Assessing intra- and inter-method agreement of functional data.

Modern medical devices are increasingly producing complex data that could offer deeper insights into physiological mechanisms of underlying diseases. One type of complex data that arises frequently in medical imaging studies is functional data, whose sampling unit is a smooth continuous function. In this work, with the goal of establishing the scientific validity of experiments involving modern medical imaging devices, we focus on the problem of evaluating reliability and reproducibility of multiple functional data that are measured on the same subjects by different methods (i.e. different technologies or raters). Specifically, we develop a series of intraclass correlation coefficient and concordance correlation coefficient indices that can assess intra-method, inter-method, and total (intra + inter) agreement based on multivariate multilevel functional data consisting of replicated functional data measurements produced by each of the different methods. For efficient estimation, the proposed indices are expressed using variance components of a multivariate multilevel functional mixed effect model, which can be smoothly estimated by functional principal component analysis. Extensive simulation studies are performed to assess the finite-sample properties of the estimators. The proposed method is applied to evaluate the reliability and reproducibility of renogram curves produced by a high-tech radionuclide image scan used to non-invasively detect kidney obstruction.

An integrative latent class model of heterogeneous data modalities for diagnosing kidney obstruction.

Radionuclide imaging plays a critical role in the diagnosis and management of kidney obstruction. However, most practicing radiologists in US hospitals have insufficient time and resources to acquire training and experience needed to interpret radionuclide images, leading to increased diagnostic errors. To tackle this problem, Emory University embarked on a study that aims to develop a computer-assisted diagnostic (CAD) tool for kidney obstruction by mining and analyzing patient data comprised of renogram curves, ordinal expert ratings on the obstruction status, pharmacokinetic variables, and demographic information. The major challenges here are the heterogeneity in data modes and the lack of gold standard for determining kidney obstruction. In this article, we develop a statistically principled CAD tool based on an integrative latent class model that leverages heterogeneous data modalities available for each patient to provide accurate prediction of kidney obstruction. Our integrative model consists of three sub-models (multilevel functional latent factor regression model, probit scalar-on-function regression model, and Gaussian mixture model), each of which is tailored to the specific data mode and depends on the unknown obstruction status (latent class). An efficient MCMC algorithm is developed to train the model and predict kidney obstruction with associated uncertainty. Extensive simulations are conducted to evaluate the performance of the proposed method. An application to an Emory renal study demonstrates the usefulness of our model as a CAD tool for kidney obstruction.

A Bayesian multiple imputation approach to bivariate functional data with missing components.

Existing missing data methods for functional data mainly focus on reconstructing missing measurements along a single function-a univariate functional data setting. Motivated by a renal study, we focus on a bivariate functional data setting, where each sampling unit is a collection of two distinct component functions, one of which may be missing. Specifically, we propose a Bayesian multiple imputation approach based on a bivariate functional latent factor model that exploits the joint changing patterns of the component functions to allow accurate and stable imputation of one component given the other. We further extend the framework to address multilevel bivariate functional data with missing components by modeling and exploiting inter-component and intra-subject correlations. We develop a Gibbs sampling algorithm that simultaneously generates multiple imputations of missing component functions and posterior samples of model parameters. For multilevel bivariate functional data, a partially collapsed Gibbs sampler is implemented to improve computational efficiency. Our simulation study demonstrates that our methods outperform other competing methods for imputing missing components of bivariate functional data under various designs and missingness rates. The motivating renal study aims to investigate the distribution and pharmacokinetic properties of baseline and post-furosemide renogram curves that provide further insights into the underlying mechanism of renal obstruction, with post-furosemide renogram curves missing for some subjects. We apply the proposed methods to impute missing post-furosemide renogram curves and obtain more refined insights.

Gamma models for estimating the odds ratio for a skewed biomarker measured in pools and subject to errors.

Measuring a biomarker in pooled samples from multiple cases or controls can lead to cost-effective estimation of a covariate-adjusted odds ratio, particularly for expensive assays. But pooled measurements may be affected by assay-related measurement error (ME) and/or pooling-related processing error (PE), which can induce bias if ignored. Building on recently developed methods for a normal biomarker subject to additive errors, we present two related estimators for a right-skewed biomarker subject to multiplicative errors: one based on logistic regression and the other based on a Gamma discriminant function model. Applied to a reproductive health dataset with a right-skewed cytokine measured in pools of size 1 and 2, both methods suggest no association with spontaneous abortion. The fitted models indicate little ME but fairly severe PE, the latter of which is much too large to ignore. Simulations mimicking these data with a non-unity odds ratio confirm validity of the estimators and illustrate how PE can detract from pooling-related gains in statistical efficiency. These methods address a key issue associated with the homogeneous pools study design and should facilitate valid odds ratio estimation at a lower cost in a wide range of scenarios.

Polybrominated Biphenyl Exposure and Menstrual Cycle Function.

BACKGROUND: Brominated flame retardants, including polybrominated biphenyls (PBB), are persistent compounds reported to affect sex hormones in animals; less is known about potential effects in humans. An industrial accident in 1973-1974 exposed Michigan residents to PBB through contaminated food. We examined whether this exposure to PBB had long-term effects on menstrual cycle function. METHODS: In 2004-2006, we recruited reproductive-aged women in the Michigan PBB Registry who were not pregnant, lactating, or taking hormonal medications. Participants kept daily diaries and provided daily urine samples for up to 6 months. We assayed the urine samples for estrone 3-glucuronide (E13G), pregnanediol 3-glucuronide (Pd3G), and follicle stimulating hormone (FSH). We fit linear mixed models among women aged 35-42 years to describe the relation between serum PBB levels and log-transformed, creatinine-adjusted daily endocrine levels among women who were premenarchal during the exposure incident in 1973-1974 (n = 70). RESULTS: We observed that high (>3.0 parts per billion [ppb]) and medium (>1.0-3.0 ppb) PBB exposure were associated with lower E13G levels across the menstrual cycle and lower FSH levels during the follicular phase, compared with low PBB exposure (≤1.0 ppb). High PBB exposure was also associated with lower Pd3G levels across the cycle compared with low PBB exposure, whereas Pd3G levels were similar in women with medium and low PBB exposure. CONCLUSION: Our results are consistent with a hypothesized effect of exposure to an exogenous estrogen agonist but the modest sample size of the study requires cautious interpretation.

Assessing alignment between functional markers and ordinal outcomes based on broad sense agreement.

Functional markers and their quantitative features (eg, maximum value, time to maximum, area under the curve [AUC], etc) are increasingly being used in clinical studies to diagnose diseases. It is thus of interest to assess the diagnostic utility of functional markers by assessing alignment between their quantitative features and an ordinal gold standard test that reflects the severity of disease. The concept of broad sense agreement (BSA) has recently been introduced for studying the relationship between continuous and ordinal measurements, and provides a promising tool to address such a question. Our strategy is to adopt a general class of summary functionals (SFs), each of which flexibly captures a different quantitative feature of a functional marker, and study its alignment according to an ordinal outcome via BSA. We further illustrate the proposed framework using three special classes of SFs (AUC-type, magnitude-specific, and time-specific) that are widely used in clinical settings. The proposed BSA estimator is proven to be consistent and asymptotically normal given a consistent estimator for the SF. We further provide an inferential framework for comparing a pair of candidate SFs in terms of their importance on the ordinal outcome. Our simulation results demonstrate satisfactory finite-sample performance of the proposed framework. We demonstrate the application of our methods using a renal study.

Overall indices for assessing agreement among multiple raters.

The need to assess agreement exists in various clinical studies where quantifying inter-rater reliability is of great importance. Use of unscaled agreement indices, such as total deviation index and coverage probability (CP), is recommended for two main reasons: (i) they are intuitive in a sense that interpretations are tied to the original measurement unit; (ii) practitioners can readily determine whether the agreement is satisfactory by directly comparing the value of the index to a prespecified tolerable CP or absolute difference. However, the unscaled indices were only defined in the context of comparing two raters or multiple raters that assume homogeneity of variances across raters. In this paper, we introduce a set of overall indices based on the root mean square of pairwise differences that are unscaled and can be used to evaluate agreement among multiple raters that often exhibit heterogeneous measurement processes in practice. Furthermore, we propose another overall agreement index based on the root mean square of pairwise differences that is scaled and extends the concept of the recently proposed relative area under CP curve in the presence of multiple raters. We present the definitions of overall indices and propose inference procedures in which bootstrap methods are used for the estimation of standard errors. We assess the performance of the proposed approach and demonstrate its superiority over the existing methods when raters exhibit heterogeneous measurement processes using simulation studies. Finally, we demonstrate the application of our methods using a renal study.

Logistic regression with a continuous exposure measured in pools and subject to errors.

In a multivariable logistic regression setting where measuring a continuous exposure requires an expensive assay, a design in which the biomarker is measured in pooled samples from multiple subjects can be very cost effective. A logistic regression model for poolwise data is available, but validity requires that the assay yields the precise mean exposure for members of each pool. To account for errors, we assume the assay returns the true mean exposure plus a measurement error (ME) and/or a processing error (PE). We pursue likelihood-based inference for a binary health-related outcome modeled by logistic regression coupled with a normal linear model relating individual-level exposure to covariates and assuming that the ME and PE components are independent and normally distributed regardless of pool size. We compare this approach with a discriminant function-based alternative, and we demonstrate the potential value of incorporating replicates into the study design. Applied to a reproductive health dataset with pools of size 2 along with individual samples and replicates, the model fit with both ME and PE had a lower AIC than a model accounting for ME only. Relative to ignoring errors, this model suggested a somewhat higher (though still nonsignificant) adjusted log-odds ratio associating the cytokine MCP-1 with risk of spontaneous abortion. Simulations modeled after these data confirm validity of the methods, demonstrate how ME and particularly PE can reduce the efficiency advantage of a pooling design, and highlight the value of replicates in improving stability when both errors are present.

A local agreement pattern measure based on hazard functions for survival outcomes.

Assessing agreement is often of interest in biomedical and clinical research when measurements are obtained on the same subjects by different raters or methods. Most classical agreement methods have been focused on global summary statistics, which cannot be used to describe various local agreement patterns. The objective of this work is to study the local agreement pattern between two continuous measurements subject to censoring. In this article, we propose a new agreement measure based on bivariate hazard functions to characterize the local agreement pattern between two correlated survival outcomes. The proposed measure naturally accommodates censored observations, fully captures the dependence structure between bivariate survival times and provides detailed information on how the strength of agreement evolves over time. We develop a nonparametric estimation method for the proposed local agreement pattern measure and study theoretical properties including strong consistency and asymptotical normality. We then evaluate the performance of the estimator through simulation studies and illustrate the method using a prostate cancer data example.

A joint modeling approach for multivariate survival data with random length.

In many biomedical studies that involve correlated data, an outcome is often repeatedly measured for each individual subject along with the number of these measurements, which is also treated as an observed outcome. This type of data has been referred as multivariate random length data by Barnhart and Sampson (1995). A common approach to handling such type of data is to jointly model the multiple measurements and the random length. In previous literature, a key assumption is the multivariate normality for the multiple measurements. Motivated by a reproductive study, we propose a new copula-based joint model which relaxes the normality assumption. Specifically, we adopt the Clayton-Oakes model for multiple measurements with flexible marginal distributions specified as semi-parametric transformation models. The random length is modeled via a generalized linear model. We develop an approximate EM algorithm to derive parameter estimators and standard errors of the estimators are obtained through bootstrapping procedures and the finite-sample performance of the proposed method is investigated using simulation studies. We apply our method to the Mount Sinai Study of Women Office Workers (MSSWOW), where women were prospectively followed for 1 year for studying fertility.

Efficacy and Safety of Glutamine-supplemented Parenteral Nutrition in Surgical ICU Patients: An American Multicenter Randomized Controlled Trial.

OBJECTIVE: To determine whether glutamine (GLN)-supplemented parenteral nutrition (PN) improves clinical outcomes in surgical intensive care unit (SICU) patients. SUMMARY BACKGROUND DATA: GLN requirements may increase with critical illness. GLN-supplemented PN may improve clinical outcomes in SICU patients. METHODS: A parallel-group, multicenter, double-blind, randomized, controlled clinical trial in 150 adults after gastrointestinal, vascular, or cardiac surgery requiring PN and SICU care. Patients were without significant renal or hepatic failure or shock at entry. All received isonitrogenous, isocaloric PN [1.5 g/kg/d amino acids (AAs) and energy at 1.3× estimated basal energy expenditure]. Controls (n = 75) received standard GLN-free PN (STD-PN); the GLN group (n = 75) received PN containing alanyl-GLN dipeptide (0.5 g/kg/d), proportionally replacing AA in PN (GLN-PN). Enteral nutrition (EN) was advanced and PN weaned as indicated. Hospital mortality and infections were primary endpoints. RESULTS: Baseline characteristics, days on study PN and daily macronutrient intakes via PN and EN, were similar between groups. There were 11 hospital deaths (14.7%) in the GLN-PN group and 13 deaths in the STD-PN group (17.3%; difference, -2.6%; 95% confidence interval, -14.6% to 9.3%; P = 0.66). The 6-month cumulative mortality was 31.4% in the GLN-PN group and 29.7% in the STD-PN group (P = 0.88). Incident bloodstream infection rate was 9.6 and 8.4 per 1000 hospital days in the GLN-PN and STD-PN groups, respectively (P = 0.73). Other clinical outcomes and adverse events were similar. CONCLUSIONS: PN supplemented with GLN dipeptide was safe, but did not alter clinical outcomes among SICU patients.

Menses resumption after cancer treatment-induced amenorrhea occurs early or not at all.

OBJECTIVE: To identify factors associated with cancer treatment-induced amenorrhea and time to return of menses. DESIGN: Population-based cohort study. SETTING: Not applicable. PATIENT(S): Female cancer survivors who were diagnosed with cancer between the ages of 20 and 35 and were at least 2 years postdiagnosis at the time of recruitment (median = 7 years; interquartile range, 5-11). INTERVENTION(S): None. MAIN OUTCOME MEASURE(S): Amenorrhea (≥6 months without menses) and resumption of menses. RESULT(S): After excluding women with hysterectomies before cancer diagnosis, 1,043 women were eligible for analysis. Amenorrhea occurred in 31.6% of women. Among women treated with chemotherapy (n = 596), older age at diagnosis (30-35 vs. 20-24 years: adjusted odds ratio [aOR] = 2.37; 95% confidence interval [CI], 1.30, 4.30) and nulligravidity (vs. gravid: aOR = 1.50; 95% CI, 1.02, 2.21) were risk factors for amenorrhea. Among amenorrheic women, menses resumed in most (70.0%), and resumption occurred within 2 years of treatment for 90.0% of women. Survivors of breast cancer were more likely to resume menses at times greater than 1 year compared with lymphoma and pelvic-area cancers. Women diagnosed at older ages, those exposed to chemotherapy, and those exposed to any radiation experienced longer times to return of menses. Women who were older at diagnosis were more likely to have irregular cycles when menses returned. CONCLUSION(S): Treatment-induced amenorrhea is common in cancer survivors, although most women resume menses within 2 years. However, once resumed, older women are more likely to have irregular cycles. Age at diagnosis and pregnancy history affect the risk of amenorrhea.

Semiparametric regression models for a right-skewed outcome subject to pooling.

Pooling specimens prior to performing laboratory assays has various benefits. Pooling can help to reduce cost, preserve irreplaceable specimens, meet minimal volume requirements for certain lab tests, and even reduce information loss when a limit of detection is present. Regardless of the motivation for pooling, appropriate analytical techniques must be applied in order to obtain valid inference from composite specimens. When biomarkers are treated as the outcome in a regression model, techniques applicable to individually measured specimens may not be valid when measurements are taken from pooled specimens, particularly when the biomarker is positive and right skewed. In this paper, we propose a novel semiparametric estimation method based on an adaptation of the quasi-likelihood approach that can be applied to a right-skewed outcome subject to pooling. We use simulation studies to compare this method with an existing estimation technique that provides valid estimates only when pools are formed from specimens with identical predictor values. Simulation results and analysis of a motivating example demonstrate that, when appropriate estimation techniques are applied to strategically formed pools, valid and efficient estimation of the regression coefficients can be achieved.

A highly efficient design strategy for regression with outcome pooling.

The potential for research involving biospecimens can be hindered by the prohibitive cost of performing laboratory assays on individual samples. To mitigate this cost, strategies such as randomly selecting a portion of specimens for analysis or randomly pooling specimens prior to performing laboratory assays may be employed. These techniques, while effective in reducing cost, are often accompanied by a considerable loss of statistical efficiency. We propose a novel pooling strategy based on the k-means clustering algorithm to reduce laboratory costs while maintaining a high level of statistical efficiency when predictor variables are measured on all subjects, but the outcome of interest is assessed in pools. We perform simulations motivated by the BioCycle study to compare this k-means pooling strategy with current pooling and selection techniques under simple and multiple linear regression models. While all of the methods considered produce unbiased estimates and confidence intervals with appropriate coverage, pooling under k-means clustering provides the most precise estimates, closely approximating results from the full data and losing minimal precision as the total number of pools decreases. The benefits of k-means clustering evident in the simulation study are then applied to an analysis of the BioCycle dataset. In conclusion, when the number of lab tests is limited by budget, pooling specimens based on k-means clustering prior to performing lab assays can be an effective way to save money with minimal information loss in a regression setting.

Regression for skewed biomarker outcomes subject to pooling.

Epidemiological studies involving biomarkers are often hindered by prohibitively expensive laboratory tests. Strategically pooling specimens prior to performing these lab assays has been shown to effectively reduce cost with minimal information loss in a logistic regression setting. When the goal is to perform regression with a continuous biomarker as the outcome, regression analysis of pooled specimens may not be straightforward, particularly if the outcome is right-skewed. In such cases, we demonstrate that a slight modification of a standard multiple linear regression model for poolwise data can provide valid and precise coefficient estimates when pools are formed by combining biospecimens from subjects with identical covariate values. When these x-homogeneous pools cannot be formed, we propose a Monte Carlo expectation maximization (MCEM) algorithm to compute maximum likelihood estimates (MLEs). Simulation studies demonstrate that these analytical methods provide essentially unbiased estimates of coefficient parameters as well as their standard errors when appropriate assumptions are met. Furthermore, we show how one can utilize the fully observed covariate data to inform the pooling strategy, yielding a high level of statistical efficiency at a fraction of the total lab cost.

New agreement measures based on survival processes.

The need to assess agreement arises in many scenarios in biomedical sciences when measurements were taken by different methods on the same subjects. When the endpoints are survival outcomes, the study of agreement becomes more challenging given the special characteristics of time-to-event data. In this article, we propose a new framework for assessing agreement based on survival processes that can be viewed as a natural representation of time-to-event outcomes. Our new agreement measure is formulated as the chance-corrected concordance between survival processes. It provides a new perspective for studying the relationship between correlated survival outcomes and offers an appealing interpretation as the agreement between survival times on the absolute distance scale. We provide a multivariate extension of the proposed agreement measure for multiple methods. Furthermore, the new framework enables a natural extension to evaluate time-dependent agreement structure. We develop nonparametric estimation of the proposed new agreement measures. Our estimators are shown to be strongly consistent and asymptotically normal. We evaluate the performance of the proposed estimators through simulation studies and then illustrate the methods using a prostate cancer data example.

Computer-aided diagnosis of renal obstruction: utility of log-linear modeling versus standard ROC and kappa analysis.

BACKGROUND: The accuracy of computer-aided diagnosis (CAD) software is best evaluated by comparison to a gold standard which represents the true status of disease. In many settings, however, knowledge of the true status of disease is not possible and accuracy is evaluated against the interpretations of an expert panel. Common statistical approaches to evaluate accuracy include receiver operating characteristic (ROC) and kappa analysis but both of these methods have significant limitations and cannot answer the question of equivalence: Is the CAD performance equivalent to that of an expert? The goal of this study is to show the strength of log-linear analysis over standard ROC and kappa statistics in evaluating the accuracy of computer-aided diagnosis of renal obstruction compared to the diagnosis provided by expert readers. METHODS: Log-linear modeling was utilized to analyze a previously published database that used ROC and kappa statistics to compare diuresis renography scan interpretations (non-obstructed, equivocal, or obstructed) generated by a renal expert system (RENEX) in 185 kidneys (95 patients) with the independent and consensus scan interpretations of three experts who were blinded to clinical information and prospectively and independently graded each kidney as obstructed, equivocal, or non-obstructed. RESULTS: Log-linear modeling showed that RENEX and the expert consensus had beyond-chance agreement in both non-obstructed and obstructed readings (both p < 0.0001). Moreover, pairwise agreement between experts and pairwise agreement between each expert and RENEX were not significantly different (p = 0.41, 0.95, 0.81 for the non-obstructed, equivocal, and obstructed categories, respectively). Similarly, the three-way agreement of the three experts and three-way agreement of two experts and RENEX was not significantly different for non-obstructed (p = 0.79) and obstructed (p = 0.49) categories. CONCLUSION: Log-linear modeling showed that RENEX was equivalent to any expert in rating kidneys, particularly in the obstructed and non-obstructed categories. This conclusion, which could not be derived from the original ROC and kappa analysis, emphasizes and illustrates the role and importance of log-linear modeling in the absence of a gold standard. The log-linear analysis also provides additional evidence that RENEX has the potential to assist in the interpretation of diuresis renography studies.

A longitudinal Model for repeated interval-observed data with informative dropouts.

We consider repeated measures interval-observed data with informative dropouts. We model the repeated outcomes via an unobserved random intercept and it is assumed that the probability of dropout during the study period is linearly related to the random intercept in a complementary log-log scale. Assuming the random effect follows the power variance function (PVF) family suggested by Hougaard (2000), we derive the marginal likelihood in a closed form. We evaluate the performance of the maximum likelihood estimation via simulation studies and apply the proposed method to a real data set.

Clustering Based on Periodicity in High-Throughput Time Course Data.

Nuclear magnetic resonance (NMR) spectroscopy, traditionally used in analytical chemistry, has recently been introduced to studies of metabolite composition of biological fluids and tissues. Metabolite levels change over time, and providing a tool for better extraction of NMR peaks exhibiting periodic behavior is of interest. We propose a method in which NMR peaks are clustered based on periodic behavior. Periodic regression is used to obtain estimates of the parameter corresponding to period for individual NMR peaks. A mixture model is then used to develop clusters of peaks, taking into account the variability of the regression parameter estimates. Methods are applied to NMR data collected from human blood plasma over a 24-hour period. Simulation studies show that the extra variance component due to the estimation of the parameter estimate should be accounted for in the clustering procedure.