Incorporation of tumor shape into an assessment of spatial heterogeneity for human sarcomas imaged with FDG-PET

We have been exploring techniques for evaluation of fluoro-deoxyglucose (FDG) utilization characteristics in human sarcomas measured with positron emission tomography. In previous work, a measure of spatial heterogeneity based on evaluating the deviation of the FDG utilization distribution within the tumor region from a unimodal elliptically contoured spatial pattern was developed. This measure was shown to be a strong prognostic indicator of time to death. The present work explores a more general measure of heterogeneity which incorporates tumor boundary information. The approach relies on the use of a non-parametric representation for the tumor boundary surface. A set of 179 sarcoma patients with follow-up are evaluated with this technique. The results are analyzed to obtain empirical insight into the factors explaining elliptical heterogeneity. In terms of patient survival, the incorporation of the more sophisticated measure of spatial heterogeneity shows some potential improvement in the prediction risk. Further data will enable us to obtain a clearer empirical understanding of the role of the surface information in the measurement of tumor heterogeneity.     

Nonparametric estimation of the concordance correlation coefficient under univariate censoring

Assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects. Lin's (1989, Biometrics 45, 255-268) concordance correlation coefficient (CCC) has become a popular measure of agreement for correlated continuous outcomes. However, commonly used estimation methods for the CCC do not accommodate censored observations and are, therefore, not applicable for survival outcomes. In this article, we estimate the CCC nonparametrically through the bivariate survival function. The proposed estimator of the CCC is proven to be strongly consistent and asymptotically normal, with a consistent bootstrap variance estimator. Furthermore, we propose a time-dependent agreement coefficient as an extension of Lin's (1989) CCC for measuring the agreement between survival times among subjects who survive beyond a specified time point. A nonparametric estimator is developed for the time-dependent agreement coefficient as well. It has the same asymptotic properties as the estimator of the CCC. Simulation studies are conducted to evaluate the performance of the proposed estimators. A real data example from a prostate cancer study is used to illustrate the method.     

Quantification of the Heterogeneity of Prognostic Cellular Biomarkers in Ewing Sarcoma Using Automated Image and Random Survival Forest Analysis

Driven by genomic somatic variation, tumour tissues are typically heterogeneous, yet unbiased quantitative methods are rarely used to analyse heterogeneity at the protein level. Motivated by this problem, we developed automated image segmentation of images of multiple biomarkers in Ewing sarcoma to generate distributions of biomarkers between and within tumour cells. We further integrate high dimensional data with patient clinical outcomes utilising random survival forest (RSF) machine learning. Using material from cohorts of genetically diagnosed Ewing sarcoma with EWSR1 chromosomal translocations, confocal images of tissue microarrays were segmented with level sets and watershed algorithms. Each cell nucleus and cytoplasm were identified in relation to DAPI and CD99, respectively, and protein biomarkers (e.g. Ki67, pS6, Foxo3a, EGR1, MAPK) localised relative to nuclear and cytoplasmic regions of each cell in order to generate image feature distributions. The image distribution features were analysed with RSF in relation to known overall patient survival from three separate cohorts (185 informative cases). Variation in pre-analytical processing resulted in elimination of a high number of non-informative images that had poor DAPI localisation or biomarker preservation (67 cases, 36%). The distribution of image features for biomarkers in the remaining high quality material (118 cases, 10⁴ features per case) were analysed by RSF with feature selection, and performance assessed using internal cross-validation, rather than a separate validation cohort. A prognostic classifier for Ewing sarcoma with low cross-validation error rates (0.36) was comprised of multiple features, including the Ki67 proliferative marker and a sub-population of cells with low cytoplasmic/nuclear ratio of CD99. Through elimination of bias, the evaluation of high-dimensionality biomarker distribution within cell populations of a tumour using random forest analysis in quality controlled tumour material could be achieved. Such an automated and integrated methodology has potential application in the identification of prognostic classifiers based on tumour cell heterogeneity.     

Multiple statistical analysis techniques corroborate intratumor heterogeneity in imaging mass spectrometry datasets of myxofibrosarcoma

MALDI mass spectrometry can generate profiles that contain hundreds of biomolecular ions directly from tissue. Spatially-correlated analysis, MALDI imaging MS, can simultaneously reveal how each of these biomolecular ions varies in clinical tissue samples. The use of statistical data analysis tools to identify regions containing correlated mass spectrometry profiles is referred to as imaging MS-based molecular histology because of its ability to annotate tissues solely on the basis of the imaging MS data. Several reports have indicated that imaging MS-based molecular histology may be able to complement established histological and histochemical techniques by distinguishing between pathologies with overlapping/identical morphologies and revealing biomolecular intratumor heterogeneity. A data analysis pipeline that identifies regions of imaging MS datasets with correlated mass spectrometry profiles could lead to the development of novel methods for improved diagnosis (differentiating subgroups within distinct histological groups) and annotating the spatio-chemical makeup of tumors. Here it is demonstrated that highlighting the regions within imaging MS datasets whose mass spectrometry profiles were found to be correlated by five independent multivariate methods provides a consistently accurate summary of the spatio-chemical heterogeneity. The corroboration provided by using multiple multivariate methods, efficiently applied in an automated routine, provides assurance that the identified regions are indeed characterized by distinct mass spectrometry profiles, a crucial requirement for its development as a complementary histological tool. When simultaneously applied to imaging MS datasets from multiple patient samples of intermediate-grade myxofibrosarcoma, a heterogeneous soft tissue sarcoma, nodules with mass spectrometry profiles found to be distinct by five different multivariate methods were detected within morphologically identical regions of all patient tissue samples. To aid the further development of imaging MS based molecular histology as a complementary histological tool the Matlab code of the agreement analysis, instructions and a reduced dataset are included as supporting information.     

A Robust Alternative to the Schemper–Henderson Estimator of Prediction Error

Summary In clinical applications, the prediction error of survival models has to be taken into consideration to assess the practical suitability of conclusions drawn from these models. Different approaches to evaluate the predictive performance of survival models have been suggested in the literature. In this article, we analyze the properties of the estimator of prediction error developed by Schemper and Henderson (2000 , Biometrics 56, 249–255), which quantifies the absolute distance between predicted and observed survival functions. We provide a formal proof that the estimator proposed by Schemper and Henderson is not robust against misspecification of the survival model, that is, the estimator will only be meaningful if the model family used for deriving predictions has been specified correctly. To remedy this problem, we construct a new estimator of the absolute distance between predicted and observed survival functions. We show that this modified Schemper–Henderson estimator is robust against model misspecification, allowing its practical application to a wide class of survival models. The properties of the Schemper–Henderson estimator and its new modification are illustrated by means of a simulation study and the analysis of two clinical data sets.     

Clinical implication of pretreatment neutrophil to lymphocyte ratio in soft tissue sarcoma

Introduction: Elevated neutrophil to lymphocyte ratio has been identified as a prognostic indicator in malignancies whereas; its association with extremity and trunk soft tissue sarcoma remain unclear. The aim of this study is to determine the utility of full blood neutrophil lymphocyte ratio (NLR) in preoperative diagnosis and its predictive value for survival in patients managed for soft tissue sarcoma of the trunk and extremities. Method: 223 patients who presented with a soft tissue tumor were retrospectively reviewed. The study period was from January 2002-December 2009. Preoperative NLR as well as demographics, clinical and histopathological data were analysed. Results: Full blood NLR was significantly higher in patient with a soft tissue sarcoma compared to benign soft tissue tumors (p < 0.001). Cox regression analysis demonstrated that elevated NLR >5 (p < 0.05) may be an adverse prognostic factor for Overall Survival. Conclusion: The preoperative NLR is a simple, investigation predicting the preoperative diagnosis of a soft tissue sarcoma and a predictor of worse overall survival for patient with a soft tissue sarcoma.     

Logistic regression in capture-recapture models

The effect of population heterogeneity in capture-recapture, or dual registration, models is discussed. An estimator of the unknown population size based on a logistic regression model is introduced. The model allows different capture probabilities across individuals and across capture times. The probabilities are estimated from the observed data using conditional maximum likelihood. The resulting population estimator is shown to be consistent and asymptotically normal. A variance estimator under population heterogeneity is derived. The finite-sample properties of the estimators are studied via simulation. An application to Finnish occupational disease registration data is presented.     

Uniformly minimum variance unbiased estimation of gene diversity

Gene diversity is an important measure of genetic variability in inbred populations. The survival of species in changing environments depends on, among other factors, the genetic variability of the population. In this communication, I have derived the uniformly minimum variance unbiased estimator of gene diversity. The proposed estimator of gene diversity does not assume that the inbreeding coefficient is known. I have also provided the approximate variance of this estimator according to Fisher's method. In addition, I have developed a numerical resampling-based method for obtaining variances and confidence intervals based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. Efficiency in estimation of the gene diversity based on these two estimators is discussed. In accordance with the simulation results, I found that the uniformly minimum variance estimator developed in this report is more accurate for estimation of gene diversity than the maximum likelihood estimator.     

Heterogeneity mapping of protein expression in tumors using quantitative immunofluorescence

Morphologic heterogeneity within an individual tumor is well-recognized by histopathologists in surgical practice. While this often takes the form of areas of distinct differentiation into recognized histological subtypes, or different pathological grade, often there are more subtle differences in phenotype which defy accurate classification (Figure 1). Ultimately, since morphology is dictated by the underlying molecular phenotype, areas with visible differences are likely to be accompanied by differences in the expression of proteins which orchestrate cellular function and behavior, and therefore, appearance. The significance of visible and invisible (molecular) heterogeneity for prognosis is unknown, but recent evidence suggests that, at least at the genetic level, heterogeneity exists in the primary tumor(1,2), and some of these sub-clones give rise to metastatic (and therefore lethal) disease. Moreover, some proteins are measured as biomarkers because they are the targets of therapy (for instance ER and HER2 for tamoxifen and trastuzumab (Herceptin), respectively). If these proteins show variable expression within a tumor then therapeutic responses may also be variable. The widely used histopathologic scoring schemes for immunohistochemistry either ignore, or numerically homogenize the quantification of protein expression. Similarly, in destructive techniques, where the tumor samples are homogenized (such as gene expression profiling), quantitative information can be elucidated, but spatial information is lost. Genetic heterogeneity mapping approaches in pancreatic cancer have relied either on generation of a single cell suspension(3), or on macrodissection(4). A recent study has used quantum dots in order to map morphologic and molecular heterogeneity in prostate cancer tissue(5), providing proof of principle that morphology and molecular mapping is feasible, but falling short of quantifying the heterogeneity. Since immunohistochemistry is, at best, only semi-quantitative and subject to intra- and inter-observer bias, more sensitive and quantitative methodologies are required in order to accurately map and quantify tissue heterogeneity in situ. We have developed and applied an experimental and statistical methodology in order to systematically quantify the heterogeneity of protein expression in whole tissue sections of tumors, based on the Automated QUantitative Analysis (AQUA) system(6). Tissue sections are labeled with specific antibodies directed against cytokeratins and targets of interest, coupled to fluorophore-labeled secondary antibodies. Slides are imaged using a whole-slide fluorescence scanner. Images are subdivided into hundreds to thousands of tiles, and each tile is then assigned an AQUA score which is a measure of protein concentration within the epithelial (tumor) component of the tissue. Heatmaps are generated to represent tissue expression of the proteins and a heterogeneity score assigned, using a statistical measure of heterogeneity originally used in ecology, based on the Simpson's biodiversity index(7). To date there have been no attempts to systematically map and quantify this variability in tandem with protein expression, in histological preparations. Here, we illustrate the first use of the method applied to ER and HER2 biomarker expression in ovarian cancer. Using this method paves the way for analyzing heterogeneity as an independent variable in studies of biomarker expression in translational studies, in order to establish the significance of heterogeneity in prognosis and prediction of responses to therapy.     

Sample size recalculation in multicenter randomized controlled clinical trials based on noncomparative data

Many late-phase clinical trials recruit subjects at multiple study sites. This introduces a hierarchical structure into the data that can result in a power-loss compared to a more homogeneous single-center trial. Building on a recently proposed approach to sample size determination, we suggest a sample size recalculation procedure for multicenter trials with continuous endpoints. The procedure estimates nuisance parameters at interim from noncomparative data and recalculates the sample size required based on these estimates. In contrast to other sample size calculation methods for multicenter trials, our approach assumes a mixed effects model and does not rely on balanced data within centers. It is therefore advantageous, especially for sample size recalculation at interim. We illustrate the proposed methodology by a study evaluating a diabetes management system. Monte Carlo simulations are carried out to evaluate operation characteristics of the sample size recalculation procedure using comparative as well as noncomparative data, assessing their dependence on parameters such as between-center heterogeneity, residual variance of observations, treatment effect size and number of centers. We compare two different estimators for between-center heterogeneity, an unadjusted and a bias-adjusted estimator, both based on quadratic forms. The type 1 error probability as well as statistical power are close to their nominal levels for all parameter combinations considered in our simulation study for the proposed unadjusted estimator, whereas the adjusted estimator exhibits some type 1 error rate inflation. Overall, the sample size recalculation procedure can be recommended to mitigate risks arising from misspecified nuisance parameters at the planning stage.     

Prediction of Recurrence by Preoperative Intratumoral FDG Uptake Heterogeneity in Endometrioid Endometrial Cancer

PURPOSE: To investigate the prognostic value of preoperative intratumoral ¹⁸F-FDG uptake heterogeneity (IFH) derived from positron emission tomography (PET)/computed tomography (CT) in patients with endometrioid endometrial cancer. METHODS: We retrospectively evaluated clinicopathological data from patients with pathologically proven endometrioid endometrial cancer who had undergone ¹⁸F-FDG PET/CT scans before surgery. Patients were divided into two groups according to their IFH. The main outcome measure was disease-free survival (DFS). RESULTS: Between January 2010 and January 2015, data from 72 patients were available for analysis. The median duration of DFS was 23 months (range, 6 to 57 months), and 4 (5.6%) patients experienced recurrence. There were significant differences in tumor size, IFH, and DFS between patients with and without recurrence. In regression analysis, high IFH value [P = .007, hazard ratio (HR) 2.545, 95% confidence interval (CI) 1.468-8.674] was the only independent risk factor for recurrence. The Kaplan-Meier survival graphs showed that DFS significantly differed in groups categorized based on IFH (P < .001, log-rank test). CONCLUSIONS: Preoperative IFH measured by ¹⁸F-FDG PET/CT was associated with recurrence of endometrioid endometrial cancer. The finding supports evidence that FDG-based heterogeneity can be a novel and useful predictor of endometrioid endometrial cancer recurrence.     

Quality-adjusted survival estimation with periodic observations

Quality-adjusted survival is a measure that integrates both longevity and quality-of-life information. The analysis of quality-adjusted survival in a clinical study with data collected at periodic intervals encounters difficulties due to incomplete information. Based on observed time points, the time axis is partitioned into a set of disjoint time intervals, and under a Markovian assumption on patient's health status, the expected quality-adjusted survival is estimated as the summed product of the quality of life and its mean sojourn time of each health state within partitioned intervals. It is shown that the estimator is asymptotically normal with a simple variance calculation. A simulation study is conducted to investigate the behavior of the estimator, and a stroke study illustrates the use of the estimator.     

A quality control algorithm for DNA sequencing projects.

Heterologous DNA sequences from rearrangements with the genomes of host cells, genomic fragments from hybrid cells, or impure tissue sources can threaten the purity of libraries that are derived from RNA or DNA. Hybridization methods can only detect contaminants from known or suspected heterologous sources, and whole library screening is technically very difficult. Detection of contaminating heterologous clones by sequence alignment is only possible when related sequences are present in a known database. We have developed a statistical test to identify heterologous sequences that is based on the differences in hexamer composition of DNA from different organisms. This test does not require that sequences similar to potential heterologous contaminants are present in the database, and can in principle detect contamination by previously unknown organisms. We have applied this test to the major public expressed sequence tag (EST) data sets to evaluate its utility as a quality control measure and a peer evaluation tool. There is detectable heterogeneity in most human and C.elegans EST data sets but it is not apparently associated with cross-species contamination. However, there is direct evidence for both yeast and bacterial sequence contamination in some public database sequences annotated as human. Results obtained with the hexamer test have been confirmed with similarity searches using sequences from the relevant data sets.     

Branching tree model with fractal vascular resistance explains fractal perfusion heterogeneity

Perfusion heterogeneities in organs such as the heart obey a power law as a function of scale, a behavior termed "fractal." An explanation of why vascular systems produce such a specific perfusion pattern is still lacking. An intuitive branching tree model is presented that reveals how this behavior can be generated as a consequence of scale-independent branching asymmetry and fractal vessel resistance. Comparison of computer simulations to experimental data from the sheep heart shows that the values of the two free model parameters are realistic. Branching asymmetry within the model is defined by the relative tissue volume being fed by each branch. Vessel ordering for fractal analysis of morphology based on fed or drained tissue volumes is preferable to the commonly used Strahler system, which is shown to depend on branching asymmetry. Recently, noninvasive imaging techniques such as PET and MRI have been used to measure perfusion heterogeneity. The model allows a physiological interpretation of the measured fractal parameters, which could in turn be used to characterize vascular morphology and function.     

Efficient estimation of the distribution of quality-adjusted survival time

Quality of life is an important aspect in evaluation of clinical trials of chronic diseases, such as cancer and AIDS. Quality-adjusted survival analysis is a method that combines both the quantity and quality of a patient's life into one single measure. In this paper, we discuss the efficiency of weighted estimators for the distribution of quality-adjusted survival time. Using the general representation theorem for missing data processes, we are able to derive an estimator that is more efficient than the one proposed in Zhao and Tsiatis (1997, Biometrika 84, 339-348). Simulation experiments are conducted to assess the small sample properties of this estimator and to compare it with the semiparametric efficiency bound. The value of this estimator is demonstrated from an application of the method to a data set obtained from a breast cancer clinical trial.     

Nonparametric estimation of the survival function when cause of death is uncertain

A nonparametric estimator for the survival function, accommodating censored survival times and uncertainty in the assignment of cause of death, is proposed. For example, in a carcinogenicity experiment the data on each animal may consist of an observed age-at-death and some indication of the probability that the tumor type under study caused death. An estimator of the net survival function, for time-to-death due to the cause of interest, is developed. Under certain assumptions, the proposed estimator is consistent and asymptotically normally distributed. Monte Carlo simulations were used to compare this estimator with the Kaplan-Meier estimator. Forcing the cause of death to be specified with certainty, as required by the Kaplan-Meier estimator, may result in substantial biases.     

Multispecies coexistence of trees in tropical forests: spatial signals of topographic niche differentiation increase with environmental heterogeneity

Neutral and niche theories give contrasting explanations for the maintenance of tropical tree species diversity. Both have some empirical support, but methods to disentangle their effects have not yet been developed. We applied a statistical measure of spatial structure to data from 14 large tropical forest plots to test a prediction of niche theory that is incompatible with neutral theory: that species in heterogeneous environments should separate out in space according to their niche preferences. We chose plots across a range of topographic heterogeneity, and tested whether pairwise spatial associations among species were more variable in more heterogeneous sites. We found strong support for this prediction, based on a strong positive relationship between variance in the spatial structure of species pairs and topographic heterogeneity across sites. We interpret this pattern as evidence of pervasive niche differentiation, which increases in importance with increasing environmental heterogeneity.     

Using the tangle: a consistent construction of phylogenetic distance matrices for quartets

Distance based algorithms are a common technique in the construction of phylogenetic trees from taxonomic sequence data. The first step in the implementation of these algorithms is the calculation of a pairwise distance matrix to give a measure of the evolutionary change between any pair of the extant taxa. A standard technique is to use the log det formula to construct pairwise distances from aligned sequence data. We review a distance measure valid for the most general models, and show how the log det formula can be used as an estimator thereof. We then show that the foundation upon which the log det formula is constructed can be generalized to produce a previously unknown estimator which improves the consistency of the distance matrices constructed from the log det formula. This distance estimator provides a consistent technique for constructing quartets from phylogenetic sequence data under the assumption of the most general Markov model of sequence evolution.     

Clinical implication of pretreatment neutrophil to lymphocyte ratio in soft tissue sarcoma

Introduction: Elevated neutrophil to lymphocyte ratio has been identified as a prognostic indicator in malignancies whereas; its association with extremity and trunk soft tissue sarcoma remain unclear. The aim of this study is to determine the utility of full blood neutrophil lymphocyte ratio (NLR) in preoperative diagnosis and its predictive value for survival in patients managed for soft tissue sarcoma of the trunk and extremities.

Method: 223 patients who presented with a soft tissue tumor were retrospectively reviewed. The study period was from January 2002–December 2009. Preoperative NLR as well as demographics, clinical and histopathological data were analysed.

Results: Full blood NLR was significantly higher in patient with a soft tissue sarcoma compared to benign soft tissue tumors (p < 0.001). Cox regression analysis demonstrated that elevated NLR >5 (p < 0.05) may be an adverse prognostic factor for Overall Survival.

Conclusion: The preoperative NLR is a simple, investigation predicting the preoperative diagnosis of a soft tissue sarcoma and a predictor of worse overall survival for patient with a soft tissue sarcoma.