Discretizing a Normal Prior for Change Point Estimation in Switching Regressions

Bayes decision procedures are considered for change point estimation in the simple bilinear segmented model. A discretized normal prior density is employed as the prior distribution for the change point index. Posterior probability functions are developed for this index under a vague prior formulation on the regression parameters. The procedure is applied to an example involving mercury toxicity data.     

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.     

Adjusted regression trend test for a multicenter clinical trial

Studies using a series of increasing doses of a compound, including a zero dose control, are often conducted to study the effect of the compound on the response of interest. For a one-way design, Tukey et al. (1985, Biometrics 41, 295-301) suggested assessing trend by examining the slopes of regression lines under arithmetic, ordinal, and arithmetic-logarithmic dose scalings. They reported the smallest p-value for the three significance tests on the three slopes for safety assessments. Capizzi et al. (1992, Biometrical Journal 34, 275-289) suggested an adjusted trend test, which adjusts the p-value using a trivariate t-distribution, the joint distribution of the three slope estimators. In this paper, we propose an adjusted regression trend test suitable for two-way designs, particularly for multicenter clinical trials. In a step-down fashion, the proposed trend test can be applied to a multicenter clinical trial to compare each dose with the control. This sequential procedure is a closed testing procedure for a trend alternative. Therefore, it adjusts p-values and maintains experimentwise error rate. Simulation results show that the step-down trend test is overall more powerful than a step-down least significant difference test.     

Analysis of dose-response effects on gene expression data with comparison of two microarray platforms

MOTIVATION: The problems of analyzing dose effects on gene expression are gaining attention in biomedical research. A specific challenge is to detect genes with expression levels that change according to dose levels in a non-random manner, but nonetheless may be considered as potential biomarkers. METHOD: We are among the first to formally apply a tool that uses an isotonic (monotonic) regression approach to this area of study. We introduce a test statistic to select genes with significant dose-response expression in a monotonic fashion based on a permutation procedure. We then compare the results with those achieved from the application of a likelihood ratio-based test. RESULTS: We apply the isotonic regression approach to a study of gene expression in the RKO colon carcinoma cell line in response to varying dosage levels of the chemotherapeutic agent 5-fluorouracil. A feature of both Affymetrix and printed 75mer oligomer cDNA arrays produced from the same samples provides an opportunity to compare the two microarray platforms. AVAILABILITY: Statistical software S-plus Code to implement the method is available from the authors. CONTACT: kcoombes@mdanderson.org     

Precision Intervals for Estimates of the Difference in Success Rates for Binary Random Variables Based on the Permutation Principle

Fisher's exact test is a very commonly applied test in clinical trials with a binary outcome variable (e.g. success/failure). However confidence statements about the difference of success rates are usually based on the normal approximation. This may sometimes lead to the confusing statement that the test is statistically significant at a prespecified level while the corresponding confidence interval includes the zero difference and vice versa. Here, we construct precision intervals for the difference of success rates from two independent samples based on the permutation principle which are in perfect agreement with the discrete (permutation) test and compare it to examples from the literature. APL programs are provided.     

An age-stratified poisson model for comparing trends in cancer rates across overlapping regions

The annual percent change (APC) has been used as a measure to describe the trend in the age-adjusted cancer incidence or mortality rate over relatively short time intervals. The yearly data on these age-adjusted rates are available from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute. The traditional methods to estimate the APC is to fit a linear regression of logarithm of age-adjusted rates on time using the least squares method or the weighted least squares method, and use the estimate of the slope parameter to define the APC as the percent change in the rates between two consecutive years. For comparing the APC for two regions, one uses a t-test which assumes that the two datasets on the logarithm of the age-adjusted rates are independent and normally distributed with a common variance. Two modifications of this test, when there is an overlap between the two regions or between the time intervals for the two datasets have been recently developed. The first modification relaxes the assumption of the independence of the two datasets but still assumes the common variance. The second modification relaxes the assumption of the common variance also, but assumes that the variances of the age-adjusted rates are obtained using Poisson distributions for the mortality or incidence counts. In this paper, a unified approach to the problem of estimating the APC is undertaken by modeling the counts to follow an age-stratified Poisson regression model, and by deriving a corrected Z -test for testing the equality of two APCs. A simulation study is carried out to assess the performance of the test and an application of the test to compare the trends, for a selected number of cancer sites, for two overlapping regions and with varied degree of overlapping time intervals is presented.     

Unconditional Exact Tests for Equivalence or Noninferiority for Paired Binary Endpoints

Problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions. When the sample size is small, the asymptotic tests may not be reliable. This article proposes an unconditional exact test procedure to assess equivalence or noninferiority. Two statistics, a sample-based test statistic and a restricted maximum likelihood estimation (RMLE)-based test statistic, to define the rejection region of the exact test are considered. We show the p-value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis. Assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits. We also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics. A typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods. The p-value from the unconditional exact tests is generally larger than the p-value from the asymptotic tests. In other words, an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test.     

A support vector machine based test for incongruence between sets of trees in tree space

ABSTRACT: BACKGROUND: The increased use of multi-locus data sets for phylogenetic reconstruction has increased the need to determine whether a set of gene trees significantly deviate from the phylogenetic patterns of other genes. Such unusual gene trees may have been influenced by other evolutionary processes such as selection, gene duplication, or horizontal gene transfer. RESULTS: Motivated by this problem we propose a nonparametric goodness-of-fit test for two empirical distributions of gene trees, and we developed the software GeneOut to estimate a p-value for the test. Our approach maps trees into a multi-dimensional vector space and then applies support vector machines (SVMs) to measure the separation between two sets of pre-defined trees. We use a permutation test to assess the significance of the SVM separation. To demonstrate the performance of GeneOut, we applied it to the comparison of gene trees simulated within different species trees across a range of species tree depths. Applied directly to sets of simulated gene trees with large sample sizes, GeneOut was able to detect very small differences between two set of gene trees generated under different species trees. Our statistical test can also include tree reconstruction into its test framework through a variety of phylogenetic optimality criteria. When applied to DNA sequence data simulated from different sets of gene trees, results in the form of receiver operating characteristic (ROC) curves indicated that GeneOut performed well in the detection of differences between sets of trees with different distributions in a multi-dimensional space. Furthermore, it controlled false positive and false negative rates very well, indicating a high degree of accuracy. CONCLUSIONS: The non-parametric nature of our statistical test provides fast and efficient analyses, and makes it an applicable test for any scenario where evolutionary or other factors can lead to trees with different multi-dimensional distributions. The software GeneOut is freely available under the GNU public license.     

Rapid Testing of SNPs and Gene-Environment Interactions in Case-Parent Trio Data Based on Exact Analytic Parameter Estimation

Summary Case-parent trio studies concerned with children affected by a disease and their parents aim to detect single nucleotide polymorphisms (SNPs) showing a preferential transmission of alleles from the parents to their affected offspring. A popular statistical test for detecting such SNPs associated with disease in this study design is the genotypic transmission/disequilibrium test (gTDT) based on a conditional logistic regression model, which usually needs to be fitted by an iterative procedure. In this article, we derive exact closed-form solutions for the parameter estimates of the conditional logistic regression models when testing for an additive, a dominant, or a recessive effect of a SNP, and show that such analytic parameter estimates also exist when considering gene-environment interactions with binary environmental variables. Because the genetic model underlying the association between a SNP and a disease is typically unknown, it might further be beneficial to use the maximum over the gTDT statistics for the possible effects of a SNP as test statistic. We therefore propose a procedure enabling a fast computation of the test statistic and the permutation-based p-value of this MAX gTDT. All these methods are applied to whole-genome scans of the case-parent trios from the International Cleft Consortium. These applications show our procedures dramatically reduce the required computing time compared to the conventional iterative methods allowing, for example, the analysis of hundreds of thousands of SNPs in a few minutes instead of several hours.     

Testing inflated zeros in binomial regression models

Binomial regression models are commonly applied to proportion data such as those relating to the mortality and infection rates of diseases. However, it is often the case that the responses may exhibit excessive zeros; in such cases a zero‐inflated binomial (ZIB) regression model can be applied instead. In practice, it is essential to test if there are excessive zeros in the outcome to help choose an appropriate model. The binomial models can yield biased inference if there are excessive zeros, while ZIB models may be unnecessarily complex and hard to interpret, and even face convergence issues, if there are no excessive zeros. In this paper, we develop a new test for testing zero inflation in binomial regression models by directly comparing the amount of observed zeros with what would be expected under the binomial regression model. A closed form of the test statistic, as well as the asymptotic properties of the test, is derived based on estimating equations. Our systematic simulation studies show that the new test performs very well in most cases, and outperforms the classical Wald, likelihood ratio, and score tests, especially in controlling type I errors. Two real data examples are also included for illustrative purpose.     

RDCurve: a nonparametric method to evaluate the stability of ranking procedures

Great concerns have been raised about the reproducibility of gene signatures based on high-throughput techniques such as microarray. Studies analyzing similar samples often report poorly overlapping results, and the p-value usually lacks biological context. We propose a nonparametric ReDiscovery Curve (RDCurve) method, to estimate the frequency of rediscovery of gene signature identified. Given a ranking procedure and a data set with replicated measurements, the RDCurve bootstraps the data set and repeatedly applies the ranking procedure, selects a subset of k important genes, and estimates the probability of rediscovery of the selected subset of genes. We also propose a permutation scheme to estimate the confidence band under the Null hypothesis for the significance of the RDCurve. The method is nonparametric and model-independent. With the RDCurve, we can assess the signal-to-noise ratio of the data, compare the performance of ranking procedures in term of their expected rediscovery rates, and choose the number of genes to be reported.     

Exact log-rank tests for unequal follow-up

The asymptotic log-rank and generalized Wilcoxon tests are the standard procedures for comparing samples of possibly censored survival times. For comparison of samples of very different sizes, an exact test is available that is based on a complete permutation of log-rank or Wilcoxon scores. While the asymptotic tests do not keep their nominal sizes if sample sizes differ substantially, the exact complete permutation test requires equal follow-up of the samples. Therefore, we have developed and present two new exact tests also suitable for unequal follow-up. The first of these is an exact analogue of the asymptotic log-rank test and conditions on observed risk sets, whereas the second approach permutes survival times while conditioning on the realized follow-up in each group. In an empirical study, we compare the new procedures with the asymptotic log-rank test, the exact complete permutation test, and an earlier proposed approach that equalizes the follow-up distributions using artificial censoring. Results confirm highly satisfactory performance of the exact procedure conditioning on realized follow-up, particularly in case of unequal follow-up. The advantage of this test over other options of analysis is finally exemplified in the analysis of a breast cancer study.     

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.     

Penalized discriminant methods for the classification of tumors from gene expression data

Due to the advent of high-throughput microarray technology, it has become possible to develop molecular classification systems for various types of cancer. In this article, we propose a methodology using regularized regression models for the classification of tumors in microarray experiments. The performances of principal components, partial least squares, and ridge regression models are studied; these regression procedures are adapted to the classification setting using the optimal scoring algorithm. We also develop a procedure for ranking genes based on the fitted regression models. The proposed methodologies are applied to two microarray studies in cancer.     

Declining plasma fibrinogen alpha fragment identifies HER2-positive breast cancer patients and reverts to normal levels after surgery

Breast cancer is the most common nonskin malignancy affecting women. Currently, no simple, blood-based diagnostic test exists to complement radiological screening and increase sensitivity of detection. To screen plasma specimens and identify biomarkers that detect HER2-positive breast cancer, automated robotic sample processing followed by surface-enhanced laser desorption ionization time-of-flight (SELDI-TOF) mass spectroscopy was used. Multiple statistical algorithms were used to select biomarkers that segregate cancer patients versus controls and produced average CV rates ranging from 20% to 29%. A set of seven biomarkers were validated on an independent test data set and achieved the best error rate of 19.1%. A permutation test indicated a p-value for CV error less than 0.002. Moreover, a ROC curve using these biomarkers achieved an area-under-the-curve value of 0.95 on an independent test data set. The marker responsible for most of the resolving power was identified as a fragment of Fibrinogen Alpha (FGA) encompassing residues 605-629. This marker was present at lower levels in cancer patients as compared to controls. The importance of this biomarker was validated in a longitudinal study comparing pre- and post-operative levels and was shown to revert to normal levels after surgery. This fragment may serve as a useful diagnostic and treatment-monitoring marker.     

Secular trends in incidence and mortality of bladder cancer in China, 1990–2017: A joinpoint and age-period-cohort analysis

BackgroundBladder cancer is closely related to occupational carcinogens, and China is undergoing a rapid industrialization. However, trend of bladder cancer incidence and mortality remains unknown in China.MethodsIncidence and mortality rates of bladder cancer (1990–2017) were collected for each 5-year age group stratified by gender (males/females) from the Global Burden of Disease (GBD) 2017 study. The average annual percentage change (AAPC) of rates were analyzed by joinpoint regression analysis; age, period and cohort effects on incidence and mortality were simultaneously estimated by age-period-cohort model.ResultsThrough 1990–2017, age-standardized incidence rates significantly rose in men (AAPC = 0.72%, 95% CI: 0.5%, 0.9%) while decreased in women (-1.25%: -1.6%, -0.9%); age-standardized mortality rates decreased in both men (-1.09%: -1.2%, -0.9%) and women (-2.48%: -2.8%, -2.2%). The joinpoint regression analysis showed the mortality almost decreased in all age groups; while the incidence increased in men for older age groups (from 45 to 49 to 80–84). Moreover, age effect showed the incidence and mortality increased with age; the incidence and mortality increased with time period, while in women period effect stop decreasing and began to increase since 2007; cohort effect showed them decreased with birth cohorts.ConclusionsThe incidence of bladder cancer is increasing in men but mortality decreases in both sexes. Both the incidence and mortality in men substantially increase with age and period, while the rates in women increased with period since 2007. The period effect may indicate the increased risks to bladder cancer in Chinese men. Etiological studies are needed to identify the factors driving these trends of bladder cancer.     

Trends in Lung Cancer Incidence Rates,Oklahoma 2005–2010

Purpose

Lung cancer is the second most frequently diagnosed cancer among men and women in the United States. With cigarette smoking causing the majority of cases, patterns in lung cancer are often monitored to understand the impact of anti-tobacco efforts. The purpose of this research was to investigate trends in lung cancer incidence rates for the period 2005–2010 in Oklahoma.

Methods

Data on Oklahoma’s incident cases of lung cancer (2005–2010) were obtained from the Centers for Disease Control and Prevention WONDER system. Annual percent change (APC) was calculated by linear regression to characterize trends in lung cancer incidence rates over time for the overall population, by gender, by age group, and by age group within gender. Rates were considered to increase or decrease if the p-value for trend was <0.05.

Results

From 2005 through 2010, lung cancer incidence rates declined from 81.96 to 68.19 per 100,000 population, with an APC of -3.58% (p-value: 0.0220). When subgroups were examined, declines were observed among all males (APC: -4.25%; p-value: 0.0270), males <65 years (APC: -5.32%; p-value: 0.0008), females <65 years (APC: -4.85%; p-value: 0.0044), and persons aged 55–64 years (APC: -6.38%; p-value: 0.0017).

Conclusions

Declines in lung cancer incidence rates occurred during 2005–2010 among the overall population and within select demographic groups in Oklahoma. Although trends were stable for several demographic groups, rates of lung cancer incidence were lower in 2010 compared to 2005. Continued evidence-based tobacco control efforts are needed to ensure further reductions in lung cancer incidence rates in the state of Oklahoma.     

ETA: Robust software for determination of cell specific rates from extracellular time courses

Accurate quantification of cell specific rates and their uncertainties is of critical importance for assessing metabolic phenotypes of cultured cells. We applied two different methods of regression and error analysis to estimate specific metabolic rates from time‐course measurements obtained in exponentially growing cell cultures. Using simulated data sets to compute specific rates of growth, glucose uptake, and lactate excretion, we found that Gaussian error propagation from prime variables to the final calculated rates was the most accurate method for estimating parameter uncertainty. We incorporated this method into a MATLAB‐based software package called Extracellular Time‐Course Analysis (ETA), which automates the analysis workflow required to (i) compute cell specific metabolic rates and their uncertainties; (ii) test the goodness‐of‐fit of the experimental data to the regression model; and (iii) rapidly compare the results across multiple experiments. ETA was used to estimate the uptake or excretion rate of glucose, lactate, and 18 different amino acids in a B‐cell model of c‐Myc‐driven cancer. We found that P493‐6 cells with High Myc expression increased their specific uptake of glutamine, arginine, serine, lysine, and branched‐chain amino acids by two‐ to threefold in comparison to low Myc cells, but exhibited only modest increases in glucose uptake and lactate excretion. By making the ETA software package freely available to the scientific community, we expect that it will become an important tool for rigorous estimation of specific rates required for metabolic flux analysis and other quantitative metabolic studies. Biotechnol. Bioeng. 2013; 110: 1748–1758. © 2013 Wiley Periodicals, Inc.     

Health Behaviors of Korean Gastric Cancer Survivors with Hypertension: A Propensity Analysis of KNHANES III-V (2005–2012)

ObjectiveThis study provides a comparison of health behaviors between gastric cancer survivors with hypertension and non-cancer subjects in Korea.MethodsData from the Korean National Health and Nutrition Examination Survey (KNHANES) for the period of 2005-2012 were used in this study. A propensity score matching method was used to compare health behaviors. Before the matching of propensity scores, the number of participants was 11034 (102 gastric cancer survivors and 10932 non-cancer participants). A 1:5 propensity score matching procedure yielded a total of 480 participants (80 gastric cancer survivors and 400 non-cancer participants) for the final analysis. Drinking, smoking, physical activity, antihypertensive medication adherence, self-reported diet control, and sodium intake accordance in the two groups were compared. A complex samples logistic regression analysis was conducted to assess any differences between the two groups.ResultsThe group of hypertensive gastric cancer survivors had lower alcohol consumption (OR = 0.30; 95% CI: 0.14-0.66; p-value = 0.003). They were more likely to be on dietary control than the control group (OR = 3.12; 95% CI: 1.60-6.10; p-value = 0.001). However, there was no significant (p > 0.05) difference in sodium intake accordance or other health behaviors (including medication adherence, smoking, and physical activity) between the two groups.ConclusionsOur results revealed that gastric cancer survivors with hypertension were more likely to be on dietary control with lower alcohol consumption than the control group. However, there was no significant difference in sodium intake accordance or other health behaviors between the two groups. Therefore, primary care physicians should inform cancer survivors about the appropriate health behaviors to reduce their risk of cardiovascular disease and improve their overall survival rate, even though they say they have been doing health behaviors.     

Significance tests for cancer screening trials

The goal of a cancer screening program is to reduce cancer mortality by detecting tumors at earlier stages of their development. For some types of cancer, screening tests may allow the preclinical detection of benign precursors of a tumor, and thus a screening program could result in reductions in both cancer incidence and mortality. For other types of cancer, a screening program will not reduce cancer incidence, and thus the expected outcome in a randomized cancer screening trial would be equal cancer incidence rates in control and study groups, but reduced cancer mortality in the study group. For the latter situation, we employ a variety of Poisson models for cancer incidence and mortality to derive optimal tests for equality of cancer mortality rates in a cancer screening trial, and we compare the asymptotic relative efficiencies of the test statistics under various alternatives. We demonstrate that testing equality of case mortality rates using Fisher's exact test or its Pearson chi-square approximation is nearly optimal when cancer incidence rates are equal and is fully efficient when cancer incidence rates are unequal. When valid, this comparison of case mortality rates in the study and control groups can be considerably more powerful than the standard comparison of population mortality rates. We illustrate the results using data from a clinical trial of a breast cancer screening program.