H. Malcolm Hudson

A clinical perspective of accelerated statistical reconstruction

Although the potential benefits of maximum likelihood reconstruction have been recognised for many years, the technique has only recently found widespread popularity in clinical practice. Factors which have contributed to the wider acceptance include improved models for the emission process, better understanding of the properties of the algorithm and, not least, the practicality of application with the development of acceleration schemes and the improved speed of computers. The objective in this article is to present a framework for applying maximum likelihood reconstruction for a wide range of clinically based problems. The article draws particularly on the experience of the three authors in applying an acceleration scheme involving use of ordered subsets to a range of applications. The potential advantages of statistical reconstruction techniques include: (a) the ability to better model the emission and detection process, in order to make the reconstruction converge to a quantitative image, (b) the inclusion of a statistical noise model which results in better noise characteristics, and (c) the possibility to incorporate prior knowledge about the distribution being imaged. The great flexibility in adapting the reconstruction for a specific model results in these techniques having wide applicability to problems in clinical nuclear medicine.

A MANOVA STATISTIC IS JUST AS POWERFUL AS DISTANCE-BASED STATISTICS, FOR MULTIVARIATE ABUNDANCES

There is now quite an extensive literature based on analysis of multivariate abundances, which have often been collected according to a MANOVA design. Many test statistics have been proposed specifically for this case, yet remarkably the power of these methods has not previously been compared. In this paper, the power of distance-based statistics (e.g., Mantel, analysis of similarities) is compared to variable-based statistics (e.g., redundancy analysis, the sum of ANOVA F statistics), when using permutation tests to assess significance of all statistics. Different choice of transformation, standardization, and distance measure were considered. For 19 data sets taken from the literature, P values for the different statistics were compared. Power simulations were then conducted, where data were generated to mimic the properties of each of the 19 data sets. For transformed data, using different distance measures (Euclidean, Manhattan, Bray-Curtis) and different distance-based statistics had little effect on power. Overall, statistics based on multivariate analysis of variance (MANOVA) were at least as powerful as others, although particular data sets gave different results. The distance-based statistics most commonly used in the literature do not standardize abundances, so these were more powerful when effects are present in taxa that are more variable (on the transformed scale), and less powerful otherwise. There are several reasons to prefer a statistic based on MANOVA to others (e.g., interpretability, generalization to more complex designs), and so we generally recommend that the MANOVA-based statistics used here be preferred to distance-based statistics.

Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise

Abstract Image degradation by blurring is a well-known phenomenon often described by the mathematical operation of convolution. Fourier methods are well developed for recovery, or restoration, of the true image from an observed image affected by convolution blur and additive constant variance Gaussian noise. One focus of this paper is to describe another statistical restoration method which is available when the image data exhibits Poisson variability. This is a common situation when counts of recorded activity form the image, as in medical imaging contexts. We apply Maximum Likelihood (ML) and Maximum Penalized Likelihood (MPL) procedures to deconvolve image data which has been degraded by blurring and Poisson variability in recorded activity. A second focus is formulation and comparison of automated selection procedures for regularization (smoothing) parameters in this context.

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fishers method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

Deriving a Patient-Based Utility Index from a Cancer-Specific Quality of Life Questionnaire

OBJECTIVES The aim of this study was to derive a scoring algorithm for a validated disease-specific quality of life instrument called the Utility-Based Questionnaire-Cancer (UBQ-C) that provided a utility index designed to inform clinical decisions about cancer treatments. METHODS The UBQ-C includes a scale for global health status (1 item); and subscales for physical function (3 items), social/usual activities (4 items), self-care (1 item), and distresses because of physical and psychological symptoms (21 items). A scoring algorithm was derived to convert the subscales into a subset index, and combine it with the global scale into an overall health-related quality of life (HRQL) index, which was converted to a utility index with a power transformation. The valuation survey consisted of 204 advanced cancer patients who completed the UBQ-C and assigned time trade-off (TTO) utilities about their own health state. Preliminary validation involved comparing these derived utilities with other measures of HRQL. RESULTS Weights for the subset index were: physical function 0.28, social/usual activities 0.06, self-care 0.01, and distresses 0.64. Weights for the overall HRQL index were health status 0.65 and subset index 0.35. The mean of the utility index scores was similar to the mean of the TTO utilities (0.92 vs. 0.91, P = 0.6). The utility index was substantially correlated with other measures of HRQL. CONCLUSIONS Data from a simple, self-rated, disease-specific questionnaire can be converted into a utility index suitable for comparing the net effect of cancer treatments on quality of life, and to evaluate trade-offs between quality and quantity of life in quality-adjusted survival analyses.

Simultaneous Poisson Estimators for a Priori Hypotheses about Means

Abstract Estimators are presented for the simultaneous estimation of p means of Poisson variables. These have significantly smaller mean square errors of estimation in the region of a pre-specified set of values, and are conservative, in the sense that their mean errors are never worse than that of the minimum variance unbiased estimator, when p > 3.

Preliminary Validation of an Optimally Weighted Patient-Based Utility Index by Application to Randomized Trials in Breast Cancer

OBJECTIVES To optimize, apply, and validate a scoring algorithm that provides a utility index from a cancer-specific quality of life questionnaire called the Utility-Based Questionnaire-Cancer (UBQ-C) using data sets from randomized trials in breast cancer. The index is designed to reflect the perspective of cancer patients in a specific clinical context so as to best inform clinical decisions. METHODS We applied the UBQ-C scoring algorithm to trials of chemotherapy for advanced (n = 325) and early (n = 126) breast cancer. The algorithm converts UBQ-C subscales into a subset index, and combines it with a global health status item into an overall HRQL index, which is then converted to a utility index using a power transformation. The optimal subscale weights were determined by their correlations with the global scale in the relevant data set. The validity of the utility index was tested against other patient characteristics. RESULTS Optimal weights (range 0-1) for the subset index in advanced (early) breast cancer were: physical function 0.20 (0.09); social/usual activities 0.23 (0.25); self-care 0.04 (0.01); and distresses 0.53 (0.64). Weights for the overall HRQL index were health status 0.66 (0.63) and subset index 0.34 (0.37). The utility index discriminated between breast cancer that was advanced rather than early (means 0.88 vs. 0.94, P < 0.0001) and was responsive to the toxic effects of chemotherapy in early breast cancer (mean change 0.07, P < 0.0001). CONCLUSIONS The scoring algorithm for the UBQ-C utility index can be optimized in different clinical contexts to reflect the relative importance of different aspects of quality of life to the patients in a trial. It can be used to generate sensitive and responsive utility scores, and quality-adjusted life-years that can be used within a trial to compare the net benefit of treatments and inform clinical decision-making.

Risk of mortality after acute myocardial infarction: Performance of model updating methods for application in different geographical regions

Using the large Hirulog and Early Reperfusion or Occlusion (HERO-2) trial a parsimonious multivariable model for 30-day mortality risk assessment in acute myocardial infarction (AMI) was developed. HERO-2 was an international randomized trial of two antithrombotic therapies-unfractionated heparin and bivalirudin-for the treatment of AMI. This trial recruited 17073 patients from 46 countries from Europe, North and Latin America and Asia, including Australia, New Zealand and Russia. An important issue in applying findings from randomized clinical trials is the procedure to estimate risk among members of other patient populations. Methods for updating risk models for AMI are compared. Simple re-calibration (re-estimation of the intercept and slope of the linear predictor within regions) and model revision (re-estimation of all regression coefficients within regions) with and without shrinkage were compared to a global additive model with a built-in region effect. The relative performance of these methods in the different geographical regions, which vary in sample size, is of primary interest. Model revision only provided a slight improvement in predictive performance when applied with shrinkage in the smallest region Asia (N=756). In conclusion, a global model with regional re-calibration is adequate: region-specific coefficients did not provide worthwhile improvements in any region.

Model fitting for sequences of images

The aim of this paper is to introduce methods for estimating mixture probabilities which specify time-activity curves (distributions of activity in time) in sequences of medical images. These parameters are of medical significance as they represent metabolic processes (functioning) occurring within each voxel within an imaged region within the body. Each distribution of activity by time is modelled as a mixture of specified (basis) components. The component distributions are those in a large (spectral) class of specified densities, for instance, exponential decay distributions with specified half-life. We describe the integration of maximum likelihood expectation maximization (ML-EM) reconstruction from indirect data with mixture modelling of the original time activity, and assess our ability to determine the distribution of this activity, varying in space and time.

Performance of four published risk models to predict sentinel lymph-node involvement in Australian women with early breast cancer

BACKGROUND Sentinel lymph-node biopsy has reduced the need for extensive axillary surgery for staging. It still exposes women to associated morbidity. Risk models that use clinical and pathology information of the primary tumour to predict sentinel lymph-node metastasis may allow further improvements in care. This study assessed the performance of four published risk models for predicting sentinel lymph-node metastasis in Australian women with early breast cancer; including one model developed in an Australian population. METHODS The Sentinel Node Biopsy Versus Axillary Clearance (SNAC) trial dataset was used to assess model discrimination by calculating the area under the receiver-operating-characteristic curve (AUC) and the false-negative rate for sentinel lymph-node metastasis using model-predicted risk cut-points of 10%, 20%, 30%, and calibration using Hosmer-Lemeshow tests and calibration plots. RESULTS The sentinel node was positive in 248 of 982 (25.2%) women (158 macrometastasis, 90 micrometastasis). The AUCs of risk models ranged from 0.70 to 0.74 for prediction of any sentinel-node metastasis; 0.72 to 0.75 for macrometastasis. Calibration was poor for the three models developed outside of Australia (lack-of-fit statistics, P < 0.001). For women with a model-predicted risk of sentinel lymph-node metastasis ≤10%, observed risk was 0-13% (three models <10%), false-negative rate 0-9%; 1-17% of women were classified in this range. CONCLUSION All four models showed good discrimination for predicting sentinel lymph-node metastasis, in particular for macrometastasis. With further development such risk models could have a role in the provision of reassurance to low risk women with normal nodes sonographicaally for whom no axillary surgery is contemplated.