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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.
Consider a two-armed, placebo-controlled trial in which subjects may experience treatment failure. For ethical reasons, it is necessary to administer emergency or rescue medications for such subjects. However, the emergency medications may bias the set of response measurements. When analyzing the data from clinical trials, the standard approach is to perform an intent-to-treat (ITT) analysis, wherein the data are analyzed according to treatment assignment. Secondary statistical analyses that supplement the ITT analysis can be performed to account for the impact of treatment failures and emergency medications. A likelihood-based, counterfactual approach to supplemental analyses uses the expectation maximization (EM) algorithm for parameter estimation and a likelihood ratio test to test the equality of the placebo and experimental treatment means for subjects who would not fail under either treatment assignment. A simulation study is performed to assess the operating characteristics of the likelihood ratio test. An example from the Asthma Clinical Research Network (ACRN) is used to draw comparisons between the standard ITT procedure and the developed supplemental analysis.
Shwachman-Diamond syndrome is a rare disorder of unknown cause. Reports have indicated the occurrence of affected siblings, but formal segregation analysis has not been performed. In families collected for genetic studies, the mean paternal age and mean difference in parental ages were found to be consistent with the general population. We determined estimates of segregation proportion in a cohort of 84 patients with complete sibship data under the assumption of complete ascertainment, using the Li and Mantel estimator, and of single ascertainment with the Davie modification. A third estimate was also computed with the expectation-maximization (EM) algorithm. All three estimates supported an autosomal recessive mode of inheritance, but complete ascertainment was found to be unlikely. Although there are no overt signs of disease in adult carriers (parents), the use of serum trypsinogen levels to indicate exocrine pancreatic dysfunction was evaluated as a potential measure for heterozygote expression. No consistent differences were found in levels between parents and a normal control population. Although genetic heterogeneity cannot be excluded, our results indicate that simulation and genetic analyses of Shwachman-Diamond syndrome should consider a recessive model of inheritance.
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.
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.
Study of the maximum likelihood by EM algorithm (ML) with a reconstruction kernel equal to the intrinsic detector resolution and sieve regularization has demonstrated that any image improvements over filtered backprojection (FBP) are a function of image resolution. Comparing different reconstruction algorithms potentially requires measuring and matching the image resolution. Since there are no standard methods for describing the resolution of images from a nonlinear algorithm such as ML, we have defined measures of effective local Gaussian resolution (ELGR) and effective global Gaussian resolution (EGGR) and examined their behaviour in FBP images and in ML images using two different measurement techniques. For FBP these two resolution measures are equal and exhibit the standard convolution behaviour of linear systems. For ML, the FWHM of the ELGR monotonically increased with decreasing Gaussian object size due to slower convergence rates for smaller objects. For the simple simulated phantom used, this resolution dependence is independent of object position. With increasing object size, number of iterations and sieve size the object size dependence of the ELGR decreased. The FWHM of the EGGR converged after approximately 200 iterations, masking the fact that the ELGR for small objects was far from convergence. When FBP is compared to a nonlinear algorithm such as ML, it is recommended that at least the EGGR be matched; for ML this requires more than the number of iterations (e.g., < 100) that are typically run to minimize the mean square error or to satisfy a feasibility or similar stopping criterion. For many tasks, matching the EGGR of ML to FBP images may be insufficient and >> 200 iterations may be needed, particularly for small objects in the ML image because their ELGR has not yet converged.
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.
In order to model photon attenuation and detector resolution variation as a depth-dependent convolution for efficient reconstruction of quantitative SPECT, a central-ray approximation is necessary. This work investigates the impact of the approximation upon reconstruction accuracy and computational efficiency. A patient chest CT image was acquired and converted into an object-specific attenuation map. From a segmentation of the map, an emission thorax phantom was constructed with a cardiac insert. To generate a system-specific resolution-variant kernal, a point source was measured at several depths from the surface of a low-energy, high-resolution, parallel-hole collimator of a SPECT system. Projections of parallel-beam geometry were simulated from the phantom, the map, and the kernel on an elliptical orbit. Reconstruction was performed by the ML-EM algorithm with and without the central-ray approximation. The approximation cuts down dramatically (more than 100 fold) the computing time with a negligible loss (less than 1%) of reconstruction accuracy.
Effects of different scatter compensation methods incorporated in fully 3D iterative reconstruction are investigated. The methods are: (i) the inclusion of an 'ideal scatter estimate' (ISE); (ii) like (i) but with a noiseless scatter estimate (ISE-NF); (iii) incorporation of scatter in the point spread function during iterative reconstruction ('ideal scatter model', ISM); (iv) no scatter compensation (NSC); (v) ideal scatter rejection (ISR), as can be approximated by using a camera with a perfect energy resolution. The iterative method used was an ordered subset expectation maximization (OS-EM) algorithm. A cylinder containing small cold spheres was used to calculate contrast-to-noise curves. For a brain study, global errors between reconstruction and 'true' distributions were calculated. Results show that ISR is superior to all other methods. In all cases considered, ISM is superior to ISE and performs approximately as well as (brain study) or better than (cylinder data) ISE-NF. Both ISM and ISE improve contrast-to-noise curves and reduce global errors, compared with NSC. In the case of ISE, blurring of the scatter estimate with a Gaussian kernel results in slightly reduced errors in brain studies, especially at low count levels. The optimal Gaussian kernel size is strongly dependent on the noise level.
A megavoltage computed tomography (MVCT) system was developed on the University of Wisconsin tomotherapy benchtop. This system can operate either axially or helically, and collect transmission data without any bounds on delivered dose. Scan times as low as 12 s per slice are possible, and scans were run with linac output rates of 100 MU min(-1), although the system can be tuned to deliver arbitrarily low dose rates. Images were reconstructed with clinically reasonable doses ranging from 8 to 12 cGy. These images delineate contrasts below 2% and resolutions of 3.0 mm. Thus, the MVCT image quality of this system should be sufficient for verifying the patient's position and anatomy prior to radiotherapy. Additionally, synthetic data were used to test the potential for improved MVCT contrast using maximum-likelihood (ML) reconstruction. Specifically, the maximum-likelihood expectation-maximization (ML-EM) algorithm and a transmission ML algorithm were compared with filtered backprojection (FBP). It was found that for expected clinical MVCT doses enough imaging photons are used such that little benefit is conferred by the improved noise model of ML algorithms. For significantly lower doses, some quantitative improvement is achieved through ML reconstruction. Nonetheless, the image quality at those lower doses is not satisfactory for radiotherapy verification.
Accurate estimation of the 3D in vivo activity distribution is important for dose estimation in targeted radionuclide therapy (TRT). Although SPECT can potentially provide such estimates, SPECT without compensation for image degrading factors is not quantitatively accurate. In this work, we evaluated quantitative SPECT (QSPECT) reconstruction methods that include compensation for various physical effects. Experimental projection data were obtained using a GE VH/Hawkeye system and an RSD torso phantom. Known activities of In-111 chloride were placed in the lungs, liver, heart, background and two spherical compartments with inner diameters of 22 mm and 34 mm. The 3D NCAT phantom with organ activities based on clinically derived In-111 ibritumomab tiuxetan data was used for the Monte Carlo (MC) simulation studies. Low-noise projection data were simulated using previously validated MC simulation methods. Fifty sets of noisy projections with realistic count levels were generated. Reconstructions were performed using the OS-EM algorithm with various combinations of attenuation (A), scatter (S), geometric response (G), collimator-detector response (D) and partial volume compensation (PVC). The QSPECT images from the various combinations of compensations were evaluated in terms of the accuracy and precision of the estimates of the total activity in each organ. For experimental data, the errors in organ activities for ADS and PVC compensation were less than 6.5% except the smaller sphere (-11.9%). For the noisy simulated data, the errors in organ activity for ADS compensation were less than 5.5% except the lungs (20.9%) and blood vessels (15.2%). Errors for other combinations of compensations were significantly (A, AS) or somewhat (AGS) larger. With added PVC, the error in the organ activities improved slightly except for the lungs (11.5%) and blood vessels (3.6%) where the improvement was more substantial. The standard deviation/mean ratios were all less than 1.5%. We conclude that QSPECT methods with appropriate compensations provided accurate In-111 organ activity estimates. For the collimator used, AGS was almost as good as ADS and may be preferable due to the reduced reconstruction time. PVC was important for small structures such as tumours or for organs in close proximity to regions with high activity. The improved quantitative accuracy from QSPECT methods has the potential for improving organ dose estimations in TRT.
Respiratory motion is a source of artefacts and reduced image quality in PET. Proposed methodology for correction of respiratory effects involves the use of gated frames, which are however of low signal-to-noise ratio. Therefore a method accounting for respiratory motion effects without affecting the statistical quality of the reconstructed images is necessary. We have implemented an affine transformation of list mode data for the correction of respiratory motion over the thorax. The study was performed using datasets of the NCAT phantom at different points throughout the respiratory cycle. List mode data based PET simulated frames were produced by combining the NCAT datasets with a Monte Carlo simulation. Transformation parameters accounting for respiratory motion were estimated according to an affine registration and were subsequently applied on the original list mode data. The corrected and uncorrected list mode datasets were subsequently reconstructed using the one-pass list mode EM (OPL-EM) algorithm. Comparison of corrected and uncorrected respiratory motion average frames suggests that an affine transformation in the list mode data prior to reconstruction can produce significant improvements in accounting for respiratory motion artefacts in the lungs and heart. However, the application of a common set of transformation parameters across the imaging field of view does not significantly correct the respiratory effects on organs such as the stomach, liver or spleen.
Conventional phylogenetic tree estimation methods assume that all sites in a DNA multiple alignment have the same evolutionary history. This assumption is violated in data sets from certain bacteria and viruses due to recombination, a process that leads to the creation of mosaic sequences from different strains and, if undetected, causes systematic errors in phylogenetic tree estimation. In the current work, a hidden Markov model (HMM) is employed to detect recombination events in multiple alignments of DNA sequences. The emission probabilities in a given state are determined by the branching order (topology) and the branch lengths of the respective phylogenetic tree, while the transition probabilities depend on the global recombination probability. The present study improves on an earlier heuristic parameter optimization scheme and shows how the branch lengths and the recombination probability can be optimized in a maximum likelihood sense by applying the expectation maximization (EM) algorithm. The novel algorithm is tested on a synthetic benchmark problem and is found to clearly outperform the earlier heuristic approach. The paper concludes with an application of this scheme to a DNA sequence alignment of the argF gene from four Neisseria strains, where a likely recombination event is clearly detected.
The limitations of traditional targeted radionuclide therapy (TRT) dosimetry can be overcome by using voxel-based techniques. All dosimetry techniques are reliant on a sequence of quantitative emission and transmission data. The use of (131)I, for example, with NaI or mIBG, presents additional quantification challenges beyond those encountered in low-energy NM diagnostic imaging, including dead-time correction and additional photon scatter and penetration in the camera head. The Royal Marsden Dosimetry Package (RMDP) offers a complete package for the accurate processing and analysis of raw emission and transmission patient data. Quantitative SPECT reconstruction is possible using either FBP or OS-EM algorithms. Manual, marker- or voxel-based registration can be used to register images from different modalities and the sequence of SPECT studies required for 3-D dosimetry calculations. The 3-D patient-specific dosimetry routines, using either a beta-kernel or voxel S-factor, are included. Phase-fitting each voxel's activity series enables more robust maps to be generated in the presence of imaging noise, such as is encountered during late, low-count scans or when there is significant redistribution within the VOI between scans. Error analysis can be applied to each generated dose-map. Patients receiving (131)I-mIBG, (131)I-NaI, and (186)Re-HEDP therapies have been analyzed using RMDP. A Monte-Carlo package, developed specifically to address the problems of (131)I quantification by including full photon interactions in a hexagonal-hole collimator and the gamma camera crystal, has been included in the dosimetry package. It is hoped that the addition of this code will lead to improved (131)I image quantification and will contribute towards more accurate 3-D dosimetry.
Based on how chromosomes pair at meiosis, the nature of polyploids can be described by bivalent polyploids, multivalent polyploids, and mixed polyploids. In bivalent polyploids, only two chromosomes pair, during which two more similar chromosomes have a higher pairing probability (preferential pairing) than two less similar chromosomes, whereas in multivalent polyploids more than two chromosomes pair at a time, which results in double reduction. Preferential chromosome pairings and double reduction affect the frequencies of gamete formation and, therefore, linkage analysis of polymorphic markers in bivalent and multivalent polyploids, respectively. For mixed polyploids, in which both bivalent and multivalent formations occur simultaneously, linkage analysis is affected by both preferential pairings and double reduction. In this study, we develop a hierarchical maximum likelihood model for discerning gamete genotypes derived from different pairing mechanisms and different formation modes. The first-stage model in the hierarchy is formulated to characterize the relative frequencies of bivalent and multivalent pairing configurations in terms of the preferential pairing factor. The second-stage model is derived to rule out identical gamete genotypes into their different formation modes with relative probabilities determined by the recombination fraction. The first-stage pairing mechanism and second-stage formation mode are integrated to provide the simultaneous maximum likelihood estimates of the preferential pairing factor, the frequency of double reduction, and the recombination fraction, by implementing the EM algorithm. We performed extensive simulation studies to demonstrate the statistical properties of our hierarchical model for linkage analysis in tetraploids. The implications of our model for polyploid linkage mapping are discussed.
We propose a dictionary model for haplotypes. According to the model, a haplotype is constructed by randomly concatenating haplotype segments from a given dictionary of segments. A haplotype block is defined as a set of haplotype segments that begin and end with the same pair of markers. In this framework, haplotype blocks can overlap, and the model provides a setting for testing the accuracy of simpler models invoking only nonoverlapping blocks. Each haplotype segment in a dictionary has an assigned probability and alternate spellings that account for genotyping errors and mutation. The model also allows for missing data, unphased genotypes, and prior distribution of parameters. Likelihood evaluations rely on forward and backward recurrences similar to the ones encountered in hidden Markov models. Parameter estimation is carried out with an EM algorithm. The search for the optimal dictionary is particularly difficult because of the variable dimension of the model space. We define a minimum description length criteria to evaluate each dictionary and use a combination of greedy search and careful initialization to select a best dictionary for a given dataset. Application of the model to simulated data gives encouraging results. In a real dataset, we are able to reconstruct a parsimonious dictionary that captures patterns of linkage disequilibrium well.
We determined whether the polymorphism of the gene encoding adiponectin contributes to susceptibility to preeclampsia. The study involved 133 Finnish women with preeclampsia and 245 healthy control subjects. All women were genotyped for two single nucleotide polymorphisms (SNPs), SNP45 in exon 2 and SNP276 in intron 2, in the adiponectin gene. Chi2 analysis was used to assess genotype and allele frequency differences between the preeclamptic and control groups. In addition, the pair of loci haplotype analysis, using the expectation-maximization (EM) algorithm, was used to examine the estimated haplotype frequencies of the two SNPs, among the two groups. The TT genotype versus the pooled G genotypes in SNP276 was associated with protection against preeclampsia (p = 0.012) at an odds ratio of 0.27 (95% confidence interval [CI]: 0.09-0.80). Also the genotype and allele frequency distributions of SNP276 differed significantly between the preeclampsia group and the control group (p = 0.035 and p = 0.043, respectively). Single-point genotype and allele distributions in SNP45 of the adiponectin gene were not statistically different between the groups. In the haplotype estimation analysis, the pooled G haplotypes versus the TT haplotype were significantly overrepresented in the preeclampsia group (p = 0.042 +/- 0.005). Polymorphisms of the adiponectin gene show a weak, but statistically significant, haplotype association with susceptibility to preeclampsia in Finnish women.
BACKGROUND: Investigation of long time series of cancer data can still be very useful in helping to identify Cancer Control priorities and achievements. Since the partition of Ireland into the independent Republic of Ireland and Northern Ireland, which remained part of the United Kingdom, cancer mortality data have been published in an essentially similar format in both countries. The information presented here will contribute to providing a basis for the collaborative Cancer Research programme initiated recently. PATIENTS AND METHODS: Cancer mortality data have been assembled and analysed separately for the Republic of Ireland and Northern Ireland: the data have then been combined to present mortality rates for the whole of Ireland, covering the period from 1926 to 1995. Several rubrics had to be aggregated to provide data continuously over the time span (e.g. colon and rectum and cervix and body of the uterus). When data were only available in 10-year classes of age, the EM algorithm was employed to obtain 5-year age-specific rates. All rates presented are age-standardised, employing the World Standard Population. RESULTS: In women, the death rate from all neoplasms combined increased very slightly from 117 per 100 000 in 1946-1950 to 120 per 100 000 in 1991-1995. In men, the death rate increased from 127 per 100 000 to 172 per 100 000 over the same time period. The overall cancer death rate in Ireland is currently similar to the European average in men, although in women it is among the top fifth of national cancer mortality rates in European countries. While cancer is a major cause of death in Ireland, there is no evidence of an evolving epidemic building up: the death rates from most forms of cancer are declining towards the end of the time period considered. CONCLUSIONS: As demonstrated by falling death rates from Hodgkin's disease and testicular cancer, major treatment advances appear to have been incorporated effectively into clinical practice in Ireland. Progress is apparent in tobacco control and further initiatives in this area must be undertaken since tobacco appears to be the only major new carcinogen introduced recently into the Irish environment during the period covered by this study. Effective population-based screening programmes for cervix and breast cancer and, more controversially, consideration of a National Prostate Cancer Screening programme, offer scope for further improvement in mortality. Examination of this long time series of mortality data from Ireland provides information about the evolving cancer pattern and provides the necessary background to evaluate the impact of the cross-border cancer research activities now being launched.