar dating techniques: example of the Plan-de-Phasy shear zone unit (Briançonnais Zone, Western Alps)

Pressure–Temperature–time (P–T–t) estimates of the syn-kinematic strain at the peak-pressure conditions reached during shallow underthrusting of the Briançonnais Zone in the Alpine subduction zone was made by thermodynamic modelling and 40Ar/39Ar dating in the Plan-de-Phasy unit (SE of the Pelvoux Massif, Western Alps). The dated phengite minerals crystallized syn-kinematically in a shear zone indicating top-to-the-N motion. By combining X-ray mapping with multi-equilibrium calculations, we estimate the phengite crystallization conditions at 270 ± 50 °C and 8.1 ± 2 kbar at an age of 45.9 ± 1.1 Ma. Combining this P–T–t estimate with data from the literature allows us to constrain the timing and geometry of Alpine continental subduction. We propose that the Briançonnais units were scalped on top of the slab during ongoing continental subduction and exhumed continuously until collision.

Estimation of reference curves for the urinary steroid metabolome in the first year of life in healthy children: tracing the complexity of human postnatal steroidogenesis

CONTEXT Complex steroid disorders such as P450 oxidoreductase deficiency or apparent cortisone reductase deficiency may be recognized by steroid profiling using chromatographic mass spectrometric methods. These methods are highly specific and sensitive, and provide a complete spectrum of steroid metabolites in a single measurement of one sample which makes them superior to immunoassays. The steroid metabolome during the fetal-neonatal transition is characterized by a) the metabolites of the fetal-placental unit at birth, b) the fetal adrenal androgens until its involution 3-6 months postnatally, and c) the steroid metabolites produced by the developing endocrine organs. All these developmental events change the steroid metabolome in an age- and sex-dependent manner during the first year of life. OBJECTIVE The aim of this study was to provide normative values for the urinary steroid metabolome of healthy newborns at short time intervals in the first year of life. METHODS We conducted a prospective, longitudinal study to measure 67 urinary steroid metabolites in 21 male and 22 female term healthy newborn infants at 13 time-points from week 1 to week 49 of life. Urine samples were collected from newborn infants before discharge from hospital and from healthy infants at home. Steroid metabolites were measured by gas chromatography-mass spectrometry (GC-MS) and steroid concentrations corrected for urinary creatinine excretion were calculated. RESULTS 61 steroids showed age and 15 steroids sex specificity. Highest urinary steroid concentrations were found in both sexes for progesterone derivatives, in particular 20α-DH-5α-DH-progesterone, and for highly polar 6α-hydroxylated glucocorticoids. The steroids peaked at week 3 and decreased by ∼80% at week 25 in both sexes. The decline of progestins, androgens and estrogens was more pronounced than of glucocorticoids whereas the excretion of corticosterone and its metabolites and of mineralocorticoids remained constant during the first year of life. CONCLUSION The urinary steroid profile changes dramatically during the first year of life and correlates with the physiologic developmental changes during the fetal-neonatal transition. Thus detailed normative data during this time period permit the use of steroid profiling as a powerful diagnostic tool.

Body Height Estimation from Femur Measurements in Postmortem Computed Tomography

After attending this presentation, attendees will: (1) understand how body height from computed tomography data can be estimated; and, (2) gain knowledge about the accuracy of estimated body height and limitations. The presentation will impact the forensic science community by providing knowledge and competence which will enable attendees to develop formulas for single bones to reconstruct body height using postmortem Computer Tomography (p-CT) data. The estimation of Body Height (BH) is an important component of the identification of corpses and skeletal remains. Stature can be estimated with relative accuracy via the measurement of long bones, such as the femora. Compared to time-consuming maceration procedures, p-CT allows fast and simple measurements of bones. This study undertook four objectives concerning the accuracy of BH estimation via p-CT: (1) accuracy between measurements on native bone and p-CT imaged bone (F1 according to Martin 1914); (2) intra-observer p-CT measurement precision; (3) accuracy between formula-based estimation of the BH and conventional body length measurement during autopsy; and, (4) accuracy of different estimation formulas available.1 In the first step, the accuracy of measurements in the CT compared to those obtained using an osteometric board was evaluated on the basis of eight defleshed femora. Then the femora of 83 female and 144 male corpses of a Swiss population for which p-CTs had been performed, were measured at the Institute of Forensic Medicine in Bern. After two months, 20 individuals were measured again in order to assess the intraobserver error. The mean age of the men was 53±17 years and that of the women was 61±20 years. Additionally, the body length of the corpses was measured conventionally. The mean body length was 176.6±7.2cm for men and 163.6±7.8cm for women. The images that were obtained using a six-slice CT were reconstructed with a slice thickness of 1.25mm. Analysis and measurements of CT images were performed on a multipurpose workstation. As a forensic standard procedure, stature was estimated by means of the regression equations by Penning & Riepert developed on a Southern German population and for comparison, also those referenced by Trotter & Gleser “American White.”2,3 All statistical tests were performed with a statistical software. No significant differences were found between the CT and osteometric board measurements. The double p-CT measurement of 20 individuals resulted in an absolute intra-observer difference of 0.4±0.3mm. For both sexes, the correlation between the body length and the estimated BH using the F1 measurements was highly significant. The correlation coefficient was slightly higher for women. The differences in accuracy of the different formulas were small. While the errors of BH estimation were generally ±4.5–5.0cm, the consideration of age led to an increase in accuracy of a few millimetres to about 1cm. BH estimations according to Penning & Riepert and Trotter & Gleser were slightly more accurate when age-at-death was taken into account.2,3 That way, stature estimations in the group of individuals older than 60 years were improved by about 2.4cm and 3.1cm.2,3 The error of estimation is therefore about a third of the common ±4.7cm error range. Femur measurements in p-CT allow very accurate BH estimations. Estimations according to Penning led to good results that (barely) come closer to the true value than the frequently used formulas by Trotter & Gleser “American White.”2,3 Therefore, the formulas by Penning & Riepert are also validated for this substantial recent Swiss population.

Body height estimation from post-mortem CT femoral F1 measurements in a contemporary Swiss population.

PURPOSE The present study aimed at the comparison of body height estimations from cadaver length with body height estimations according to Trotter and Gleser (1952) and Penning and Riepert (2003) on the basis of femoral F1 section measurements in post-mortem computed tomography (PMCT) images. METHODS In a post-mortem study in a contemporary Swiss population (226 corpses: 143 males (mean age: 53±17years) and 83 females (mean age: 61±20years)) femoral F1 measurements (403 femora: 199 right and 204 left; 177 pairs) were conducted in PMCT images and F1 was used for body height estimation using the equations after Trotter and Gleser (1952, "American Whites"), and Penning and Riepert (2003). RESULTS The mean observed cadaver length was 176.6cm in males and 163.6cm in females. Mean measured femoral length F1 was 47.5cm (males) and 44.1cm (females) respectively. Comparison of body height estimated from PMCT F1 measurements with body height calculated from cadaver length showed a close congruence (mean difference less than 0.95cm in males and less than 1.99cm in females) for equations both applied after Penning and Riepert and Trotter and Gleser. CONCLUSIONS Femoral F1 measurements in PMCT images are very accurate, reproducible and feasible for body height estimation of a contemporary Swiss population when using the equations after Penning and Riepert (2003) or Trotter and Gleser (1952).

A categorical data analysis approach to estimation of demographic characteristics for Texas county populations

The need for timely population data for health planning and Indicators of need has Increased the demand for population estimates. The data required to produce estimates is difficult to obtain and the process is time consuming. Estimation methods that require less effort and fewer data are needed. The structure preserving estimator (SPREE) is a promising technique not previously used to estimate county population characteristics. This study first uses traditional regression estimation techniques to produce estimates of county population totals. Then the structure preserving estimator, using the results produced in the first phase as constraints, is evaluated.^ Regression methods are among the most frequently used demographic methods for estimating populations. These methods use symptomatic indicators to predict population change. This research evaluates three regression methods to determine which will produce the best estimates based on the 1970 to 1980 indicators of population change. Strategies for stratifying data to improve the ability of the methods to predict change were tested. Difference-correlation using PMSA strata produced the equation which fit the data the best. Regression diagnostics were used to evaluate the residuals.^ The second phase of this study is to evaluate use of the structure preserving estimator in making estimates of population characteristics. The SPREE estimation approach uses existing data (the association structure) to establish the relationship between the variable of interest and the associated variable(s) at the county level. Marginals at the state level (the allocation structure) supply the current relationship between the variables. The full allocation structure model uses current estimates of county population totals to limit the magnitude of county estimates. The limited full allocation structure model has no constraints on county size. The 1970 county census age - gender population provides the association structure, the allocation structure is the 1980 state age - gender distribution.^ The full allocation model produces good estimates of the 1980 county age - gender populations. An unanticipated finding of this research is that the limited full allocation model produces estimates of county population totals that are superior to those produced by the regression methods. The full allocation model is used to produce estimates of 1986 county population characteristics. ^

AN ESTIMATION OF IN UTERO DRUG EXPOSURE BY DETERMINANTS OF FREQUENCY AND DISTRIBUTION OF MATERNAL DRUG CONSUMPTION

Data derived from 1,194 gravidas presenting at the observation unit of a city/county hospital between October 11, 1979 through December 7, 1979 were evaluated with respect to the proportion ingesting drugs during pregnancy. The mean age of the mother at the time of the interview was 22.0 years; 43.0 percent were Black; 34.0 percent Latin-American, 21.0 percent White and 2.0 percent other; mean gravida was 2.5 pregnancies; mean parity was 1.0; and mean number of previous abortions was 0.34. Completed interview data was available for 1,119 gravida, corresponding urinalyses for 997 subjects. Ninety and one-tenth percent (90.1 percent) of the subjects reported ingestion of one or more drug preparation(s) (prescription, OTC, or substances used for recreational purposes) during pregnancy with a range of 0 to 11 substances and a mean of 2.7. Dietary supplements (vitamins and minerals) were most frequently reported followed by non-narcotic analgesics. Seventy-six and one tenth percent (76.1 percent) of the population reported consumption of prescription medication, 42.5 percent reported consumption of over-the-counter medications, 45.7 percent reported consumption of a substance for recreational purposes and 4.3 percent reported illicit consumption of a substance. For selected substances, no measurable difference was found between obtaining the information from the interview method or from a urinalysis assay. ^

AN EMPIRICAL ESTIMATION OF MEDICAL AND NON-MEDICAL INPUTS IN THE PRODUCTION OF CARDIO-RESPIRATORY PHYSICAL HEALTH STATUS

The purpose of this study was to examine, in the context of an economic model of health production, the relationship between inputs (health influencing activities) and fitness.^ Primary data were collected from 204 employees of a large insurance company at the time of their enrollment in an industrially-based health promotion program. The inputs of production included medical care use, exercise, smoking, drinking, eating, coronary disease history, and obesity. The variables of age, gender and education known to affect the production process were also examined. Two estimates of fitness were used; self-report and a physiologic estimate based on exercise treadmill performance. Ordinary least squares and two-stage least squares regression analyses were used to estimate the fitness production functions.^ In the production of self-reported fitness status the coefficients for the exercise, smoking, eating, and drinking production inputs, and the control variable of gender were statistically significant and possessed theoretically correct signs. In the production of physiologic fitness exercise, smoking and gender were statistically significant. Exercise and gender were theoretically consistent while smoking was not. Results are compared with previous analyses of health production. ^