Classification of array CGH data using smoothed logistic regression model

Array comparative genomic hybridization (aCGH) provides a genome‐wide information of DNA copy number that is potentially useful for disease classification. One immediate problem is that the data contain many features (probes) but only a few samples. Existing approaches to overcome this problem include features selection, ridge regression and partial least squares. However, these methods typically ignore the spatial characteristic of aCGH data. To explicitly make use of this spatial information we develop a procedure called smoothed logistic regression (SLR) model. The procedure is based on a mixed logistic regression model, where the random component is a mixture distribution that controls smoothness and sparseness. Conceptually such a procedure is straightforward, but its implementation is complicated due to computational problems. We develop a fast and reliable iterative weighted least‐squares algorithm based on the singular value decomposition. Simulated data and two real data sets are used to illustrate the procedure. For real data sets, error rates are calculated using the leave‐one‐out cross validation procedure. For both simulated and real data examples, SLR achieves better misclassification error rates compared with previous methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Understanding MCP‐MOD dose finding as a method based on linear regression

MCP‐MOD is a testing and model selection approach for clinical dose finding studies. During testing, contrasts of dose group means are derived from candidate dose response models. A multiple‐comparison procedure is applied that controls the alpha level for the family of null hypotheses associated with the contrasts. Provided at least one contrast is significant, a corresponding set of “good” candidate models is identified. The model generating the most significant contrast is typically selected. There have been numerous publications on the method. It was endorsed by the European Medicines Agency. The MCP‐MOD procedure can be alternatively represented as a method based on simple linear regression, where “simple” refers to the inclusion of an intercept and a single predictor variable, which is a transformation of dose. It is shown that the contrasts are equal to least squares linear regression slope estimates after a rescaling of the predictor variables. The test for each contrast is the usual t statistic for a null slope parameter, except that a variance estimate with fewer degrees of freedom is used in the standard error. Selecting the model corresponding to the most significant contrast P value is equivalent to selecting the predictor variable yielding the smallest residual sum of squares. This criteria orders the models like a common goodness‐of‐fit test, but it does not assure a good fit. Common inferential methods applied to the selected model are subject to distortions that are often present following data‐based model selection.     

Bayesian joint ordinal and survival modeling for breast cancer risk assessment

We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional‐odds cumulative logit model. Time‐to‐event is modeled through a left‐truncated proportional‐hazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects. General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the assessment of the impact of the baseline covariates and the longitudinal marker on the hazard function. The flexibility provided by the joint model makes possible to dynamically estimate individual event‐free probabilities and predict future longitudinal marker values. The model is applied to the assessment of breast cancer risk in women attending a population‐based screening program. The longitudinal ordinal marker is mammographic breast density measured with the Breast Imaging Reporting and Data System (BI‐RADS) scale in biennial screening exams. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Bayesian semiparametric regression models for evaluating pathway effects on continuous and binary clinical outcomes

Many statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. Limited work has been carried out in the regression setting to study the effects of clinical covariates and expression levels of genes in a pathway either on a continuous or on a binary clinical outcome. Hence, we propose a Bayesian approach for identifying pathways related to both types of outcomes. We compare our Bayesian approaches with a likelihood‐based approach that was developed by relating a least squares kernel machine for nonparametric pathway effect with a restricted maximum likelihood for variance components. Unlike the likelihood‐based approach, the Bayesian approach allows us to directly estimate all parameters and pathway effects. It can incorporate prior knowledge into Bayesian hierarchical model formulation and makes inference by using the posterior samples without asymptotic theory. We consider several kernels (Gaussian, polynomial, and neural network kernels) to characterize gene expression effects in a pathway on clinical outcomes. Our simulation results suggest that the Bayesian approach has more accurate coverage probability than the likelihood‐based approach, and this is especially so when the sample size is small compared with the number of genes being studied in a pathway. We demonstrate the usefulness of our approaches through its applications to a type II diabetes mellitus data set. Our approaches can also be applied to other settings where a large number of strongly correlated predictors are present. Copyright © 2012 John Wiley & Sons, Ltd.     

Improving health care efficiency and quality using tablet personal computers to collect research-quality, patient-reported data

Objective. To determine whether e/Tablets (wireless tablet computers used in community oncology clinics to collect review of systems information at point of care) are feasible, acceptable, and valid for collecting research‐quality data in academic oncology. Data/Setting. Primary/Duke Breast Cancer Clinic. Design. Pilot study enrolling sample of 66 breast cancer patients. Methods. Data were collected using paper‐ and e/Tablet‐based surveys: Functional Assessment of Cancer Therapy General, Functional Assessment of Cancer Therapy‐Breast, MD Anderson Symptom Inventory, Functional Assessment of Chronic Illness Therapy (FACIT), Self‐Efficacy; and two questionnaires: feasibility, satisfaction. Principal Findings. Patients supported e/Tablets as: easy to read (94 percent), easy to respond to (98 percent), comfortable weight (87 percent). Generally, electronic responses validly reflected responses provided by standard paper data collection on nearly all subscales tested. Conclusions. e/Tablets offer a valid, feasible, acceptable method for collecting research‐quality, patient‐reported outcomes data in outpatient academic oncology.     

使用最小二乘支持向量机技术预测传染病发病率的研究

目的将最小二乘支持向量机(LS-SVM)技术应用到传染病预测中,寻找更加理想的预测结果。方法以某市1991—2002年乙型肝炎(乙肝)月发病率数据建立最小二乘支持向量机预测模型,对2003年1—6月的月发病率进行预测。结果 IS-SVM预测值分别为0.709 9,0.668 1,0.502 5,0.685 1、0.578 5,0.773 7,通过与径向基函数(RBF)神经网络模型和累积式自回归动平均模型(ARIMA)预测结果进行比较,预测精度明显高于RBF网络模型和ARIMA模型,相对误差明显减少,仅为ARIMA模型的23.62%,RBF网络模型的54.69%。结论 LS-SVM模型对乙肝发病率的预测精度更高,效果更好,也验证了支持向量机方法预测能力出色的理论优点,证明了支持向量机技术在传染病预测领域同样有着良好的表现。     

Shedding new light onto the ceiling and floor? A quantile regression approach to compare EQ‐5D and SF‐6D responses

An important issue in the measurement of health status concerns the extent to which an instrument displays lack of sensitivity to changes in health status at the extremes of the distribution, known as floor and ceiling effects. Previous studies use relatively simple methods that focus on the mean of the distribution to examine these effects. The aim of this paper is to determine whether quantile regression using longitudinal data improves our understanding of the relationship between quality of life instruments. The study uses EQ‐5D and SF‐36 (converted to SF‐6D values) instruments with both baseline and follow‐up data. Relative to ordinary least least‐squares (OLS), a first difference model shows much lower association between the measures, suggesting that OLS methods may lead to biased estimates of the association, due to unobservable patient characteristics. The novel finding, revealed by quantile regression, is that the strength of association between the instruments is different across different parts of the health distribution, and is dependent on whether health improves or deteriorates. The results suggest that choosing one instrument at the expense of another is difficult without good prior information surrounding the expected magnitude and direction of health improvement related to a health‐care intervention. Copyright © 2009 John Wiley & Sons, Ltd.     

Neither fixed nor random: weighted least squares meta‐analysis

This study challenges two core conventional meta‐analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random‐effects meta‐analysis when there is publication (or small‐sample) bias and better than a fixed‐effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small‐sample) bias and identical to fixed‐effect meta‐analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed‐effect meta‐analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects. Copyright © 2015 John Wiley & Sons, Ltd.     

Reduce dimension or reduce weights? Comparing two approaches to multi‐arm studies in network meta‐analysis

Network meta‐analysis is a statistical method combining information from randomised trials that compare two or more treatments for a given medical condition. Consistent treatment effects are estimated for all possible treatment comparisons. For estimation, weighted least squares regression that in a natural way generalises standard pairwise meta‐analysis can be used. Typically, as part of the network, multi‐arm studies are found. In a multi‐arm study, observed pairwise comparisons are correlated, which must be accounted for. To this aim, two methods have been proposed, a standard regression approach and a new approach coming from graph theory and based on contrast‐based data (Rücker 2012). In the standard approach, the dimension of the design matrix is appropriately reduced until it is invertible (‘reduce dimension’). In the alternative approach, the weights of comparisons coming from multi‐arm studies are appropriately reduced (‘reduce weights’). As it was unclear, to date, how these approaches are related to each other, we give a mathematical proof that both approaches lead to identical estimates. The ‘reduce weights’ approach can be interpreted as the construction of a network of independent two‐arm studies, which is basically equivalent to the given network with multi‐arm studies. Thus, a simple random‐effects model is obtained, with one additional parameter for a common heterogeneity variance. This is applied to a systematic review in depression. Copyright © 2014 John Wiley & Sons, Ltd.     

半参数回归模型及模拟实例分析

目的 放宽经典线性模型中的解释变量的线性假定和探讨半参数回归分析模型。方法 利用最小惩罚二乘原理构造加权惩罚平方和,通过广义交互有效得分函数自动选择光滑参数值,用直接法求解方程组。结果 用SAS程序实现了半参数回归分析。得到了回归系数向量和样条函数的最小惩罚二乘估计,模拟实例表明,半参数回归模型较传统的线性模型有较强的适应性。结论 半参数回归模型是经典线性模型和非参数回归模型的一个混合体。可作为回归分析的一种新技术得到广泛应用。     

Flexibly modeling the baseline risk in meta‐analysis

This paper investigates a likelihood‐based approach in meta‐analysis of clinical trials involving the baseline risk as explanatory variable. The approach takes account of the errors affecting the measure of either the treatment effect or the baseline risk, while facing the potential misspecification of the baseline risk distribution. To this aim, we suggest to model the baseline risk through a flexible family of distributions represented by the skew‐normal. We describe how to carry out inference within this framework and evaluate the performance of the approach through simulation. The method is compared with the routine likelihood approach based on the restrictive normality assumption for the baseline risk distribution and with the weighted least‐squares regression. We apply the competing approaches to the analysis of two published datasets. Copyright © 2012 John Wiley & Sons, Ltd.     

Predictive value of statistical models

A review is given of different ways of estimating the error rate of a prediction rule based on a statistical model. A distinction is drawn between apparent, optimum and actual error rates. Moreover it is shown how cross-validation can be used to obtain an adjusted predictor with smaller error rate. A detailed discussion is given for ordinary least squares, logistic regression and Cox regression in survival analysis. Finally, the splitsample approach is discussed and demonstrated on two data sets.     

A Bayesian proportional hazards regression model with non-ignorably missing time-varying covariates

Missing covariate data are common in observational studies of time to an event, especially when covariates are repeatedly measured over time. Failure to account for the missing data can lead to bias or loss of efficiency, especially when the data are non-ignorably missing. Previous work has focused on the case of fixed covariates rather than those that are repeatedly measured over the follow-up period, hence, here we present a selection model that allows for proportional hazards regression with time-varying covariates when some covariates may be non-ignorably missing. We develop a fully Bayesian model and obtain posterior estimates of the parameters via the Gibbs sampler in WinBUGS. We illustrate our model with an analysis of post-diagnosis weight change and survival after breast cancer diagnosis in the Long Island Breast Cancer Study Project follow-up study. Our results indicate that post-diagnosis weight gain is associated with lower all-cause and breast cancer-specific survival among women diagnosed with new primary breast cancer. Our sensitivity analysis showed only slight differences between models with different assumptions on the missing data mechanism yet the complete-case analysis yielded markedly different results.     

Inferring gene regulatory relationships with a high‐dimensional robust approach

Gene expression (GE) levels have important biological and clinical implications. They are regulated by copy number alterations (CNAs). Modeling the regulatory relationships between GEs and CNAs facilitates understanding disease biology and can also have values in translational medicine. The expression level of a gene can be regulated by its cis‐acting as well as trans‐acting CNAs, and the set of trans‐acting CNAs is usually not known, which poses a high‐dimensional selection and estimation problem. Most of the existing studies share a common limitation in that they cannot accommodate long‐tailed distributions or contamination of GE data. In this study, we develop a high‐dimensional robust regression approach to infer the regulatory relationships between GEs and CNAs. A high‐dimensional regression model is used to accommodate the effects of both cis‐acting and trans‐acting CNAs. A density power divergence loss function is used to accommodate long‐tailed GE distributions and contamination. Penalization is adopted for regularized estimation and selection of relevant CNAs. The proposed approach is effectively realized using a coordinate descent algorithm. Simulation shows that it has competitive performance compared to the nonrobust benchmark and the robust LAD (least absolute deviation) approach. We analyze TCGA (The Cancer Genome Atlas) data on cutaneous melanoma and study GE‐CNA regulations in the RAP (regulation of apoptosis) pathway, which further demonstrates the satisfactory performance of the proposed approach.     

Utilisation of home‐based physician,nurse and personal support worker services within a palliative care programme in Ontario,Canada: trends over 2005–2015

With health system restructuring in Canada and a general preference by care recipients and their families to receive palliative care at home, attention to home‐based palliative care continues to increase. A multidisciplinary team of health professionals is the most common delivery model for home‐based palliative care in Canada. However, little is known about the changing temporal trends in the propensity and intensity of home‐based palliative care. The purpose of this study was to assess the propensity to use home‐based palliative care services, and once used, the intensity of that use for three main service categories: physician visits, nurse visits and care by personal support workers (PSWs) over the last decade. Three prospective cohort data sets were used to track changes in service use over the period 2005 to 2015. Service use for each category was assessed using a two‐part model, and a Heckit regression was performed to assess the presence of selectivity bias. Service propensity was modelled using multivariate logistic regression analysis and service intensity was modelled using log‐transformed ordinary least squares regression analysis. Both the propensity and intensity to use home‐based physician visits and PSWs increased over the last decade, while service propensity and the intensity of nurse visits decreased. Meanwhile, there was a general tendency for service propensity and intensity to increase as the end of life approached. These findings demonstrate temporal changes towards increased use of home‐based palliative care, and a shift to substitute care away from nursing to less expensive forms of care, specifically PSWs. These findings may provide a general idea of the types of services that are used more intensely and require more resources from multidisciplinary teams, as increased use of home‐based palliative care has placed dramatic pressures on the budgets of local home and community care organisations.     

Kernel Machine SNP‐Set Testing Under Multiple Candidate Kernels

Joint testing for the cumulative effect of multiple single‐nucleotide polymorphisms grouped on the basis of prior biological knowledge has become a popular and powerful strategy for the analysis of large‐scale genetic association studies. The kernel machine (KM)‐testing framework is a useful approach that has been proposed for testing associations between multiple genetic variants and many different types of complex traits by comparing pairwise similarity in phenotype between subjects to pairwise similarity in genotype, with similarity in genotype defined via a kernel function. An advantage of the KM framework is its flexibility: choosing different kernel functions allows for different assumptions concerning the underlying model and can allow for improved power. In practice, it is difficult to know which kernel to use a priori because this depends on the unknown underlying trait architecture and selecting the kernel which gives the lowest P‐value can lead to inflated type I error. Therefore, we propose practical strategies for KM testing when multiple candidate kernels are present based on constructing composite kernels and based on efficient perturbation procedures. We demonstrate through simulations and real data applications that the procedures protect the type I error rate and can lead to substantially improved power over poor choices of kernels and only modest differences in power vs. using the best candidate kernel.     

The dynamic relationships between economic status and health measures among working‐age adults in the United States

We examine the dynamic relationships between economic status and health measures using data from 8 waves of the Panel Study of Income Dynamics from 1999 to 2013. Health measures are self‐rated health (SRH) and functional limitations; economic status measures are labor income (earnings), family income, and net wealth. We use 3 different types of models: (a) ordinary least squares regression, (b) first‐difference, and (c) system‐generalized method of moment (GMM). Using ordinary least squares regression and first difference models, we find that higher levels of economic status are associated with better SRH and functional status among both men and women, although declines in income and wealth are associated with a decline in health for men only. Using system‐GMM estimators, we find evidence of a causal link from labor income to SRH and functional status for both genders. Among men only, system‐GMM results indicate that there is a causal link from net wealth to SRH and functional status. Results overall highlight the need for integrated economic and health policies, and for policies that mitigate the potential adverse health effects of short‐term changes in economic status.     

Regression analysis of mean quality‐adjusted survival time based on pseudo‐observations

Regression models for the mean quality‐adjusted survival time are specified from hazard functions of transitions between two states and the mean quality‐adjusted survival time may be a complex function of covariates. We discuss a regression model for the mean quality‐adjusted survival (QAS) time based on pseudo‐observations, which has the advantage of directly modeling the effect of covariates in the QAS time. Both Monte Carlo simulations and a real data set are studied. Copyright © 2009 John Wiley & Sons, Ltd.     

Using Quantile and Asymmetric Least Squares Regression for Optimal Risk Adjustment

In this paper, we analyze optimal risk adjustment for direct risk selection (DRS). Integrating insurers' activities for risk selection into a discrete choice model of individuals' health insurance choice shows that DRS has the structure of a contest. For the contest success function (csf) used in most of the contest literature (the Tullock‐csf), optimal transfers for a risk adjustment scheme have to be determined by means of a restricted quantile regression, irrespective of whether insurers are primarily engaged in positive DRS (attracting low risks) or negative DRS (repelling high risks). This is at odds with the common practice of determining transfers by means of a least squares regression. However, this common practice can be rationalized for a new csf, but only if positive and negative DRSs are equally important; if they are not, optimal transfers have to be calculated by means of a restricted asymmetric least squares regression. Using data from German and Swiss health insurers, we find considerable differences between the three types of regressions. Optimal transfers therefore critically depend on which csf represents insurers' incentives for DRS and, if it is not the Tullock‐csf, whether insurers are primarily engaged in positive or negative DRS. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulation from a known Cox MSM using standard parametric models for the g‐formula

It is routinely argued that, unlike standard regression‐based estimates, inverse probability weighted (IPW) estimates of the parameters of a correctly specified Cox marginal structural model (MSM) may remain unbiased in the presence of a time‐varying confounder affected by prior treatment. Previously proposed methods for simulating from a known Cox MSM lack knowledge of the law of the observed outcome conditional on the measured past. Although unbiased IPW estimation does not require this knowledge, standard regression‐based estimates rely on correct specification of this law. Thus, in typical high‐dimensional settings, such simulation methods cannot isolate bias due to complex time‐varying confounding as it may be conflated with bias due to misspecification of the outcome regression model. In this paper, we describe an approach to Cox MSM data generation that allows for a comparison of the bias of IPW estimates versus that of standard regression‐based estimates in the complete absence of model misspecification. This approach involves simulating data from a standard parametrization of the likelihood and solving for the underlying Cox MSM. We prove that solutions exist and computations are tractable under many data‐generating mechanisms. We show analytically and confirm in simulations that, in the absence of model misspecification, the bias of standard regression‐based estimates for the parameters of a Cox MSM is indeed a function of the coefficients in observed data models quantifying the presence of a time‐varying confounder affected by prior treatment. We discuss limitations of this approach including that implied by the ‘g‐null paradox’. Copyright © 2013 John Wiley & Sons, Ltd.