Geodesic shape regression with multiple geometries and sparse parameters

Many problems in medicine are inherently dynamic processes which include the aspect of change over time, such as childhood development, aging, and disease progression. From medical images, numerous geometric structures can be extracted with various representations, such as landmarks, point clouds, curves, and surfaces. Different sources of geometry may characterize different aspects of the anatomy, such as fiber tracts from DTI and subcortical shapes from structural MRI, and therefore require a modeling scheme which can include various shape representations in any combination. In this paper, we present a geodesic regression model in the large deformation (LDDMM) framework applicable to multi-object complexes in a variety of shape representations. Our model decouples the deformation parameters from the specific shape representations, allowing the complexity of the model to reflect the nature of the shape changes, rather than the sampling of the data. As a consequence, the sparse representation of diffeomorphic flow allows for the straightforward embedding of a variety of geometry in different combinations, which all contribute towards the estimation of a single deformation of the ambient space. Additionally, the sparse representation along with the geodesic constraint results in a compact statistical model of shape change by a small number of parameters defined by the user. Experimental validation on multi-object complexes demonstrate robust model estimation across a variety of parameter settings. We further demonstrate the utility of our method to support the analysis of derived shape features, such as volume, and explore shape model extrapolation. Our method is freely available in the software package deformetrica which can be downloaded at www.deformetrica.org.

Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles

Fiber bundles stemming from tractography algorithms contain many streamlines. They require therefore a great amount of computer memory and computational resources to be stored, visualised and processed. We propose an approximation scheme for fiber bundles which results in a parsimonious representation of weighted prototypes. Prototypes are chosen among the streamlines and they represent groups of similar streamlines. Their weight is related to the number of approximated streamlines. Both streamlines and prototypes are modelled as weighted currents. This computational model does not need point-to-point correspondences and two streamlines are considered similar if their endpoints are close to each other and if their pathways follow similar trajectories. Moreover, the space of weighted currents is a vector space with a closed-form metric. This permits easy computation of the approximation error and the selection of the prototypes is based on the minimisation of this error. We propose an iterative algorithm which approximates independently and simultaneously all the fascicles of the bundle in a fast and accurate way. We show that the resulting representation preserves the shape of the bundle and it can be used to accurately reconstruct the original structural connectivity. We evaluate our algorithm on bundles obtained from both deterministic and probabilistic tractography algorithms. The resulting approximations use on average only 2% of the original streamlines as prototypes. This drastically reduces the computational burden of the processes where the geometry of the streamlines is considered. We demonstrate its effectiveness using as example the registration between two fiber bundles.

Morphoarchitectural variation in South African fossil cercopithecoid endocasts

Despite the abundance of well-preserved crania and natural endocasts in the South African Plio-Pleistocene cercopithecoid record, which provide direct information relevant to the evolution of their endocranial characteristics, few studies have attempted to characterize patterns of external brain morphology in this highly successful primate Superfamily. The availability of non-destructive penetrating radiation imaging systems, together with recently developed computer-based analytical tools, allow for high resolution virtual imaging and modeling of the endocranial casts and thus disclose new perspectives in comparative paleoneurology. Here, we use X-ray microtomographic-based 3D virtual imaging and quantitative analyses to investigate the endocranial organization of 14 cercopithecoid specimens from the South African sites of Makapansgat, Sterkfontein, Swartkrans, and Taung. We present the first detailed comparative description of the external neuroanatomies that characterize these Plio-Pleistocene primates. Along with reconstruction of endocranial volumes, we combine a semi-automatic technique for extracting the neocortical sulcal pattern together with a landmark-free surface deformation method to investigate topographic differences in morphostructural organization. Besides providing and comparing for the first time endocranial volume estimates of extinct Plio-Pleistocene South African cercopithecoid taxa, we report additional information regarding the variation in the sulcal pattern of Theropithecus oswaldi subspecies, and notably of the central sulcus, and the neuroanatomical condition of the colobine taxon Cercopithecoides williamsi, suggested to be similar for some aspects to the papionin pattern, and discuss potential phylogenetic and taxonomic implications. Further research in virtual paleoneurology, applied to specimens from a wider geographic area, is needed to clarify the polarity, intensity, and timing of cortical surface evolution in cercopithecoid lineages.

Lateral Temporal Lobe: An Early Imaging Marker of the Presymptomatic GRN Disease?

The preclinical stage of frontotemporal lobar degeneration (FTLD) is not well characterized. We conducted a brain metabolism (FDG-PET) and structural (cortical thickness) study to detect early changes in asymptomatic GRN mutation carriers (aGRN+) that were evaluated longitudinally over a 20-month period. At baseline, a left lateral temporal lobe hypometabolism was present in aGRN+ without any structural changes. Importantly, this is the first longitudinal study and, across time, the metabolism more rapidly decreased in aGRN+ in lateral temporal and frontal regions. The main structural change observed in the longitudinal study was a reduction of cortical thickness in the left lateral temporal lobe in carriers. A limit of this study is the relatively small sample (n = 16); nevertheless, it provides important results. First, it evidences that the pathological processes develop a long time before clinical onset, and that early neuroimaging changes might be detected approximately 20 years before the clinical onset of disease. Second, it suggests that metabolic changes are detectable before structural modifications and cognitive deficits. Third, both the baseline and longitudinal studies provide converging results implicating lateral temporal lobe as early involved in GRN disease. Finally, our study demonstrates that structural and metabolic changes could represent possible biomarkers to monitor the progression of disease in the presymptomatic stage toward clinical onset.

Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: the CADDementia challenge

Algorithms for computer-aided diagnosis of dementia based on structural MRI have demonstrated high performance in the literature, but are difficult to compare as different data sets and methodology were used for evaluation. In addition, it is unclear how the algorithms would perform on previously unseen data, and thus, how they would perform in clinical practice when there is no real opportunity to adapt the algorithm to the data at hand. To address these comparability, generalizability and clinical applicability issues, we organized a grand challenge that aimed to objectively compare algorithms based on a clinically representative multi-center data set. Using clinical practice as the starting point, the goal was to reproduce the clinical diagnosis. Therefore, we evaluated algorithms for multi-class classification of three diagnostic groups: patients with probable Alzheimer's disease, patients with mild cognitive impairment and healthy controls. The diagnosis based on clinical criteria was used as reference standard, as it was the best available reference despite its known limitations. For evaluation, a previously unseen test set was used consisting of 354 T1-weighted MRI scans with the diagnoses blinded. Fifteen research teams participated with a total of 29 algorithms. The algorithms were trained on a small training set (n=30) and optionally on data from other sources (e.g., the Alzheimer's Disease Neuroimaging Initiative, the Australian Imaging Biomarkers and Lifestyle flagship study of aging). The best performing algorithm yielded an accuracy of 63.0% and an area under the receiver-operating-characteristic curve (AUC) of 78.8%. In general, the best performances were achieved using feature extraction based on voxel-based morphometry or a combination of features that included volume, cortical thickness, shape and intensity. The challenge is open for new submissions via the web-based framework: http://caddementia.grand-challenge.org.

Morphometry of anatomical shape complexes with dense deformations and sparse parameters

We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. The method estimates an anatomical model, the template complex, that is representative of the population under study. Its shape reflects anatomical invariants within the dataset. In addition, the method automatically places control points near the most variable parts of the template complex. Vectors attached to these points are parameters of deformations of the ambient 3D space. These deformations warp the template to each subject's complex in a way that preserves the organization of the anatomical structures. Multivariate statistical analysis is applied to these deformation parameters to test for group differences. Results of the statistical analysis are then expressed in terms of deformation patterns of the template complex, and can be visualized and interpreted. The user needs only to specify the topology of the template complex and the number of control points. The method then automatically estimates the shape of the template complex, the optimal position of control points and deformation parameters. The proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies, in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes, spikes, inconsistent orientation or irregular meshing. The approach is illustrated with a neuroimaging study of Down syndrome (DS). The results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and DS subjects. The deformation-based modelingis able to classify subjects with very high specificity and sensitivity, thus showing important generalization capability even given a low sample size. We show that the results remain significant even if the number of control points, and hence the dimension of variables in the statistical model, are drastically reduced. The analysis may even suggest that parsimonious models have an increased statistical performance. The method has been implemented in the software Deformetrica, which is publicly available at www.deformetrica.org.

Geodesic shape regression in the framework of currents

Shape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low dimensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes.

GEODESIC REGRESSION OF IMAGE AND SHAPE DATA FOR IMPROVED MODELING OF 4D TRAJECTORIES

A variety of regression schemes have been proposed on images or shapes, although available methods do not handle them jointly. In this paper, we present a framework for joint image and shape regression which incorporates images as well as anatomical shape information in a consistent manner. Evolution is described by a generative model that is the analog of linear regression, which is fully characterized by baseline images and shapes (intercept) and initial momenta vectors (slope). Further, our framework adopts a control point parameterization of deformations, where the dimensionality of the deformation is determined by the complexity of anatomical changes in time rather than the sampling of the image and/or the geometric data. We derive a gradient descent algorithm which simultaneously estimates baseline images and shapes, location of control points, and momenta. Experiments on real medical data demonstrate that our framework effectively combines image and shape information, resulting in improved modeling of 4D (3D space + time) trajectories.

Diffeomorphic shape trajectories for improved longitudinal segmentation and statistics

Longitudinal imaging studies involve tracking changes in individuals by repeated image acquisition over time. The goal of these studies is to quantify biological shape variability within and across individuals, and also to distinguish between normal and disease populations. However, data variability is influenced by outside sources such as image acquisition, image calibration, human expert judgment, and limited robustness of segmentation and registration algorithms. In this paper, we propose a two-stage method for the statistical analysis of longitudinal shape. In the first stage, we estimate diffeomorphic shape trajectories for each individual that minimize inconsistencies in segmented shapes across time. This is followed by a longitudinal mixed-effects statistical model in the second stage for testing differences in shape trajectories between groups. We apply our method to a longitudinal database from PREDICT-HD and demonstrate our approach reduces unwanted variability for both shape and derived measures, such as volume. This leads to greater statistical power to distinguish differences in shape trajectory between healthy subjects and subjects with a genetic biomarker for Huntington's disease (HD).

LONGITUDINAL GROWTH MODELING OF DISCRETE-TIME FUNCTIONS WITH APPLICATION TO DTI TRACT EVOLUTION IN EARLY NEURODEVELOPMENT

We present a new framework for spatiotemporal analysis of parameterized functions attributed by properties of 4D longitudinal image data. Our driving application is the measurement of temporal change in white matter diffusivity of fiber tracts. A smooth temporal modeling of change from a discrete-time set of functions is obtained with an extension of the logistic growth model to time-dependent spline functions, capturing growth with only a few descriptive parameters. An unbiased template baseline function is also jointly estimated. Solution is demonstrated via energy minimization with an extension to simultaneous modeling of trajectories for multiple subjects. The new framework is validated with synthetic data and applied to longitudinal DTI from 15 infants. Interpretation of estimated model growth parameters is facilitated by visualization in the original coordinate space of fiber tracts.

Bayesian atlas estimation for the variability analysis of shape complexes

In this paper we propose a Bayesian framework for multiobject atlas estimation based on the metric of currents which permits to deal with both curves and surfaces without relying on point correspondence. This approach aims to study brain morphometry as a whole and not as a set of different components, focusing mainly on the shape and relative position of different anatomical structures which is fundamental in neuro-anatomical studies. We propose a generic algorithm to estimate templates of sets of curves (fiber bundles) and closed surfaces (sub-cortical structures) which have the same "form" (topology) of the shapes present in the population. This atlas construction method is based on a Bayesian framework which brings to two main improvements with respect to previous shape based methods. First, it allows to estimate from the data set a parameter specific to each object which was previously fixed by the user: the trade-off between data-term and regularity of deformations. In a multi-object analysis these parameters balance the contributions of the different objects and the need for an automatic estimation is even more crucial. Second, the covariance matrix of the deformation parameters is estimated during the atlas construction in a way which is less sensitive to the outliers of the population.

Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data

This paper proposes an original approach for the statistical analysis of longitudinal shape data. The proposed method allows the characterization of typical growth patterns and subject-specific shape changes in repeated time-series observations of several subjects. This can be seen as the extension of usual longitudinal statistics of scalar measurements to high-dimensional shape or image data. The method is based on the estimation of continuous subject-specific growth trajectories and the comparison of such temporal shape changes across subjects. Differences between growth trajectories are decomposed into morphological deformations, which account for shape changes independent of the time, and time warps, which account for different rates of shape changes over time. Given a longitudinal shape data set, we estimate a mean growth scenario representative of the population, and the variations of this scenario both in terms of shape changes and in terms of change in growth speed. Then, intrinsic statistics are derived in the space of spatiotemporal deformations, which characterize the typical variations in shape and in growth speed within the studied population. They can be used to detect systematic developmental delays across subjects. In the context of neuroscience, we apply this method to analyze the differences in the growth of the hippocampus in children diagnosed with autism, developmental delays and in controls. Result suggest that group differences may be better characterized by a different speed of maturation rather than shape differences at a given age. In the context of anthropology, we assess the differences in the typical growth of the endocranium between chimpanzees and bonobos. We take advantage of this study to show the robustness of the method with respect to change of parameters and perturbation of the age estimates.

A framework for longitudinal data analysis via shape regression

Traditional longitudinal analysis begins by extracting desired clinical measurements, such as volume or head circumference, from discrete imaging data. Typically, the continuous evolution of a scalar measurement is estimated by choosing a 1D regression model, such as kernel regression or fitting a polynomial of fixed degree. This type of analysis not only leads to separate models for each measurement, but there is no clear anatomical or biological interpretation to aid in the selection of the appropriate paradigm. In this paper, we propose a consistent framework for the analysis of longitudinal data by estimating the continuous evolution of shape over time as twice differentiable flows of deformations. In contrast to 1D regression models, one model is chosen to realistically capture the growth of anatomical structures. From the continuous evolution of shape, we can simply extract any clinical measurements of interest. We demonstrate on real anatomical surfaces that volume extracted from a continuous shape evolution is consistent with a 1D regression performed on the discrete measurements. We further show how the visualization of shape progression can aid in the search for significant measurements. Finally, we present an example on a shape complex of the brain (left hemisphere, right hemisphere, cerebellum) that demonstrates a potential clinical application for our framework.

Analysis of longitudinal shape variability via subject specific growth modeling

Statistical analysis of longitudinal imaging data is crucial for understanding normal anatomical development as well as disease progression. This fundamental task is challenging due to the difficulty in modeling longitudinal changes, such as growth, and comparing changes across different populations. We propose a new approach for analyzing shape variability over time, and for quantifying spatiotemporal population differences. Our approach estimates 4D anatomical growth models for a reference population (an average model) and for individuals in different groups. We define a reference 4D space for our analysis as the average population model and measure shape variability through diffeomorphisms that map the reference to the individuals. Conducting our analysis on this 4D space enables straightforward statistical analysis of deformations as they are parameterized by momenta vectors that are located at homologous locations in space and time. We evaluate our method on a synthetic shape database and clinical data from a study that seeks to quantify brain growth differences in infants at risk for autism.

A statistical model for quantification and prediction of cardiac remodelling: application to tetralogy of Fallot

Cardiac remodelling plays a crucial role in heart diseases. Analyzing how the heart grows and remodels over time can provide precious insights into pathological mechanisms, eventually resulting in quantitative metrics for disease evaluation and therapy planning. This study aims to quantify the regional impacts of valve regurgitation and heart growth upon the end-diastolic right ventricle (RV) in patients with tetralogy of Fallot, a severe congenital heart defect. The ultimate goal is to determine, among clinical variables, predictors for the RV shape from which a statistical model that predicts RV remodelling is built. Our approach relies on a forward model based on currents and a diffeomorphic surface registration algorithm to estimate an unbiased template. Local effects of RV regurgitation upon the RV shape were assessed with Principal Component Analysis (PCA) and cross-sectional multivariate design. A generative 3-D model of RV growth was then estimated using partial least squares (PLS) and canonical correlation analysis (CCA). Applied on a retrospective population of 49 patients, cross-effects between growth and pathology could be identified. Qualitatively, the statistical findings were found realistic by cardiologists. 10-fold cross-validation demonstrated a promising generalization and stability of the growth model. Compared to PCA regression, PLS was more compact, more precise and provided better predictions.

Estimation of smooth growth trajectories with controlled acceleration from time series shape data

Longitudinal shape analysis often relies on the estimation of a realistic continuous growth scenario from data sparsely distributed in time. In this paper, we propose a new type of growth model parameterized by acceleration, whereas standard methods typically control the velocity. This mimics the behavior of biological tissue as a mechanical system driven by external forces. The growth trajectories are estimated as smooth flows of deformations, which are twice differentiable. This differs from piecewise geodesic regression, for which the velocity may be discontinuous. We evaluate our approach on a set of anatomical structures of the same subject, scanned 16 times between 4 and 8 years of age. We show our acceleration based method estimates smooth growth, demonstrating improved regularity compared to piecewise geodesic regression. Leave-several-out experiments show that our method is robust to missing observations, as well as being less sensitive to noise, and is therefore more likely to capture the underlying biological growth.

Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents

This paper proposes a generic framework for the registration, the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images. This framework is based on the metric on currents for the comparison of fiber bundles. This metric measures anatomical differences between fiber bundles, seen as global homologous structures across subjects. It avoids the need to establish correspondences between points or between individual fibers of different bundles. It can measure differences both in terms of the geometry of the bundles (like its boundaries) and in terms of the density of fibers within the bundle. It is robust to fiber interruptions and reconnections. In addition, a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents. First, we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects. A dense deformation of the underlying white matter is estimated, which is constrained by the bundles seen as global anatomical landmarks. By contrast, the alignment obtained from image registration is driven only by the local gradient of the image. Second, we propose a generative statistical model for the analysis of a collection of homologous bundles. This model consistently estimates prototype fiber bundles (called template), which capture the anatomical invariants in the population, a set of deformations, which align the geometry of the template to that of each subject and a set of residual perturbations. The statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry (stretching, torque, etc.) and "texture" (fiber density, etc.). Third, this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability. This gives a way to interpret the anatomical features that the model detects consistently across the subjects. This may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles.

A statistical model of white matter fiber bundles based on currents

The purpose of this paper is to measure the variability of a population of white matter fiber bundles without imposing unrealistic geometrical priors. In this respect, modeling fiber bundles as currents seems particularly relevant, as it gives a metric between bundles which relies neither on point nor on fiber correspondences and which is robust to fiber interruption. First, this metric is included in a diffeomorphic registration scheme which consistently aligns sets of fiber bundles. In particular, we show that aligning directly fiber bundles may solve the aperture problem which appears when fiber mappings are constrained by tensors only. Second, the measure of variability of a population of fiber bundles is based on a statistical model which considers every bundle as a random diffeomorphic deformation of a common template plus a random non-diffeomorphic perturbation. Thus, the variability is decomposed into a geometrical part and a "texture" part. Our results on real data show that both parts may contain interesting anatomical features.

A statistical model of right ventricle in tetralogy of Fallot for prediction of remodelling and therapy planning

Patients with repaired Tetralogy of Fallot commonly suffer from chronic pulmonary valve regurgitations and extremely dilated right ventricle (RV). To reduce risk factors, new pulmonary valves must be re-implanted. However, establishing the best timing for re-intervention is a clinical challenge because of the large variability in RV shape and in pathology evolution. This study aims at quantifying the regional impacts of growth and regurgitations upon the end-diastolic RV anatomy. The ultimate goal is to determine, among clinical variables, predictors for the shape in order to build a statistical model that predicts RV remodelling. The proposed approach relies on a forward model based on currents and LDDMM algorithm to estimate an unbiased template of 18 patients and the deformations towards each individual shape. Cross-sectional multivariate analyses are carried out to assess the effects of body surface area, tricuspid and transpulmonary valve regurgitations upon the RV shape, The statistically significant deformation modes were found clinically relevant. Canonical correlation analysis yielded a generative model that was successfully tested on two new patients.

Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets

We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution of the structures. It does not require that subjects are scanned the same number of times or at the same ages. First a regression model infers a continuous evolution of shapes from a set of observations of the same subject. Second, spatiotemporal registrations deform jointly (1) the geometry of the evolving structure via 3D deformations and (2) the dynamics of evolution via time change functions. Third, we infer from a population a prototype scenario of evolution and its 4D variability. Our method is used to analyze the morphological evolution of 2D profiles of hominids skulls and to analyze brain growth from amygdala of autistics, developmental delay and control children.

Sparse approximation of currents for statistics on curves and surfaces

Computing, processing, visualizing statistics on shapes like curves or surfaces is a real challenge with many applications ranging from medical image analysis to computational geometry. Modelling such geometrical primitives with currents avoids feature-based approach as well as point-correspondence method. This framework has been proved to be powerful to register brain surfaces or to measure geometrical invariants. However, if the state-of-the-art methods perform efficiently pairwise registrations, new numerical schemes are required to process groupwise statistics due to an increasing complexity when the size of the database is growing. Statistics such as mean and principal modes of a set of shapes often have a heavy and highly redundant representation. We propose therefore to find an adapted basis on which mean and principal modes have a sparse decomposition. Besides the computational improvement, this sparse representation offers a way to visualize and interpret statistics on currents. Experiments show the relevance of the approach on 34 sets of 70 sulcal lines and on 50 sets of 10 meshes of deep brain structures.

Study design in osteoporosis: a European perspective

The advent of effective agents for the treatment of osteoporosis has led to the view that placebo-controlled trials to test new agents for efficacy are no longer appropriate. Rather, studies of superiority, equivalence, or non-inferiority have been recommended. Such studies require very large sample sizes, and the burden of osteoporotic fracture in a trial setting is substantially increased. Studies of equivalence cannot be unambiguously interpreted because the variance in effect of active comparator agents is too large in osteoporosis. If fracture studies are required by regulatory agencies, there is still a requirement for placebo-controlled studies, although perhaps of shorter duration than demanded at present.

A confirmatory dose-ranging study of riluzole in ALS. ALS/Riluzole Study Group-II

ALS is a progressive motor neuron disease with no effective treatment. The anti-excitotoxic drug riluzole (100 mg/day) has been shown to decrease mortality and muscular deterioration in ALS patients. To confirm and extend the therapeutic effect of riluzole, we performed a double-blind, placebo-controlled, multicenter, international, dose-ranging (50, 100, 200 mg/day), stratified study in 959 ALS outpatients treated for up to 18 months. Primary efficacy criterion was survival and the effect of treatment was analyzed before (Wilcoxon and log rank tests) and after adjustment on prognostic factors (Cox model). Secondary efficacy criterion was disease progression assessed through change in functional measures. Tracheostomy-free survival rates were: 50.4% (placebo), 55.3% (50 mg riluzole) (p = 0.23, Wilcoxon test; p = 0.25, log-rank test), 56.8% (100 mg riluzole) (p = 0.05, Wilcoxon test; p = 0.076, log-rank test), and 57.8% (200 mg riluzole) (p = 0.061, Wilcoxon test; p = 0.075, log-rank test). At the end of the 18-month study, there was a significant dose-related decrease in risk of death or tracheostomy (p = 0.04). Adjustment for baseline prognostic factors showed a 35% decreased risk of death with the 100-mg dose compared with placebo (p = 0.002). No significant treatment effects were detected for the functional assessments. The most frequent dose-related adverse events included nausea, asthenia, and elevated liver enzyme levels. This study confirms the therapeutic effect of riluzole in a large representative ALS sample, over an 18-month period. Riluzole is well tolerated and decreases the risk of death or tracheostomy in ALS patients.

[Monitoring of clinical trials and interim analysis. 1. Monitoring committee]

In order to fulfil the ethical principles linked to the protection of patients randomized in a controlled clinical trial, monitoring procedures need to be set up. In this context, a committee of experts, called the data monitoring committee is in charge of reviewing regularly unblinded data to assess the quality and the relevance of the trial, to evaluate the evidence of an emerging treatment difference and to control the rate of occurrence of serious adverse events. After each meeting, the monitoring committee reports to the steering committee its recommendation to continue or to stop the trial prematurely. Protocol modifications might be proposed as well. Illustrated with several examples, this article reviews different situations a monitoring committee might have to tackle with.

[Monitoring of clinical trials and interim analysis. 2. Statistic methods]

Although the decision to continue or to stop prematurely a clinical trial is not solely based on statistical tests, they bring useful objective arguments to the data monitoring board. However, the multiple use of statistical tests leads to increase the risk of false positive conclusions in favor of one of the treatments, and several methods have been developed to address this problem. This article presents the four major strategies that are being used for monitoring clinical trials, as well as the rationale for planning and using such statistical monitoring procedures.

When to randomize?

Many clinical trials address the question of the duration of therapy or whether initial therapy can be improved by the addition of a consolidation or maintenance regimen. For such clinical trials, the question of when to perform the randomization is often difficult. Conventional statistical wisdom prescribes that randomization should take place as late as possible before treatment is effected. This is not always possible or desirable, however. In this report, we describe the factors that are influenced by the timing of randomization, quantify how timing affects these factors, and attempt to provide a tool to help investigators and statisticians determine the appropriate time to randomize for individual studies and particular circumstances.

Planning and monitoring of equivalence studies

Demonstrating therapeutic equivalence of two treatments is the goal of many clinical trials. For instance, when the toxicity of an effective standard treatment is of concern, much effort is devoted to developing new therapies that would be both as effective and less toxic. In this paper we review the special characteristics of these trials and describe sequential monitoring of equivalence studies using repeated confidence intervals. We show how sequential monitoring may be of particular value in this setting and critically discuss the choice of some important design parameters. We also provide tables for use when planning a sequential equivalence trial.

Prognostic factors for patients with diffuse large cell or immunoblastic non-Hodgkin's lymphomas: experience of the non-Hodgkin's Lymphoma Pathologic Classification Project

Prognostic factors for long-term survival of 312 patients with diffuse large cell or immunoblastic non-Hodgkin's lymphoma are presented based on analysis of the multiinstitution clinicopathologic study sponsored by the National Cancer Institute. At the time of analysis, 75% of the patients had died and the median follow-up for patients still alive was 11 years. The distribution of Ann Arbor stages was 21% stage I, 32% stage II, 17% stage III, and 30% stage IV. Factors of prognostic significance for survival included age, stage, histologic subtype, presence of B symptoms, size of the largest lesion, number of extra-lymphoid organs involved, and extent of lymphatic involvement. Recursive partitioning analysis suggested a prognostic classification system based on stage, age, size of the largest lesion, and presence of mediastinal involvement. Stage I patient less than 50 years of age had a 10 year survival rate of 65% compared to 36% for older stage I patients. Stage II patients less than 65 years old without bulky lesions or mediastinal involvement had a 10 year survival rate of 45% compared to 10% for the poorer risk stage II patients. Although statistically significant prognostic factors were identified for the stage III/IV patients, they were not strong discriminants of 5-10 year survival rate. Because of the correlation among potential prognostic factors, there is no uniquely best classification system. Reasons for discrepancies among reported prognostic factor analyses are discussed, and a prognostic grouping that synthesizes our results with those of others is proposed.

2'-Deoxycoformycin after failure of alpha-interferon in hairy cell leukemia

Alpha-interferon (IFN) and 2'-deoxycoformycin (dCF) both exhibit substantial activity in the treatment of hairy cell leukemia (HCL). Anecdotal reports have suggested that patients who failed IFN could achieve durable responses with dCF, although the frequency with which this was said to have occurred was unknown. We reviewed the available data on the responsiveness of HCL to dCF after IFN therapy by analyzing cases reported in the literature and those treated under the Special Exception mechanism of the National Cancer Institute, Division of Cancer Treatment. Of 60 such cases identified there were 22 (37%) "compete responses" and 22 (37%) "partial responses" for a total response rate of 74%. Responses appeared to be durable in many cases, lasting up to 2 years at the time of reporting. dCF is an active agent in HCL both as initial therapy and for the salvage of patients who have failed IFN. The relative activity of these two agents and the optimal strategies for their use are currently under investigation in ongoing clinical trials.

Increasing trend of ALS in France and elsewhere: are the changes real?

We analyzed 9,005 deaths from amyotrophic lateral sclerosis recorded in France between the years 1968 and 1982. The overall adjusted mortality rates were 1.45/100,000 for men and 0.90/100,000 for women. We found excess male mortality in every age group. Age-specific mortality rates increased with age until 65-74 years and then declined in the older population. There was no meaningful regional pattern. We found a substantial increase in ALS mortality over time: the adjusted rates (per 100,000) in the period 1968 to 1971 were 1.11 for men and 0.63 for women. In the period 1979 to 1982, the corresponding figures were 1.92 and 1.12. The increase was mainly due to persons over 55 years of age and affected mostly the women during the first part of the study (1968 to 1978). In the recent years, increase appeared similar in both sexes. The temporal trends are consistent across studies in different countries.

Flexible regression models with cubic splines

We describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates. This simple method can help prevent the problems that result from inappropriate linearity assumptions. We compare restricted cubic spline regression to non-parametric procedures for characterizing the relationship between age and survival in the Stanford Heart Transplant data. We also provide an illustrative example in cancer therapeutics.

The Non-Hodgkin Lymphoma Pathologic Classification Project. Long-term follow-up of 1153 patients with non-Hodgkin lymphomas

STUDY OBJECTIVE

To document the long-term prognosis of patients with non-Hodgkin lymphoma treated between 1971 and 1975 and to determine how the prognosis varies by histologic subtype and stage.

SETTING

Three cancer referral centers in the United States and one center in Italy.

PATIENTS

A consecutive sample of 1153 previously untreated patients with non-Hodgkin lymphoma. At the time of analysis, 71% of the patients had died and the median follow-up for patients still alive was 11.2 years.

MEASUREMENTS AND MAIN RESULTS

The 10-year survival proportions were 45% (CI, 40% to 50%); 26% (CI, 22% to 30%); and 23% (CI, 18% to 30%) for patients with low-, intermediate-, and high-grade lymphomas, respectively. Patients with intermediate- and high-grade lymphomas were curable, but this was not apparent for patients with advanced stage low-grade lymphomas. For the low-grade follicular small cleaved and follicular mixed lymphomas, the Ann Arbor staging system distinguished the prognosis of patients with stage I disease from those with more extensive involvement. For the diffuse large cell and immunoblastic lymphomas, the Ann Arbor staging system distinguished long-term prognosis for patients with stage I disease from patients with stage II disease and those with more disseminated involvement.

CONCLUSIONS

The probability of long-term survival for unselected patients with non-Hodgkin lymphoma can be substantial. Long-term prognosis depends on the histologic subtype of the tumor and the extent of dissemination. The Working Formulation for non-Hodgkin lymphomas is a simple and useful nomenclature for selecting treatment and reporting results. The Ann Arbor staging system is a useful but imperfect prognostic indicator.