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Results for “EM algorithm”

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PubMed1989

The analysis of titration studies in phase III clinical trials.

Clinical trials commonly employ the titration design for certain drugs such as antihypertensives. In a Phase III trial the design has purposes distinct from those of a Phase I or II trial, as well as from those of a trial with a parallel design. In this paper we compare the titration design with the usual parallel design in their respective purposes for Phase III trials, explore the relevant questions addressed, and examine typical data from such trials. We also discuss work which focuses primarily on the Phase I or II titration trials. We formulate the problem in the framework of one-way contingency table augmented with incomplete data and obtain the maximum likelihood estimates of the parameters and their estimated variances/covariances via the EM algorithm. An example of a Phase III study of an antihypertensive agent illustrates the proposed procedure.

Analysis of Variance↗

PubMed1991

Adjusting for age-related competing mortality in long-term cancer clinical trials.

Mortality related to causes other than the treated disease may have a significant impact on overall survival in long-term clinical trials. We present a model that adjusts for age-related competing mortality when cause of death is missing or only partially available. Through use of a piecewise exponential survival model, we extend relative survival methods to continuous follow-up data, allowing the competing mortality to differ from that of the general population by a scale parameter. An EM algorithm provides a simple way to compute the maximum likelihood estimators (MLEs) and to test hypotheses using widely available software. We compare the bias and relative efficiency of this model to a piecewise exponential Cox model for overall survival. Theoretical results are confirmed by simulations and illustrated with data from a clinical trial in colorectal cancer. This example also shows how age-related and disease-related mortality can be confounded in an analysis of overall survival. We conclude with a discussion of the advantages and disadvantages of the model.

Adolescent↗

PubMed1991

A method of non-parametric back-projection and its application to AIDS data.

The method of back-projection has been used to estimate the unobserved past incidence of infection with the human immunodeficiency virus (HIV) and to obtain projections of future AIDS incidence. Here a new approach to back-projection, which avoids parametric assumptions about the form of the HIV infection intensity, is described. This approach gives the data greater opportunity to determine the shape of the estimated intensity function. The method is based on a modification of an EM algorithm for maximum likelihood estimation that incorporates smoothing of the estimated parameters. It is easy to implement on a computer because the computations are based on explicit formulae. The method is illustrated with applications to AIDS data from Australia, U.S.A. and Japanese haemophiliacs.

Acquired Immunodeficiency Syndrome↗

PubMedDate not supplied

Computational aspects of analysing random effects/longitudinal models.

Random effects and longitudinal models are becoming increasingly popular in the analysis of many types of data, including medical and biopharmaceutical, because of their richness and flexibility. They can be, however, difficult to fit using traditional statistical tools. Fortunately, there now exists a burgeoning collection of newer computational methods that can be applied to draw inferences with such models. This review attempts to provide an introduction to some of these techniques by describing them as extensions of the EM algorithm, currently a standard tool for the analysis of longitudinal and random effects models. For clarity of exposition, the extensions are classified into three types: large-sample iterative; large-sample simulation, and small-sample simulation.

Longitudinal Studies↗

PubMedDate not supplied

Methods for the analysis of informatively censored longitudinal data.

This paper describes the problem of informative censoring in longitudinal studies where the primary outcome is rate of change in a continuous variable. Standard approaches based on the linear random effects model are valid only when the data are missing in a non-ignorable fashion. Informative censoring, which is a special type of non-ignorably missing data, occurs when the probability of early termination is related to an individual subject's true rate of change. When present, informative censoring causes bias in standard likelihood-based analyses, as well as in weighted averages of individual least-squares slopes. This paper reviews several methods proposed by others for analysis of informatively censored longitudinal data, and outlines a new approach based on a log-normal survival model. Maximum likelihood estimates may be obtained via the EM algorithm. Advantages of this approach are that it allows general unbalanced data caused by staggered entry and unequally-timed visits, it utilizes all available data, including data from patients with only a single measurement, and it provides a unified method for estimating all model parameters. Issues related to study design when informative censoring may occur are also discussed.

Linear Models↗

PubMed1992

A latent class model for repeated measurements experiments.

Standard models for the analysis of repeated measurements assume a common response profile for all experimental units within a treatment group. However, in many applications this under-represents the nature of the response. There may be several distinct modes of response within a group (for example, responders versus non-responders to a given treatment), or there may be a set of distinct response profiles which are common to all the treatment groups. In these situations the effect of treatment can be characterized both by the shape of the fitted profiles and by estimating the proportion of cases who exhibit each particular response profile. This paper describes how such experiments may be analysed through the introduction of a latent variable into the standard model. Maximum likelihood estimation is straight-forward using the EM algorithm. Model choice requires some care, but good-fitting models can be identified via inspection of residuals and the use of empirical semi-variogram plots. Once the number of distinct profiles has been determined, treatment effects can be investigated using likelihood-ratio statistics. The approach is illustrated with a re-analysis of a dataset first described by Grizzle and Allen.

Animals↗

PubMedDate not supplied

Studying the relationship between change and initial value in longitudinal studies.

Blomqvist's problem of studying the relationship between change and initial value in a linear growth curve setting is reformulated from a random effects model perspective. First, a maximum likelihood estimate of the between-individual covariance matrix for a simple linear regression model with stochastic parameters is obtained via an EM algorithm as discussed by Laird and Ware. Second, the regression coefficient of the individual-specific slopes on the individual-specific intercepts is estimated as a ratio of elements of the between-individual covariance matrix as discussed by Zucker et al. Then a Fieller's type confidence interval for this ratio is proposed. Discussion is facilitated by recognizing the Laird-Ware model as a special case of a more general model discussed by Hocking.

Algorithms↗

PubMedDate not supplied

Using time of first positive HIV test and other auxiliary data in back-projection of AIDS incidence.

Estimation of HIV incidence by the method of back-projection typically uses data on the time of diagnosis of AIDS cases, together with known information about the incubation distribution of AIDS. This paper discusses back-projection using auxiliary data on AIDS cases, particularly the time of first positive HIV test. We discuss the possibility that certain types of auxiliary data, including time of first positive test, can be useful in back-projection because they provide extra information about the incubation period of AIDS cases. Under a back-projection model, theoretical efficiency calculations are given comparing back-projection with and without the time of first positive HIV test of AIDS cases. These calculations suggest that such data have the potential to significantly improve HIV incidence estimates, particularly in the recent past. Smoothed non-parametric estimates of both HIV incidence and time-dependent testing rates are described. These can be obtained using the EM algorithm, in conjunction with a smoothing step or a penalized likelihood. The benefit of these methods in practice needs to be assessed as such data become available.

Acquired Immunodeficiency Syndrome↗

PubMed1995

The analysis of repeated-measures data on schizophrenic reaction times using mixture models.

Reaction times for schizophrenic individuals in a simple visual tracking experiment can be substantially more variable than for non-schizophrenic individuals. Current psychological theory suggests that at least some of this extra variability arises from an attentional lapse that delays some, but not all, of each schizophrenic's reaction times. Based on this theory, we pursue models in which measurements from non-schizophrenics arise from a normal linear model with a separate mean for each individual, whereas measurements from schizophrenics arise from a mixture of (i) a component analogous to the distribution of response times for non-schizophrenics and (ii) a mean-shifted component. We fit four mixture models within this framework, where the distinctions between models arise from assumptions about the variance of the shifted observations and the exchangeability of schizophrenic individuals. Some of these models can be fit by maximum likelihood using the EM algorithm, and all can be fit using the ECM algorithm, where the covariance matrices associated with the parameters are calculated by the SEM and SECM algorithms, respectively. Bayesian model monitoring using posterior predictive checks is invoked to discard models that fail to reproduce certain observed features of the data and to stimulate the development of better models.

Algorithms↗

PubMedDate not supplied

A computer program for the statistical analysis of disease prevalence data from survival/sacrifice experiments.

This paper presents a computer program for analyzing disease prevalence data from animal survival experiments in which there may also be some serial sacrifice. The method has been described in Biometrics 35 (1979) 221-234. The user is interrogated about the details of particular models he wishes to fit. Then a generalized EM algorithm is used to compute maximum likelihood estimates of various quantities of interest concerning the effects of treatment, time and presence of other diseases on the prevalences and lethalities of specific diseases of interest.

Animals↗

PubMed1986

Estimation of growth curves from longitudinal data collected at irregular time intervals.

A general procedure for fitting growth curves is proposed that can be applied to longitudinal data even if observations are missing or irregularly spaced. Maximum likelihood estimates for mean growths are obtained from an EM algorithm. Estimates for standard errors, percentiles, and growth velocities are also produced. The techniques are demonstrated through the use of growth data from a longitudinal study of sickle cell disease.

Algorithms↗

PubMed1994

Sensitivity and specificity of diagnostic tests in acute maxillary sinusitis determined by maximum likelihood in the absence of an external standard.

This study shows how to obtain maximum likelihood estimates of test sensitivities and specificities in case of lack of an external standard, using the Expectation Maximisation (EM) algorithm. This method is used to compare four diagnostic tests in patients suspected of acute maxillary sinusitis. Data were analyzed from published studies. Antral aspiration is the test with the highest diagnostic value. The diagnostic value of a positive clinical examination (according to explicit criteria) and of a positive radiograph or ultrasound are comparable. A negative radiograph is of more diagnostic value than a negative clinical examination or ultrasound. The width of the confidence intervals may be too small, due to model deviations which may give incorrect standard errors. However, the estimated likelihood ratios adequately reflect the relative value of the diagnostic tests considered, even when the assumption of independence is dropped.

Acute Disease↗

PubMed1992

The accuracy of DNA sequences: estimating sequence quality.

In this paper we describe a method for the statistical reconstruction of a large DNA sequence from a set of sequenced fragments. We assume that the fragments have been assembled and address the problem of determining the degree to which the reconstructed sequence is free from errors, i.e., its accuracy. A consensus distribution is derived from the assembled fragment configuration based upon the rates of sequencing errors in the individual fragments. The consensus distribution can be used to find a minimally redundant consensus sequence that meets a prespecified confidence level, either base by base or across any region of the sequence. A likelihood-based procedure for the estimation of the sequencing error rates, which utilizes an iterative EM algorithm, is described. Prior knowledge of the error rates is easily incorporated into the estimation procedure. The methods are applied to a set of assembled sequence fragments from the human G6PD locus. We close the paper with a brief discussion of the relevance and practical implications of this work.

Algorithms↗

PubMed1995

Estimation of the shelf-life of drugs with mixed effects models.

This paper proposes a normal mixed effects model for stability analysis. An EM algorithm is developed to compute the maximum likelihood estimates of regression coefficients of the fixed effects and random effects, and variance components. The likelihood ratio test is used for the preliminary testing of batch-to-batch variation. An example from a marketing stability study is given to illustrate the proposed procedure.

Algorithms↗

PubMed1991

Parallel simulated annealing for emission tomography.

A method for implementing simulated annealing in parallel to speed up the execution of emission tomography (ET) image reconstruction is presented. A high degree of parallelism can be attained by using a parallel-acceptance partitioning strategy, in which perturbations to subsets of the estimate are evaluated in parallel. However because the point spread function in ET imaging systems is globally dependent, processors cannot update the current estimate independently. Consequently, processors must be synchronized each time a perturbation is accepted to avoid introducing error. This can produce excessive communications overhead, especially when the acceptance rate is high. In this paper an energy function is constructed to reduce the synchronization requirements by using a reformulation of the log-likelihood function from the expectation maximization (EM) algorithm. The approach is to change the global dependence in the energy function from the current estimate to the estimate generated during the last iteration. The synchronization requirements for guaranteed convergence are then significantly reduced from once per acceptance to once per iteration. This parallel implementation on 54 Inmos T800 transputers connected in a ring topology resulted in execution times that were almost 50 times faster than on a VAX 8600.

Algorithms↗

PubMed1992

Truncation artifact suppression in cone-beam radionuclide transmission CT using maximum likelihood techniques: evaluation with human subjects.

Transverse image truncation can be a serious problem for human imaging using cone-beam transmission CT (CB-CT) implemented on a conventional rotating gamma camera. If this problem can be solved, CB-CT will be useful for attenuation compensation of SPECT images. This paper presents a reconstruction method to reduce or eliminate the artifacts resulting from the truncation. The method uses a previously published transmission maximum likelihood EM algorithm, adapted to the cone-beam geometry. The reconstruction method is evaluated qualitatively using three human subjects of various dimensions and various degrees of truncation. For the two smaller subjects, with moderate truncation, the maximum likelihood method is very successful, nearly eliminating the artifacts seen with conventional filtered backprojection of truncated geometries. The use of an expanded reconstructed space, which contains the entire transverse slice of the subject, is necessary for optimal truncation removal. For the largest subject investigated, the truncation was substantial, and the artifacts were only partially removed by the maximum likelihood reconstruction. Nonetheless, the images were qualitatively superior to those obtained with filtered backprojection. An added elliptical support prior moderately increased the rate of convergence, and helped to force a reasonable body contour.

Adult↗

PubMed1995

A Monte Carlo investigation of dual-energy-window scatter correction for volume-of-interest quantification in 99Tcm SPECT.

Using Monte Carlo simulation of 99Tcm single-photon-emission computed tomography (SPECT), we investigate the effects of tissue-background activity, tumour location, patient size, uncertainty of energy windows, and definition of tumour region on the accuracy of quantification. The dual-energy-window method of correction for Compton scattering is employed and the multiplier which yields correct activity for the VI as a whole calculated. The model is usually a sphere containing radioactive water located within a cylinder filled with a more dilute solution of radioactivity. Two simulation codes are employed. Reconstruction is by ML-EM algorithm with attenuation compensation. The scatter multiplier depends only slightly on the sphere location or the cylinder diameter. It also depends little on whether correction is before or after reconstruction. At low background level, it changes with VOI size, but not at higher background. For a geometrical VOI, it is 1.25 at zero background, decreases sharply to 0.56 for equal concentrations, and is 0.44 when the background concentration is very large. Quantification is accurate (less than 9% error) if the test background is reasonably close to that used in setting the universal scatter-multiplier value, or if the test backgrounds are always large and so is the universal-value background, but not if the test backgrounds cover a large range of values including zero. Results largely agree with those from experiment after the experimental data with background is re-evaluated with prejudice.

Humans↗

PubMed1994

High resolution of quantitative traits into multiple loci via interval mapping.

A very general method is described for multiple linear regression of a quantitative phenotype on genotype [putative quantitative trait loci (QTLs) and markers] in segregating generations obtained from line crosses. The method exploits two features, (a) the use of additional parental and F1 data, which fixes the joint QTL effects and the environmental error, and (b) the use of markers as cofactors, which reduces the genetic background noise. As a result, a significant increase of QTL detection power is achieved in comparison with conventional QTL mapping. The core of the method is the completion of any missing genotypic (QTL and marker) observations, which is embedded in a general and simple expectation maximization (EM) algorithm to obtain maximum likelihood estimates of the model parameters. The method is described in detail for the analysis of an F2 generation. Because of the generality of the approach, it is easily applicable to other generations, such as backcross progenies and recombinant inbred lines. An example is presented in which multiple QTLs for plant height in tomato are mapped in an F2 progeny, using additional data from the parents and their F1 progeny.

Chromosome Mapping↗