A Monte Carlo method for comparing generalized estimating equations to conventional statistical techniques for discounting data.

Myers & Broyles (2000a, 2000b) illustrate that regression coefficient analysis (RCA) is a viable alternative to a generalized estimating equation (GEE) in the analysis of correlated binomial data. Since the regression coefficients (b i ' s ) may have different precisions, we modify RCA by weighting b i ' s by the inverses of their variances for statistical optimality. We perform the simulation study to evaluate the performance of RCA, modified RCA and GEE in terms of empirical type I errors and empirical powers of the regression coefficients in repeated binary measurement designs with and without dropouts. Two thousand data sets are generated using autoregressive (AR(1)) and compound symmetry (CS) correlation structures. We compare the type I errors and powers of RCA, modified RCA and GEE for the analysis of repeated binary measurement data as affected by different dropout mechanisms such as random dropouts and treatment dependent dropouts.

Liang과 Zeger는 이산형 혹은 연속형 반복측정자료를 분석하기 위한 일반화 추정방정식 (GEE)을 제안하였다 GEE모형은 범주형 반복측정자료의 모형으로 확장될 수 있으며, 이 GEE추정량은 대표본인 경우 다변량 정규분포를 따른다. 그러나 GEE는 대표본근사이론에 기초한다. 본 논문에서는 소표본인 경우 반복 측정된 순서자료에 대한 GEE추정량의 성질을 연구한다. 우리는 두가지 방법을 사용하여 두그룹의 반복 측정된 순서자료를 생성하며 모의실험을 통하여 소표본인 경우 여러 개 범주를 갖는 순서반응 자료에 대하여 GEE추정량의 1종 오류율, 검정력, 상대효율, 두 그룹의 표본크기가 다를 경우 효과, 그리고 분산 추정량의 성질등을 연구한다. Liang and Zeger proposed generalized estimating equations(GEE) for analyzing repeated data which is discrete or continuous. GEE model can be extended to model for repeated categorical data and its estimator has asymptotic multivariate normal distribution in large sample sizes. But GEE is based on large sample asymptotic theory. In this paper, we study the properties of GEE estimators for repeated ordinal data in small sample sizes. We generate ordinal repeated measurements for two groups using two methods. Through Monte Carlo simulation studies we investigate the empirical type 1 error rates, powers, relative efficiencies of the GEE estimators, the effect of unequal sample size of two groups, and the performance of variance estimators for polytomous ordinal response variables, especially in small sample sizes.

The development of adequate models for binary time series data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz, Laird and Harrington (1991) and Liang, Zeger and Qaqish (1992)) and likelihood (see for example Fitzmaurice and Laird (1993) and Molenberghs and Lesaffre (1994)) based methods have been proposed. The number of parameters required for the full specification of these models grows exponentially with the length of the binary time series. Therefore, the analysis is often focused on marginal and first order parameters. In this case, the multivariate probit model (Ashford and Sowden (1970)) becomes an attractive alternative to the above models. The application of the multivariate probit model has been hampered by the intractability of the maximum likelihood estimator, when the length of the binary time series is large. This paper shows that this difficulty can be overcome by the use of Markov Chain Monte Carlo methods. This analysis also allows for valid point and interval estimates of the parameters in small samples. In addition, the analysis is adopted to handle the case of missing at random responses. The approach is illustrated on data involving binary responses measured at unequally spaced time points. Finally, this data analysis is compared to a GEE analysis given in Fitzmaurice and Lipsitz (1995).

Which methodological approaches are most appropriate for analyzing IVF data with multiple cycles in the context of a binary outcome? Both mixed effect models and generalized estimating equation (GEE) modeling approaches can account for multiple IVF cycles and may reduce bias over first-cycle only approaches, but CIs were narrowest with cluster-weighted generalized estimating equation models (CWGEE). There is a lack of consensus among investigators regarding how to best incorporate data from multiple cycles and whether to present odds or risks in the analysis of IVF data. Failure to account for correlated outcomes within individuals and informative cluster size may lead to invalid CIs and biased estimates. The Environment and Reproductive Health (EARTH) Study is an ongoing prospective cohort study of subfertile couples conducted at an academic medical center. This cohort was established in 2004 and follows couples seeking treatment for infertility throughout the course of their treatment and pregnancy. Women aged 18-46 years enrolled in the EARTH Study from 2004 to 2017 who initiated at least one IVF cycle were eligible. Cycle initiation was defined as beginning ovulation induction with the intent to progress through an IVF or ICSI cycle. This analysis included 442 women undergoing 642 cycles who met the study inclusion criteria. We compared the results and interpretations of log-binomial and logistic models restricting to the first cycle, as well as mixed effects models, unweighted GEE models, and CWGEE models including all cycles. This analysis was conducted for two distinct exposures: maternal age at cycle initiation, and maternal preconception urinary concentrations of di(2-ethylhexyl) phthalate (DEHP) metabolites (previously reported to be associated with a decreased probability of live birth). In general, the CIs were widest for mixed effects models and narrowest for CWGEE models. Further, in models evaluating the sum of urinary concentrations of DEHP metabolites (∑DEHP, available for 91% of women), the point estimates were surprisingly different between the first-cycle and multiple-cycle models. We observed significant associations between maternal age and live birth in all models. However, we observed no associations between ∑DEHP and live birth. This analysis was limited to an example dataset in which the true effect of any exposure is unknown. While this allows us to observe model performance in the context of real data, future analyses should be conducted within simulated datasets under various assumptions to further evaluate the appropriateness of each approach. In addition, we did not address differential loss to follow-up in our statistical approaches. The use of CWGEE models should be more widely considered in the analysis of IVF data with multiple cycles per woman. The CWGEE approach is computationally simple, addresses non-ignorable (informative) cluster size, and is robust against mis-specification of the underlying covariance structure. Among the methods compared in this analysis, CWGEE models generally yielded the narrowest CIs, possibly indicating the most precise estimates. We also stress the importance of estimating risks rather than odds in the analysis of IVF data. The project was funded by Grants (R01ES022955, R01ES009718, and P30ES000002) from the National Institutes of Health. None of the authors has any conflicts of interest to declare.

In schizophrenia research, little attention yet has been directed on methods for analyzing data from studies with repeated measurements over time. Motivation for this research stems from a project within the German Research Network on Schizophrenia, in which an algorithm is developed to guide prodrome-based early intervention strategies in stable first episode patients. We present two different approaches for the analysis of correlated response data, the Generalized Estimating Equations (GEE) method and the Artificial Neural Network (ANN) approach. We illustrate the methods using the data of the A.N.I. study, which is one of the largest German multicenter treatment studies in regard to the long-term treatment of schizophrenia conducted between 1983 and 1989. The results of statistical model selection prior to GEE analysis and various data presentation methods for ANNs are presented. The primary goal of our evaluation is to investigate if the defined prodromes are valid predictors for relapse. Additionally, it is shown that both methods are applicable on a realistic data set. It is concluded that both methods are suitable for predictor analysis especially since all variable time points of the patients are included instead of only selected, so that it can be assumed that results are not biased. With the GEE method a test of association for each predictor can be performed whereas with ANNs a general proposition can be made for prodromes depending on the type of data presentation. Using the A.N.I. data the prodrome 'trouble sleeping' seems to be the most informative predictor. Finally, the important differences of the two methods are discussed.

Logical character dependency is a major conceptual and methodological problem in phylogenetic inference of morphological data sets, as it violates the assumption of character independence that is common to all phylogenetic methods. It is more frequently observed in higher-level phylogenies or in data sets characterizing major evolutionary transitions, as these represent parts of the tree of life where (primary) anatomical characters either originate or disappear entirely. As a result, secondary traits related to these primary characters become "inapplicable" across all sampled taxa in which that character is absent. Various solutions have been explored over the last three decades to handle character dependency, such as alternative character coding schemes and, more recently, new algorithmic implementations. However, the accuracy of the proposed solutions, or the impact of character dependency across distinct optimality criteria, has never been directly tested using standard performance measures. Here, we utilize simple and complex simulated morphological data sets analyzed under different maximum parsimony optimization procedures and Bayesian inference to test the accuracy of various coding and algorithmic solutions to character dependency. This is complemented by empirical analyses using a recoded data set on palaeognathid birds. We find that in small, simulated data sets, absent coding performs better than other popular coding strategies available (contingent and multistate), whereas in more complex simulations (larger data sets controlled for different tree structure and character distribution models) contingent coding is favored more frequently. Under contingent coding, a recently proposed weighting algorithm produces the most accurate results for maximum parsimony. However, Bayesian inference outperforms all parsimony-based solutions to handle character dependency due to fundamental differences in their optimization procedures-a simple alternative that has been long overlooked. Yet, we show that the more primary characters bearing secondary (dependent) traits there are in a data set, the harder it is to estimate the true phylogenetic tree, regardless of the optimality criterion, owing to a considerable expansion of the tree parameter space. [Bayesian inference, character dependency, character coding, distance metrics, morphological phylogenetics, maximum parsimony, performance, phylogenetic accuracy.].

Two-way satellite time and frequency transfer (TWSTFT) data are typically recorded on Monday, Wednesday and Friday. This produces an unevenly spaced time series on which it is difficult to perform an accurate two-sample variance analysis. We have investigated the effect of uneven data spacing on the computation of σx(τ) [1-2]. Evenly spaced simulated data sets were generated for noise processes ranging from white phase modulation to random walk frequency modulation. σx(τ) was then calculated for each noise type. Data were subsequently removed from each simulated data set to create two unevenly spaced sets with average intervals of 2,8 and 3,6 days. These sparse sets correspond to typical TWSTFT data patterns. σx(τ) was then calculated for each sparse data set using two different approaches. First, the missing data points were replaced by linear interpolation and σx(τ) calculated from this now full data set. The second approach ignored the fact that the data were unevenly spaced and calculated σx(τ) as if the data were equally spaced with average spacing of 2,8 or 3,6 days. The impact of uneven data spacing on the results of these two approaches is significant and is discussed. Finally, techniques are presented for correcting errors caused by uneven data spacing in simulated TWSTFT data sets, and the appropriate technique is applied to a real data set.

In support of Phase A work on the proposed Hyperspectral Environment and Resource Observer (HERO) mission, the sensitivity of chlorophyll concentrations derived from vegetation red-edge analysis to a spectrally dependent error in the radiometric calibration of the hyperspectral data is investigated. A typical ground-based reflectance spectrum taken from a boreal forest Aspen leaf is converted to top-of-atmosphere (TOA) radiance using the MODTRAN atmospheric correction model as implemented in the Imaging Spectrometer Data Analysis System (ISDAS). The resulting spectrum is then subjected to a randomly generated Spectral Gain Error (SGE). This process is repeated a statistically significant number of times to produce a simulated data set. By varying the magnitude of the SGE, several simulated data sets are produced representing different levels of relative calibration accuracies in the spectral domain. The simulated TOA data sets are then converted back to ground-based reflectance, once again using MODTRAN. For each pixel in the resulting data sets, red-edge parameters are determine using an Inverted Gaussian (IG) technique (red-edge inflection point - lambdap, reflectance minimum - lambdao, and sigma = lambdap-lambdao) as well as a couple of commonly applied Vegetation Indices (R740/R720 and R710/R760)- Each of these parameters results in a distribution of results, the width of which is dependent on the magnitude of the SGE applied to the data set providing the relationship between the parameters and the SGE. In order to tie these results to chlorophyll concentration levels, the PROSPECT Vegetation Model is used to invert the original spectrum. The sensitivity of each of the indices to the chlorophyll concentration is determined by varying its value in the PROSPECT model while holding the other three model parameters constant. Using these relationships, the sensitivity of the chlorophyll concentrations to the SGE is determined. A specification of the acceptable error in the chlorophyll concentration levels would then dictate the required level of accuracy in the spectral gain calibration. The relationship between the SGE and the chlorophyll concentration retrieval based upon any of the five investigated red-edge parameters is shown to be directly proportional.

The majority of anomaly detection processes used for hyperspectral image data are based on pixel-by-pixel whitening and thresholding operations using local area statistics. This paper discusses an alternative approach to anomaly detection in which a mixture model is fitted to the whole of the image. This mixture model may be used to segment the image into component memberships and these may, in turn, be used for anomaly detection. In this study the mixture model is generated for the whole scene using the stochastic expectation maximization (SEM) algorithm. This is parameterized such that mixture components consisting of small numbers of pixels are eliminated. The maximum a-posteriori probability (MAP) mixture component for each pixel is then determined. The pixel may then be examined using a conventional statistical hypothesis test to see whether it is plausible that it was drawn from the distribution of the identified component, at a given significance level. This anomaly detection process has been examined using both synthetic and real hyperspectral imagery and results are presented here for real data containing no known military targets and for synthesized imagery which includes military target pixels. A range of results is presented for different parameterizations of the SEM algorithm and significance test. These results include the component map of the imagery and anomalous pixel maps at given significance levels.

Periodontal data typically have a hierarchical structure, with sites grouped within individuals, and individuals grouped within communities. Also, the occasion may be regarded as another level since the acquired knowledge indicates that periodontal disease activity may vary over time. Conventional statistical tests are based on unilevel analysis of data. However, this approach to statistical analysis is often inconvenient in periodontal research because of the variation in the outcome variables between the various levels in the hierarchy. Lately there have been important developments in the statistical theory which have made available powerful statistical techniques for analyzing multilevel or hierarchical data. This report describes a new approach for analyzing periodontal data and uses an illustrative example to build a model which explains part of the variability in the response variable. The results from this analysis are then compared to results from an earlier report which uses unilevel methods and the findings discussed. The present multilevel approach has several advantages over unilevel methods, mainly due to its statistical validity and efficiency. Further, it permits the incorporation of explanatory variables measured at the site and the subject levels, and those which vary across the time points. Multilevel analyses have a promising potential and are expected to have a significant impact on periodontal research.

BackgroundWhile treatment satisfaction has been associated with better outcomes in substance abuse treatment, there is an obvious need for a more profound understanding of what predicts client’s satisfaction with treatment. This study elucidates factors relevant to treatment outcome measured at follow-up in terms of satisfaction with the treatment received.MethodsThe research was implemented as a multisite study in outpatient clinics (N = 7) in southern and western Finland. Data consists of therapists (N = 33) and their clients (N = 327). Each consenting client beginning a treatment period was accepted as a research subject and all therapists at the clinics in question participated. The study was conducted as part of the clinic’s normal activity. Clients were allocated to therapists according to a randomization list drawn up in advance. Apart from the randomisation and the completion of questionnaires, it did not interfere with the progress of treatment. Follow-up lasted 6 months. Multiple Classification Analysis (MCA) was used through combinations of variables organized by content, e.g. client demographics, previous substance use, therapist’s characteristics and client’s expectations. The analyses were based in part on conventional statistical testing (t -test, χ2-test, ANOVA).ResultsAmong 37 independent variables few were statistically significant in the final model. The results suggest that high treatment expectations at baseline are a strong predictor of satisfaction at follow-up. Also, previous substance use predicted treatment satisfaction; people using multiple substances were less satisfied than those taking only one substance. Stronger predictors reduced the statistical significance of those independent variables that were statistically significant in the first analyses. Therefore, therapist’s role in recovery and readiness to change should be also seen as antecedents to treatment satisfaction.ConclusionsIt seems that treatment expectations are fulfilled among those participating in follow-up. Yet many are lost during treatment and by follow-up. Service users have experiential knowledge that differs from professionals’ and policymakers’ knowledge. It is clinically relevant to understand what factors affect client’s satisfaction. Hence, it is possible to identify the population whose treatment should receive the most attention, how the client’s experience, their commitment to treatment, and treatment effectiveness could be improved.

Recently a number of modeling techniques have been developed for data mining and machine learning in relational and network domains where the instances are not independent and identically distributed (i.i.d.). These methods specifically exploit the statistical dependencies among instances in order to improve classification accuracy. However, there has been little focus on how these same dependencies affect our ability to draw accurate conclusions about the performance of the models. More specifically, the complex link structure and attribute dependencies in network data violate the assumptions of many conventional statistical tests and make it difficult to use these tests to assess the models in an unbiased manner. In this work, we examine the task of within-network classification and the question of whether two algorithms will learn models which will result in significantly different levels of performance. We show that the commonly-used form of evaluation (paired t-test on overlapping network samples) can result in an unacceptable level of Type I error. Furthermore we show that Type I error increases as (1) the correlation among instances increases and (2) the size of the evaluation set increases (i.e., the proportion of labeled nodes in the network decreases). We propose a method for network cross-validation that combined with paired t-tests produces more acceptable levels of Type I error while still providing reasonable levels of statistical power (i.e., Type II error).

Technology is defined as recognisable and relatively consistent patterns of getting work done situated in specific contexts and undertaken for defined purposes. A fable of technology development and transfer is presented, to set the stage for the need to be specific about what technology and transfer mean as a precondition for measuring it. This fable illustrates how the different perspectives of science, commercialisation, and political policy can clash over a single technology. A different approach is required to measure the value of technology compared to the techniques used for its development. Value and understanding are inferences about technology. Tools that are sensitive to context are offered for measuring technology. Additional tools are explored that include purpose as part of the definition of technology. These approaches go beyond metrics based on means and standard deviations and conventional statistical tests. They also have the effect of pushing the concepts of technology development and transfer closer together.

ABSTRACTHarmonizing osteoporosis‐related data across multiple data sets is essential for improving the accuracy and generalizability of bone mineral density (BMD) assessments. This study developed a harmonization framework to standardize phenotypic and genomic variables across three major US osteoporosis data sets: GDBF, GWAS, and NHANES. We standardized key phenotypic variables (BMD, body mass index (BMI), age, sex, and race/ethnicity) using cohort‐specific data dictionaries and applied multiple imputations by chained equations (MICEs) to manage missing data. Genomic data were harmonized using principal component analysis (PCA)‐based batch effect corrections. Residual regression methods were applied to standardize BMD values. The effectiveness of harmonization on BMD prediction was evaluated using generalized estimating equations (GEEs) and mixed‐effects models. Post‐harmonization, inter‐study variability in BMI was significantly reduced (Ω2 = 0.0028), and BMD associations with covariates remained consistent across data sets. Harmonized models showed improved predictive performance, with explained variance in BMD increasing (R2 = 0.14%). PCA confirmed the effective alignment of genetic data, reducing batch effects and improving cross‐study compatibility. This study demonstrates the feasibility and effectiveness of harmonizing phenotypic and genomic data for osteoporosis research. The harmonization framework enhances BMD prediction accuracy, supports more inclusive osteoporosis risk assessment, and improves the integration of multi‐cohort data sets for future research. These findings highlight the potential of data harmonization in advancing precision medicine for osteoporosis prevention and management.

BackgroundHealth recommender systems show promise in delivering remote support and improving coping among family caregivers of persons with dementia.ObjectiveTo evaluate the effectiveness of a mobile-based intelligent recommender system for dementia care (DCIRS) in enhancing psychological well-being among family caregivers and to explore the mechanisms underlying its effects.MethodsData from a randomized controlled trial (RCT) were used. Of the 250 eligible participants, 125 caregivers were randomly allocated to the intervention group (receiving DCIRS) and 125 to the waitlist control group. Outcomes, including benefit finding, depressive symptoms, self-efficacy, and coping styles, were assessed at baseline (T0), 6 weeks (T1), and 12 weeks (T2). Generalized estimating equations (GEE) was used to evaluate changes over time and between-group differences, while path analysis examined mediation pathways.ResultsAt 12 weeks, the intervention group showed significant within-group improvements in coping, self-efficacy, and benefit finding (all p < 0.05 for group × time interaction). Between-group analyses revealed greater reductions in depressive symptoms at T1 and T2, though the group × time interaction was non-significant (p = 0.393). Path analysis indicated that reduced depressive symptoms were mediated primarily by increased self-efficacy.ConclusionsThis DCIRS demonstrated the potential to reduce depressive symptoms and enhance benefit finding in caregivers of people with dementia. Strengthening self-efficacy and active coping styles should remain a core focus in digital health interventions, providing meaningful guidance to healthcare professionals in developing caregiver support program.