Regression on Quantile Residual Life

Summary A time‐specific log‐linear regression method on quantile residual lifetime is proposed. Under the proposed regression model, any quantile of a time‐to‐event distribution among survivors beyond a certain time point is associated with selected covariates under right censoring. Consistency and asymptotic normality of the regression estimator are established. An asymptotic test statistic is proposed to evaluate the covariate effects on the quantile residual lifetimes at a specific time point. Evaluation of the test statistic does not require estimation of the variance–covariance matrix of the regression estimators, which involves the probability density function of the survival distribution with censoring. Simulation studies are performed to assess finite sample properties of the regression parameter estimator and test statistic. The new regression method is applied to a breast cancer data set with long‐term follow‐up to estimate the patients' median residual lifetimes, adjusting for important prognostic factors.     

Nonparametric inference on cause‐specific quantile residual life

In medical research, investigators are often interested in inferring time‐to‐event distributions under competing risks. It is well known, however, that the naive approach based on the Kaplan–Meier method to estimate the proportion of cause‐specific events overestimates the true quantity. In this paper, we show that the quantile residual life function, a natural and popular summary measure of survival data, could be also seriously affected by the competing events. An existing two‐sample test statistic for inference on median residual life is modified for competing risks data, which does not involve estimation of the improper probability density function of the subdistribution of cause‐specific events under censoring. Simulation results demonstrate that the test statistic controls the type 1 error probabilities reasonably well. The proposed method is applied to a real data example from a large‐scale phase III breast cancer study.     

Testing equality of survival functions of quality-adjusted lifetime

We present a method for comparing the survival functions of quality-adjusted lifetime from two treatments. This test statistic becomes the ordinary log-rank test when quality-adjusted lifetime is the same as the survival time. Simulation experiments are conducted to examine the behavior of our proposed test statistic under both null and alternative hypotheses. In addition, we apply our method to a breast cancer trial for comparing the distribution of quality-adjusted lifetime between two treatment regimes.     

Median Tests for Censored Survival Data; a Contingency Table Approach

Summary The median failure time is often utilized to summarize survival data because it has a more straightforward interpretation for investigators in practice than the popular hazard function. However, existing methods for comparing median failure times for censored survival data either require estimation of the probability density function or involve complicated formulas to calculate the variance of the estimates. In this article, we modify a K ‐sample median test for censored survival data ( Brookmeyer and Crowley, 1982 , Journal of the American Statistical Association 77, 433–440) through a simple contingency table approach where each cell counts the number of observations in each sample that are greater than the pooled median or vice versa. Under censoring, this approach would generate noninteger entries for the cells in the contingency table. We propose to construct a weighted asymptotic test statistic that aggregates dependent χ² ‐statistics formed at the nearest integer points to the original noninteger entries. We show that this statistic follows approximately a χ² ‐distribution with k? 1 degrees of freedom. For a small sample case, we propose a test statistic based on combined p ‐values from Fisher’s exact tests, which follows a χ² ‐distribution with 2 degrees of freedom. Simulation studies are performed to show that the proposed method provides reasonable type I error probabilities and powers. The proposed method is illustrated with two real datasets from phase III breast cancer clinical trials.     

Comparability of segmented line regression models

Segmented line regression models, which are composed of continuous linear phases, have been applied to describe changes in rate trend patterns. In this article, we propose a procedure to compare two segmented line regression functions, specifically to test (i) whether the two segmented line regression functions are identical or (ii) whether the two mean functions are parallel allowing different intercepts. A general form of the test statistic is described and then the permutation procedure is proposed to estimate the p-value of the test. The permutation test is compared to an approximate F-test in terms of the p-value estimation and the performance of the permutation test is studied via simulations. The tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states.     

Semiparametric estimation of proportional mean residual life model in presence of censoring

A mean residual life function is the average remaining life of a surviving subject, as it varies with time. The proportional mean residual life model was proposed by Oakes and Dasu (1990, Biometrika77, 409-410) in regression analysis to study its association with related covariates in absence of censoring. In this article, we develop some semiparametric estimation procedures to take censoring into account. The proposed methodology is evaluated via simulation studies, and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients.     

Identifying gene expression changes in breast cancer that distinguish early and late relapse among uncured patients

MOTIVATION: In recent years, microarray technology has revealed many tumor-expressed genes prognostic of clinical outcomes in early-stage breast cancer patients. However, in the presence of cured patients, evaluating gene effect on time to relapse is quite complex since it may affect either the probability of never experiencing a relapse (cure effect) or the time to relapse among the uncured patients (disease progression effect) or both. In this context, we propose a simple and an efficient method for identifying gene expression changes that characterize early and late recurrence for uncured patients. RESULTS: Simulation results show the good performance of the proposed statistic for detecting a disease progression effect. In a study of early-stage breast cancer, our results show that the proposed statistic provides a more powerful basis for gene selection than the classical Cox model-based statistic. From a biological perspective, many of the genes identified here as associated with the speed of disease recurrence have known roles in tumorigenesis.     

In vivo resolution of multiexponential decays of multiple near-infrared molecular probes by fluorescence lifetime-gated whole-body time-resolved diffuse optical imaging

The biodistribution of two near-infrared fluorescent agents was assessed in vivo by time-resolved diffuse optical imaging. Bacteriochlorophyll a (BC) and cypate-glysine-arginine-aspartic acid-serine-proline-lysine-OH (Cyp-GRD) were administered separately or combined to mice with subcutaneous xenografts of human breast adenocarcinoma and slow-release estradiol pellets for improved tumor growth. The same excitation (780 nm) and emission (830 nm) wavelengths were used to image the distinct fluorescence lifetime distribution of the fluorescent molecular probes in the mouse cancer model. Fluorescence intensity and lifetime maps were reconstructed after raster-scanning whole-body regions of interest by time-correlated single-photon counting. Each captured temporal point-spread function (TPSF) was deconvolved using both a single and a multiexponental decay model to best determine the measured fluorescence lifetimes. The relative signal from each fluorophore was estimated for any region of interest included in the scanned area. Deconvolution of the individual TPSFs from whole-body fluorescence intensity scans provided corresponding lifetime images for comparing individual component biodistribution. In vivo fluorescence lifetimes were determined to be 0.8 ns (Cyp-GRD) and 2 ns (BC). This study demonstrates that the relative biodistribution of individual fluorophores with similar spectral characteristics can be compartmentalized by using the time-domain fluorescence lifetime gating method.     

Maximum of the weighted Kaplan-Meier tests with application to cancer prevention and screening trials

A class of maximum weighted Kaplan-Meier test statistics is described where the weight functions are chosen from a family of smooth functions. The investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials. A simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones. We illustrate the procedure using data from a clinical trial of a breast cancer screening program.     

A bayesian random-effects markov model for tumor progression in women with a family history of breast cancer

SUMMARY: It makes intuitive sense to model the natural history of breast cancer, tumor progression from preclinical screen-detectable phase (PCDP) to clinical disease, as a multistate process, but the multilevel structure of the available data, which generally comes from cluster (family)-based service screening programs, makes the required parameter estimation intractable because there is a correlation between screening rounds in the same individual, and between subjects within clusters (families). There is also residual heterogeneity after adjusting for covariates. We therefore proposed a Bayesian hierarchical multistate Markov model with fixed and random effects and applied it to data from a high-risk group (women with a family history of breast cancer) participating in a family-based screening program for breast cancer. A total of 4867 women attended (representing 4464 families) and by the end of 2002, a total of 130 breast cancer cases were identified. Parameter estimation was carried out using Markov chain Monte Carlo (MCMC) simulation and the Bayesian software package WinBUGS. Models with and without random effects were considered. Our preferred model included a random-effect term for the transition rate from preclinical to clinical disease (sigma(2)(2f)), which was estimated to be 0.50 (95% credible interval = 0.22-1.49). Failure to account for this random effect was shown to lead to bias. The incorporation of covariates into multistate models with random effect not only reduced residual heterogeneity but also improved the convergence of stationary distribution. Our proposed Bayesian hierarchical multistate model is a valuable tool for estimating the rate of transitions between disease states in the natural history of breast cancer (and possibly other conditions). Unlike existing models, it can cope with the correlation structure of multilevel screening data, covariates, and residual (unexplained) variation.     

Local multiplicity adjustment for the spatial scan statistic using the Gumbel distribution

The spatial scan statistic is an important and widely used tool for cluster detection. It is based on the simultaneous evaluation of the statistical significance of the maximum likelihood ratio test statistic over a large collection of potential clusters. In most cluster detection problems, there is variation in the extent of local multiplicity across the study region. For example, using a fixed maximum geographic radius for clusters, urban areas typically have many overlapping potential clusters, whereas rural areas have relatively few. The spatial scan statistic does not account for local multiplicity variation. We describe a previously proposed local multiplicity adjustment based on a nested Bonferroni correction and propose a novel adjustment based on a Gumbel distribution approximation to the distribution of a local scan statistic. We compare the performance of all three statistics in terms of power and a novel unbiased cluster detection criterion. These methods are then applied to the well-known New York leukemia dataset and a Wisconsin breast cancer incidence dataset.     

Regression analysis of grouped survival data with application to breast cancer data

Use of the proportional hazards regression model (Cox 1972) substantially liberalized the analysis of censored survival data with covariates. Available procedures for estimation of the relative risk parameter, however, do not adequately handle grouped survival data, or large data sets with many tied failure times. The grouped data version of the proportional hazards model is proposed here for such estimation. Asymptotic likelihood results are given, both for the estimation of the regression coefficient and the survivor function. Some special results are given for testing the hypothesis of a zero regression coefficient which leads, for example, to a generalization of the log-rank test for the comparison of several survival curves. Application to breast cancer data, from the National Cancer Institute-sponsored End Results Group, indicates that previously noted race differences in breast cancer survival times are explained to a large extent by differences in disease extent and other demographic characteristics at diagnosis.     

The favorable prognostic significance of surgery-induced hyperprolactinemia in node-positive breast cancer patients: ten-year disease-free survival results

It has been shown that each manipulation of the mammary region, including breast surgery, may stimulate prolactin secretion. However, it has also been observed that in more than 50% of breast cancer patients surgical removal of the tumor is not followed by enhanced prolactin secretion. This might be indicative of an altered psychoneuroendocrine control of the mammary gland, which could lead to the onset of more biologically aggressive breast cancer. In fact, surgery-induced hyperprolactinemia has been proven to be associated with a better prognosis in terms of survival in node-negative breast cancer patients. The present study was performed to investigate the impact of postoperative hyperprolactinemia on the disease-free survival (DFS) of breast cancer patients with axillary node involvement. The study included 100 consecutive node-positive breast cancer patients who were followed for at least 10 years. Surgery-induced hyperprolactinemia occurred in 45/100 (45%) patients without any significant correlation with the main prognostic variables including number of involved nodes and ER status. The two groups of patients received the same adjuvant therapies. After a median follow-up of 151 months, the recurrence rate in patients with surgery-induced hyperprolactinemia was significantly lower than in patients with no postoperative hyperprolactinemia (23/45 vs 43/55, p<0.01). Moreover, DFS was significantly longer in hyperprolactinemic patients than in patients who had no enhanced secretion of prolactin postoperatively. In agreement with the results described previously in node-negative breast cancer, our study demonstrates the favorable prognostic significance of surgery-induced hyperprolactinemia in terms of DFS duration also in breast cancer patients with axillary node involvement, independent of the other well-known prognostic variables, thereby confirming that the psychoneuroendocrine status of cancer patients may influence the prognosis of their disease.     

Efficient p-value evaluation for resampling-based tests

The resampling-based test, which often relies on permutation or bootstrap procedures, has been widely used for statistical hypothesis testing when the asymptotic distribution of the test statistic is unavailable or unreliable. It requires repeated calculations of the test statistic on a large number of simulated data sets for its significance level assessment, and thus it could become very computationally intensive. Here, we propose an efficient p-value evaluation procedure by adapting the stochastic approximation Markov chain Monte Carlo algorithm. The new procedure can be used easily for estimating the p-value for any resampling-based test. We show through numeric simulations that the proposed procedure can be 100-500 000 times as efficient (in term of computing time) as the standard resampling-based procedure when evaluating a test statistic with a small p-value (e.g. less than 10( - 6)). With its computational burden reduced by this proposed procedure, the versatile resampling-based test would become computationally feasible for a much wider range of applications. We demonstrate the application of the new method by applying it to a large-scale genetic association study of prostate cancer.     

Interpretation of fluorescence decays using a power-like model

A power-like decay function, characterized by the mean excited-state lifetime and relative variance of lifetime fluctuation around the mean value, was applied in analysis of fluorescence decays measured with the aid of time-correlated single photon counting. We have examined the fluorescence decay, in neutral aqueous medium, of tyrosine (L-tyrosine and N-acetyl-L-tyrosinamide), and of the tyrosine residues in a tryptophan-free protein, the enzyme purine nucleoside phosphorylase from Escherichia coli in a complex with formycin A (an inhibitor), and orthophosphate (a co-substrate). Tryptophan fluorescence decay was examined in neutral aqueous medium for L-tryptophan, N-acetyl-L-tryptophanamide, and for two tryptophan residues in horse liver alcohol dehydrogenase. To detect solvent effect, fluorescence decay of Nz-acetyl-L-tryptophanamide in aqueous medium was compared with that in dioxan. Hitherto, complex fluorescence decays have usually been analyzed with the aid of a multiexponential model, but interpretation of the individual exponential terms (i.e., pre-exponential amplitudes and fluorescence lifetimes), has not been adequately characterized. In such cases the intensity decays were also analyzed in terms of the lifetime distribution as a consequence of an interaction of fluorophore with environment. We show that the power-like decay function, which can be directly obtained from the gamma distribution of fluorescence lifetimes, is simpler and provides good fits to highly complex fluorescence decays as well as to a purely single-exponential decay. Possible interpretation of the power-like model is discussed.     

Human small breast epithelial mucin: the promise of a new breast tumor biomarker

Breast cancer remains one of the most frequently diagnosed cancers today. In developed countries, one in eight women is expected to present with breast cancer within her lifetime and an estimated 1,000,000 cases are detected each year worldwide (Canadian Cancer Statistics, http://www.cancer.ca/vgn/images/ portal/cit_86751114/14/33/1959864 11niw_stats2004_en.pdf). For women with recurrent disease, the median time of survival is about 2 years. Despite optimal surgery, adjuvant irradiation, hormonal treatment, and chemotherapy, approximately 30% of patients with localized breast cancer finally develop distant metastases. Early detection, which enables intervention at a localized and potentially curable stage, remains a central goal in breast cancer treatment. Indeed, the 5-year survival rate for women with breast cancer has been shown to increase dramatically when the disease is diagnosed at an early stage: from less than 25% in women with disseminated cancer to about 75% in patients with regional disease and over 95% in women with a localized tumor (Breast Cancer Facts and Figures, 2001-2002, http://www.cancer.org/downloads/STT/BrCaFF 2001.pdf). Unfortunately, only 60% of all breast cancers are diagnosed at a local stage. Any improvement in early detection through identification of tumor biomarkers would have a significant impact on reducing overall breast cancer mortality.     

Median percent change: A robust alternative for assessing temporal trends

A typical summary statistic for temporal trends is the average percent change (APC). The APC is estimated by using a generalized linear model, usually under the assumption of linearity on the logarithmic scale. A serious limitation of least-squares type estimators is their sensitivity to outliers. The goal of this study is twofold: firstly, we propose a robust and easy-to-compute measure of the temporal trend based on the median of the rates (median percent change – MPC), rather than their mean, under the hypothesis of constant relative change; secondly, we investigate the performance of several models for estimating the rate of change when some of the most common model assumptions are violated. We provide some guidance on the practices of the estimation of temporal trends when using different models under different circumstances. The robustness property of the median is assessed in a simulation study, which shows that the MPC provides strong reductions in estimation bias and variance in presence of outliers. We also demonstrate how a mathematical property of the median helps addressing the issue of zero counts when estimating trends on the log-scale. Finally, we analyzed an English cancer registration dataset to illustrate the proposed method. We believe that, as a good practice, both APC and MPC should be presented when sensitivity issues arise.     

Camera: a competitive gene set test accounting for inter-gene correlation

Competitive gene set tests are commonly used in molecular pathway analysis to test for enrichment of a particular gene annotation category amongst the differential expression results from a microarray experiment. Existing gene set tests that rely on gene permutation are shown here to be extremely sensitive to inter-gene correlation. Several data sets are analyzed to show that inter-gene correlation is non-ignorable even for experiments on homogeneous cell populations using genetically identical model organisms. A new gene set test procedure (CAMERA) is proposed based on the idea of estimating the inter-gene correlation from the data, and using it to adjust the gene set test statistic. An efficient procedure is developed for estimating the inter-gene correlation and characterizing its precision. CAMERA is shown to control the type I error rate correctly regardless of inter-gene correlations, yet retains excellent power for detecting genuine differential expression. Analysis of breast cancer data shows that CAMERA recovers known relationships between tumor subtypes in very convincing terms. CAMERA can be used to analyze specified sets or as a pathway analysis tool using a database of molecular signatures.     

Parallel assessment of circulatory cell-free DNA by PCR and nucleosomes by ELISA in breast tumors

OBJECTIVES: In order to assess the potential biomolecules for breast cancer, we analyzed in parallel the levels of cell-free glyceraldehyde 3-phosphate dehydrogenase (GAPDH) and cell-free nucleosomes in serum samples from patients with benign and malignant breast tumors. The levels of cell-free DNA obtained by quantitative PCR were compared with those obtained by enzyme-linked immunosorbent assay (ELISA). METHODS: Twenty-three patients with benign breast tumors, 27 patients with breast cancer, and 32 age-matched healthy women were recruited. The amounts of serum nucleosomes were analyzed by ELISA and the levels of cell-free GAPDH were measured by real-time quantitative PCR. The correlation between nucleosome and cell-free GAPDH levels was examined using the Spearman rank test. RESULTS: The levels of cell-free GAPDH were significantly higher in the serum samples of patients with benign and malignant breast tumors than in those of the control group (median 37,966 GE/mL, range 3,802-130,104 versus 11,770 GE/mL, range 2,198-73,522, p=0.035 and median 40,698 GE/mL, range 3,644-192,482 versus 11,770 GE/mL range 2,198-73,522, p=0.001). The concentration of cell-free GAPDH correlated significantly with the quantities of nucleosomes in serum samples (r=0.451, p=0.000). There was, however, no significant difference between healthy individuals and women with benign breast tumors or breast cancer in terms of nucleosomes determined by ELISA. CONCLUSION: Our data suggest that the cell-free serum GAPDH DNA assayed by quantitative PCR is a better biomarker than nucleosomes assayed by ELISA in patients with breast tumors.     

Modified test statistics by inter-voxel variance shrinkage with an application to f MRI

Functional magnetic resonance imaging (f MRI) is a noninvasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of f MRI studies is to identify localized brain regions where neuronal activation levels vary between groups. Single voxel t-tests have been commonly used to determine whether activation related to the protocol differs across groups. Due to the generally limited number of subjects within each study, accurate estimation of variance at each voxel is difficult. Thus, combining information across voxels is desirable in order to improve efficiency. Here, we construct a hierarchical model and apply an empirical Bayesian framework for the analysis of group f MRI data, employing techniques used in high-throughput genomic studies. The key idea is to shrink residual variances by combining information across voxels and subsequently to construct an improved test statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances toward a common value. The shrunken estimator for voxel-specific variance components on the group analyses outperforms the classical residual error estimator in terms of mean-squared error. Moreover, the shrunken test statistic decreases false-positive rates when testing differences in brain contrast maps across a wide range of simulation studies. This methodology was also applied to experimental data regarding a cognitive activation task.