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PubMed1993

Estimating incidence and diagnostic error rates for bivariate progressive processes.

Estimating the times until incidences of bivariate progressive processes that are categorical is a common problem in ophthalmology, audiology, pulmonary medicine, and other fields of medical research. We consider study designs in which diagnoses of subject's bivariate status are performed repeatedly across time and when diagnosis is subject to error. In such situations, error confounds the interpretation of the time until an event. A composite model is proposed for parameterizing both the incidence and error distributions, which allows for correlation between sites with respect to both incidence and diagnostic error. An EM algorithm is described for this model, which allows categorical covariates for both incidence and error. The methodology is applied to two examples. The first represents a situation in which bivariate incidence and error can reasonably be assumed symmetric: prospective data concerning the development of ocular lens opacities in a large pharmaceutical clinical trial. The second example represents a situation in which bivariate incidence and error may not be symmetric: clinical evaluations of sexual maturation status with respect to two different anatomical indices in the Cooperative Study of Sickle Cell Disease. The methodology described in this paper is used, in each case, to estimate incidence, characterize error rates, and assess bivariate correlations.

Adolescent↗

PubMed1993

Analysis of infectious disease data from partner studies with unknown source of infection.

Partner studies are useful for estimating the transmission probabilities of infectious diseases. However, it is often not known which partner was the source of the infection (the index case). The objective of this paper is to develop statistical methods for analyzing partner studies when it is uncertain which partners acquired the infection from sources outside the partnership. The approach involves simultaneously modelling the probability of acquisition of infection from outside the partnership, and the probability of transmission within the partnership as a function of covariates. An EM algorithm is presented. Efficiency and simulation results are given in some special situations involving heterosexual transmission studies. In heterosexual partner studies, the methods depend crucially on the availability of a covariate that provides information about which partner was the likely source of infection.

Algorithms↗

PubMed1996

Fitting a multiplicative incidence model to age- and time-specific prevalence data.

We discuss the assessment of age- and time-specific disease incidence using prevalence data. A method is described for conveniently fitting a discrete-time multiplicative model, subject to positivity constraints, using the EM-algorithm. Together with smoothing, it allows essentially nonparametric assessment of incidence trends. The method is illustrated using previously analyzed data on toxoplasmosis.

Adolescent↗

PubMed1996

[Assessment of pharmacokinetic parameters of amikacin in a group of neutropenic patients in onco-hematology].

The pharmacokinetics of Amikacin were studied in 56 febrile episodes for 45 patients with severe neutropenia while using the USC*Pack PC Clinical Programs for adaptive control of their dosage regimens [223 drug levels]. The purpose of this study are: i] to estimate the pharmacokinetic parameters in this neutropenic population [56 episodes, I], ii] to evaluate the effect of the dosage regimen: once-a-day [22 episodes, II] versus bid or tid [34 episodes, III]. Patients [mean age 53.3 +/- 17.9], 23 men and 22 women, received amikacin [17.7 +/- 3.6 mg/kg/d at day 1] in a 30 minutes infusion. The mean estimated creatinine clearance [CCr] was 76 +/- 22.5 ml/min/1.73 m2 at day 1. The method used for the population modeling was the Non Parametric EM algorithm [NPEM2] which computes the complete probability density function for a 1 or a 2 compartment model. The parametrizations studied are: Clearance/Volume [CL/VOL], Elimination rate constant/Volume [Kel/VOL] and KS/VS with Kel = KS * CCr + 0.00693, VS = VOL/Weight for a 1 compartment pharmacokinetic model. The main results concerned CL and VS with: CL[I] = 4.94 +/- 2.71, CL[II] = 4.74 +/- 2.65, CL[III] = 5.14 +/- 2.75 l/h and VS[I] = 0.31 +/- 0.11, VS[II] = 0.34 +/- 0.10, VS[III] = 0.30 +/- 0.11 l/kg. Volume of distribution VS is not so large as expected and a slight difference appears between II and III. The pharmacokinetic parameters obtained for this population of neutropenic patients will be used thereafter for the daily adaptive control of Amikacine therapy in our haematologic/oncologic patients. The variability observed remains important and requires an individualization of the dosage regimen for each patient.

Adult↗

PubMed1996

Parameter estimation from incomplete data in binomial regression when the missing data mechanism is nonignorable.

We propose a method for estimating parameters in binomial regression models when the response variable is missing and the missing data mechanism is nonignorable. We assume throughout that the covariates are fully observed. Using a logit model for the missing data mechanism, we show how parameter estimation can be accomplished using the EM algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). An example from the Six Cities Study (Ware et al., 1984, American Review of Respiratory Diseases 129, 366-374) is presented to illustrate the method.

Air Pollution↗

PubMed1996

A competing risks analysis of presenting AIDS diagnoses trends.

The proportions of gay men presenting with various AIDS diagnoses display temporal trends. In particular, the proportion of initial diagnoses reported as Kaposi's sarcoma (KS) has declined over time. Epidemiologists have hypothesized that (a) KS may require a cofactor, whose prevalence has declined over time, or (b) KS may have a shorter incubation period than other presenting diagnoses. We examine whether this latter hypothesis, considered in a competing risks framework, could account for the observed decline in KS. We nonparametrically estimate the relevant cause-specific hazard functions from the doubly-censored data of the San Francisco City Clinic Cohort by maximizing a roughness penalized likelihood using an EM algorithm. These estimates suggest that differences in the underlying cause-specific hazard functions account for a substantial portion of the observed diagnoses trends.

Acquired Immunodeficiency Syndrome↗

PubMed1997

Semiparametric estimation of major gene and family-specific random effects for age of onset.

Analysis of familial diseases with variable age of onset is a common problem in human genetics. Most existing methods make some parametric distributional assumption on age of onset, and few methods have been designed with the goal of testing the hypothesis of a Mendelian gene against other hypotheses of familial dependence. We introduce the Cox model with major genetic and random familial effects to model age-of-onset dependence patterns among family members and to incorporate family heterogeneity. This model allows testing for and estimating major gene effects in the presence of residual correlations. Generalized maximum likelihood estimation using a Monte Carlo EM algorithm is used for parameter estimation. The methods are illustrated by a simulated data set and a data set from a case-control family study of breast cancer.

Adult↗

PubMed1997

Expectation maximization reconstruction of positron emission tomography images using anatomical magnetic resonance information.

Using statistical methods the reconstruction of positron emission tomography (PET) images can be improved by high-resolution anatomical information obtained from magnetic resonance (MR) images. We implemented two approaches that utilize MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the expectation maximization (EM)-type algorithm with a maximum a posteriori (MAP) estimator is derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighboring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. A basic assumption of these methods is that the radioactivity is homogeneously distributed inside anatomical regions. Simulated and phantom data are investigated under the following aspects: count density, object size, missing anatomical information, and misregistration of the anatomical information. Compared with the maximum likelihood-expectation maximization (ML-EM) algorithm the results of both algorithms show a large reduction of noise with a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction (up to 50%). Regarding incorrect a priori information the Gauss-EM algorithm is very sensitive, whereas the Markov-GEM algorithm proved to be stable with a small change of recovery coefficients between 0.5 and 3%.

Algorithms↗

PubMed1995

An analytical approach for compensation of non-uniform attenuation in cardiac SPECT imaging.

Photon attenuation can reduce the diagnostic accuracy of cardiac SPECT imaging. Bellini et al have previously derived a mathematically exact method to compensate for attenuation in a uniform attenuator. Since the human thorax contains structures with differing attenuation properties, non-uniform attenuation compensation is required in cardiac SPECT. Given an estimate of the patient attenuation map, we show that the Bellini attenuation compensation method can be used in cardiac SPECT to provide a quantitatively accurate reconstruction of a central region in the image which includes the heart and surrounding soft tissue. Simulations using a mathematical cardiac-torso phantom were conducted to evaluate the Bellini method and to compare its performance to the ML-EM iterative algorithm, and to 180 degrees and 360 degrees filtered backprojection (FBP) with no attenuation compensation. 'Bulls-eye' polar maps and circumferential profiles showed that both the Bellini method and the ML-EM algorithm provided quantitatively accurate reconstructions of the myocardium, with a substantial reduction in attenuation-induced artifacts that were observed in the FBP images. The computational load required to implement the Bellini method is approximately equivalent to that required for one iteration of the ML-EM algorithm, thus it is suitable for routine clinical use.

Algorithms↗

PubMed1991

Quantitative SPECT reconstruction of iodine-123 data.

Many clinical and research studies in nuclear medicine require quantitation of iodine-123 (123I) distribution for the determination of kinetics or localization. The objective of this study was to implement several reconstruction methods designed for single-photon emission computed tomography (SPECT) using 123I and to evaluate their performance in terms of quantitative accuracy, image artifacts, and noise. The methods consisted of four attenuation and scatter compensation schemes incorporated into both the filtered backprojection/Chang (FBP) and maximum likelihood-expectation maximization (ML-EM) reconstruction algorithms. The methods were evaluated on data acquired of a phantom containing a hot sphere of 123I activity in a lower level background 123I distribution and nonuniform density media. For both reconstruction algorithms, nonuniform attenuation compensation combined with either scatter subtraction or Metz filtering produced images that were quantitatively accurate to within 15% of the true value. The ML-EM algorithm demonstrated quantitative accuracy comparable to FBP and smaller relative noise magnitude for all compensation schemes.

Humans↗

PubMed1989

Estimation of parameters and missing values under a regression model with non-normally distributed and non-randomly incomplete data.

We carried out a simulation study to compare the performance of three algorithms (complete cases, ALLVALUE, and expectation maximization, EM) in estimating regression parameters and missing values for situations that have varying amounts of missing data, distributions (normal, mixture of normals and lognormal), patterns of incomplete data (random, related and censored), and degrees of correlational structure among the dependent and independent variables. We found that the EM and complete cases algorithms performed equally well regardless of the correlational structure, when the percentage of incomplete data was only 5 per cent. When this percentage increased to 25 per cent, the EM algorithm was generally best for estimation, but the complete cases algorithm was safe and conservative. This finding may be attributed to the study design, which required that the slopes be the same in the population of all cases, and in the population of complete cases. In addition, the one-step imputing method (ALLVALUE) was competitive only for situations with weak correlational structure and/or little missing data. In that situation the bias caused with use of all available information was less than that caused with use of only complete cases. On the other hand, for imputation, the EM algorithm performed optimally, even in situations of censored or log-normally distributed data.

Algorithms↗

PubMed1996

A non-negative fast multiplicative algorithm in 3D scatter-compensated SPET reconstruction.

Single-photon emission tomographic (SPET) reconstruction can be improved, especially for noisy images, by using the iterative expectation-maximization of the maximum-likelihood (EM-ML) algorithm. Its application to clinical routine is, however, hampered by the high number of iterations necessary to achieve acceptable results. Therefore various methods have been developed to accelerate the EM-ML algorithm. In this paper a new accelerated EM-ML-like multiplicative algorithm is proposed for SPET reconstruction. Contrary to some other accelerating methods, it preserves two of the most important properties of the EM-ML, namely pixel positivity inside the patient body and null activity outside. The convergence speed is improved by a factor which can reach 100 in high spatial frequency or low count regions. Good estimates in the low count region are obtained without any smoothing, even at typical routine clinical count rates. The algorithm used in conjunction with the 3D effective one scatter path model provides high-quality SPET images and accurate quantitation.

Adult↗

PubMed1997

A focus-of-attention preprocessing scheme for EM-ML PET reconstruction.

The expectation-maximization maximum-likelihood (EM-ML) algorithm belongs to a family of algorithms that compute positron emission tomography (PET) reconstructions by iteratively solving a large linear system of equations. We describe a preprocessing scheme for automatically focusing the attention, and thus the computational resources, on a subset of the equations and unknowns. Experimental work with a CM-5 parallel computer implementation using a simulated phantom as well as real data obtained from an ECAT 921 PET scanner indicates that quite significant savings can be obtained with respect to both time and space requirements of the EM-ML algorithm without compromising the quality of the reconstructed images.

Abdomen↗

PubMed1995

A two-step iterative algorithm for estimation in nonlinear mixed-effect models with an evaluation in population pharmacokinetics.

This article proposes an EM-like algorithm for estimating, by maximum likelihood, the population parameters of a nonlinear mixed-effect model given sparse individual data. The first step involves Bayesian estimation of the individual parameters. During the second step, population parameters are estimated using a linearization about those Bayesian estimates. This algorithm (implemented in P-PHARM) is evaluated on simulated data, mimicking pharmacokinetic analyses and compared to the First-Order method and the First-Order Conditional Estimates method (both implemented in NONMEM). The accuracy of the results, within few iterations, shows the estimation capabilities of the proposed approach.

Algorithms↗

PubMed2026

A flexible framework for robust and efficient Mendelian randomization with debiasing.

Mendelian randomization (MR) has been widely used to infer causal relationships between exposures and outcomes in epidemiological studies. However, classical MR assumptions can be violated when genetic variants are associated with outcomes through pathways other than the exposure, leading to uncorrelated and/or correlated pleiotropy. Additionally, measurement error arising from the inherent uncertainty in summary statistics obtained from large-scale genome-wide association studies can introduce bias into the causal effect estimate. To address these issues, we develop a debiased mixture inverse variance weighting ($\mathsf{dmIVW}$) method with three major advantages. First, it is capable of simultaneously handling various types of pleiotropy and eliminating the bias caused by uncertainty. Second, it can guard against distortion caused by invalid genetic variants while effectively harnessing their information. Third, our unified framework facilitates a fair comparison and combination of a series of submodels, encompassing several popular MR methods as special cases. Through real data applications, the effectiveness and robustness of $\mathsf{dmIVW}$ in estimating the causal effects of risk factors on common diseases are demonstrated.

Mendelian Randomization Analysis↗

PubMedDate not supplied

Iterative algebraic reconstruction algorithms for emission computed tomography: a unified framework and its application to positron emission tomography.

In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence property of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE-EM, and have performance advantages over FBP in terms of contrast recovery and/or noise-to-signal ratios (NSRs) in regions of interest.

Algorithms↗

PubMed1992

An evaluation of maximum likelihood-expectation maximization reconstruction for SPECT by ROC analysis.

A ROC study was performed in order to evaluate whether the maximum likelihood expectation maximization (ML-EM) reconstruction algorithm improves diagnostic performance compared to the conventional filtered backprojection method in SPECT. Several implementations of the algorithm were tested including 25 and 50 iteration stopping points, with and without nonuniform attenuation compensation, and with and without Metz filtering. Filtered backprojection was with Metz filter and without attenuation compensation. The test data were computer simulated to model cardiac 201Tl SPECT. The data incorporated the effects of nonuniform attenuation, distance-dependent collimator response, and scatter. Patient CT images provided realistic anatomy and attenuation information for the data simulation. Four observers each viewed 120 images for each of the reconstruction methods. Lesion detectability with ML-EM increased with Metz filtering and decreased with nonuniform attenuation compensation. The best MIL-EM implementation, 50 iterations with Metz filtering and without attenuation compensation, was not statistically better than filtered backprojection.

Algorithms↗

PubMed1993

Restricted maximum likelihood estimation of variance components from field data for number of pigs born alive.

Variance components for number of pigs born alive (NBA) were estimated from sow productivity field records collected by purebred breed associations. Data sets analyzed were as follows: Hampshire (n = 13,537), Landrace (n = 10,822), and Spotted (n = 3,949). Variance components for service sire, sire of sow, dam of sow, and residual effects on NBA (adjusted for parity) were estimated. The single-trait model included relationships between service sires, sires of sows, and dams of sows. The model was implemented using an expectation maximization (EM) REML algorithm. A sparse-matrix solver was also used. Heritability estimates for NBA were .13, .13, and .12 for Hampshire, Spotted, and Landrace, respectively. Estimates of maternal genetic (co)variances (m2) expressed as a proportion of the phenotypic variance were .05, .01, and .03 for Hampshire, Spotted, and Landrace, respectively. Results indicated that service sires account for 1 to 2% of the total variation for NBA. Genetic effects influencing NBA seem to be small in these data sets, but selection for increased NBA should be effective.

Analysis of Variance↗