A permutation test for inference in logistic regression with small- and moderate-sized data sets

Inference based on large sample results can be highly inaccurate if applied to logistic regression with small data sets. Furthermore, maximum likelihood estimates for the regression parameters will on occasion not exist, and large sample results will be invalid. Exact conditional logistic regression is an alternative that can be used whether or not maximum likelihood estimates exist, but can be overly conservative. This approach also requires grouping the values of continuous variables corresponding to nuisance parameters, and inference can depend on how this is done. A simple permutation test of the hypothesis that a regression parameter is zero can overcome these limitations. The variable of interest is replaced by the residuals from a linear regression of it on all other independent variables. Logistic regressions are then done for permutations of these residuals, and a p-value is computed by comparing the resulting likelihood ratio statistics to the original observed value. Simulations of binary outcome data with two independent variables that have binary or lognormal distributions yield the following results: (a) in small data sets consisting of 20 observations, type I error is well-controlled by the permutation test, but poorly controlled by the asymptotic likelihood ratio test; (b) in large data sets consisting of 1000 observations, performance of the permutation test appears equivalent to that of the asymptotic test; and (c) in small data sets, the p-value for the permutation test is usually similar to the mid-p-value for exact conditional logistic regression.     

A mixed effect model for bivariate meta‐analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta‐analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re‐analysing the data of two published meta‐analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R . Copyright © 2015 John Wiley & Sons, Ltd.     

A score‐type test for heterogeneity in zero‐inflated models in a stratified population

We propose a score‐type statistic to evaluate heterogeneity in zero‐inflated models for count data in a stratified population, where heterogeneity is defined as instances in which the zero counts are generated from two sources. Evaluating heterogeneity in this class of models has attracted considerable attention in the literature, but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis. In this paper, we extend the literature by describing a score‐type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis. The limiting null distribution of the proposed test statistic is a mixture of chi‐squared distributions that can be well approximated by a simple parametric bootstrap procedure. Our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information. An empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population. Copyright © 2014 John Wiley & Sons, Ltd.     

Perils and pitfalls of permutation tests for distinguishing the effects of neighbouring polymorphisms

In a small region several marker loci may be associated with a trait, either because they directly influence the trait or because they are in linkage disequilibrium (LD) with a causal variant. Having established a potentially causal effect at a primary variant, we may ask if any other variants in the region appear to further contribute to the trait, indicating that the additional variant is either causal or is in LD with another causal locus. Methods of approaching this problem using case-parent trio data include the stepwise conditional logistic regression approach described by Cordell and Clayton ([2002] Am. J. Hum. Genet. 70:124-141), and a constrained-permutation method recently proposed by Spijker et al. ([2005] Ann. Hum. Genet. 69:90-101). Through simulation we demonstrate that the procedure described by Spijker et al. [2005], as well as unconditional logistic regression with "affected family-based controls" (AFBACs), can lead to inflated type 1 errors in situations when haplotypes are not inferable for all trios, whereas the conditional logistic regression approach gives correct significance levels. We propose an alternative to the permutation method of Spijker et al. [2005], which does not rely on haplotyping, and results in correct type 1 errors and potentially high power when assumptions of random mating, Hardy-Weinberg Equilibrium, and multiplicative effects of disease alleles are satisfied.     

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data.     

A test for comparing current status survival data with crossing hazard functions and its application to immunogenicity of biotherapeutics

Several tests have been recently implemented in the nonparametric comparison of current status survival data. However, they are not suited for the situation of crossing hazards. In this setting, we propose a new test specifically designed for crossing hazards alternatives. The proposed test is compared to classical implemented tests through simulations mimicking crossing hazards situations with various schemes of censoring. The results show that the proposed test has a correct type I error and generally outperforms the existing methods. The application of the proposed test on a real dataset on immunogenicity of interferon‐β among multiple sclerosis patients highlights the interest of the proposed test.     

A comparison of stratified and adjusted trend tests for binomial proportions

For the problem of testing for a monotonic trend between an ordinal exposure and a binary response while controlling for categorical cofactors, we derived stratified and adjusted versions of two single contrast tests. Using simulations, we compared their statistical properties to those of the commonly used stratified Mantel-extension trend (MET) test. All tests had high power in case of monotonic relationships between exposure and response. In case of non-monotonic relationships, the stratified and adjusted contrast tests were markedly less powerful than the stratified MET-test particularly for five exposure levels, a favourable feature when the aim is to test for the existence of a monotonic dose-response relationship. These results are illustrated by an example.     

Joint analysis of bivariate longitudinal ordinal outcomes and competing risks survival times with nonparametric distributions for random effects

We propose a semiparametric joint model for bivariate longitudinal ordinal outcomes and competing risks failure time data. The association between the longitudinal and survival endpoints is captured by latent random effects. This approach generalizes previous joint analysis that considers only one response variable at the longitudinal endpoint. One unique feature of the proposed model is that we relax the commonly used normality assumption for random effects and leave the distribution completely unspecified. We use a modified version of the vertex exchange method in conjunction with an expectation-maximization algorithm to estimate the random effects distribution and model parameters. We show via simulations that robust parameter estimates are obtained from the proposed method under various scenarios. We illustrate the approach using cough severity and frequency data from a scleroderma lung study.     

A comparison of permutation and mixed-model regression methods for the analysis of simulated data in the context of a group-randomized trial

Our first purpose was to determine whether, in the context of a group-randomized trial (GRT) with Gaussian errors, permutation or mixed-model regression methods fare better in the presence of measurable confounding in terms of their Monte Carlo type I error rates and power. Our results indicate that given a proper randomization, the type I error rate is similar for both methods, whether unadjusted or adjusted, even in small studies. However, our results also show that should the investigator face the unfortunate circumstance in which modest confounding exists in the only realization available, the unadjusted analysis risks a type I error; in this regard, there was little to distinguish the two methods. Finally, our results show that power is similar for the two methods and, not surprisingly, better for the adjusted tests.Our second purpose was to examine the relative performance of permutation and mixed-model regression methods in the context of a GRT when the normality assumptions underlying the mixed model are violated. Published studies have examined the impact of violation of this assumption at the member level only. Our findings indicate that both methods perform well when the assumption is violated so long as the ICC is very small and the design is balanced at the group level. However, at ICC>or=0.01, the permutation test carries the nominal type I error rate while the model-based test is conservative and so less powerful. Binomial group- and member-level errors did not otherwise change the relative performance of the two methods with regard to confounding.     

A modified Wilcoxon test for non‐negative distributions with a clump of zeros

Comparing two samples with a continuous non‐negative score, e.g. a utility score over [0, 1], with a substantial proportion, say 50 per cent, scoring 0 presents distributional problems for most standard tests. A Wilcoxon rank test can be used, but the large number of ties reduces power. I propose a new test, the Wilcoxon rank‐sum test performed after removing an equal (and maximal) number of 0's from each sample. This test recovers much of the power. Compared with a (directional) modification of a two‐part test proposed by Lachenbruch, the truncated Wilcoxon has similar power when the non‐zero scores are independent of the proportion of zeros, but, unlike the two‐part test, the truncated Wilcoxon is relatively unaffected when these processes are dependent. Copyright © 2009 John Wiley & Sons, Ltd.     

Health care visits during the COVID-19 pandemic: A spatial and temporal analysis of mobile device data

Transportation disruptions caused by COVID-19 have exacerbated difficulties in health care delivery and access, which may lead to changes in health care use. This study uses mobile device data from SafeGraph to explore the temporal patterns of visits to health care points of interest (POIs) during 2020 and examines how these patterns are associated with socio-demographic and spatial characteristics at the Census Block Group level in North Carolina. Specifically, using the K-medoid time-series clustering method, we identify three distinct types of temporal patterns of visits to health care facilities. Furthermore, by estimating multinomial logit models, we find that Census Block Groups with higher percentages of elderly persons, minorities, low-income individuals, and people without vehicle access are areas most at-risk for decreased health care access during the pandemic and exhibit lower health care access prior to the pandemic. The results suggest that the ability to conduct in-person medical visits during the pandemic has been unequally distributed, which highlights the importance of tailoring policy strategies for specific socio-demographic groups to ensure equitable health care access and delivery.     

Alternative methods for testing treatment effects on the basis of multiple outcomes: simulation and case study

In clinical trials multiple outcomes are often used to assess treatment interventions. This paper presents an evaluation of likelihood-based methods for jointly testing treatment effects in clinical trials with multiple continuous outcomes. Specifically, we compare the power of joint tests of treatment effects obtained from joint models for the multiple outcomes with univariate tests based on modeling the outcomes separately. We also consider the power and bias of tests when data are missing, a common feature of many trials, especially in psychiatry. Our results suggest that joint tests capitalize on the correlation of multiple outcomes and are more powerful than standard univariate methods, especially when outcomes are missing completely at random. When outcomes are missing at random, test procedures based on correctly specified joint models are unbiased, while standard univariate procedures are not. Results of a simulation study are reported, and the methods are illustrated in an example from the Clinical Antipsychotic Trials of Intervention Effectiveness for schizophrenia.     

A modified test for small-study effects in meta-analyses of controlled trials with binary endpoints

Publication bias and related bias in meta-analysis is often examined by visually checking for asymmetry in funnel plots of treatment effect against its standard error. Formal statistical tests of funnel plot asymmetry have been proposed, but when applied to binary outcome data these can give false-positive rates that are higher than the nominal level in some situations (large treatment effects, or few events per trial, or all trials of similar sizes). We develop a modified linear regression test for funnel plot asymmetry based on the efficient score and its variance, Fisher's information. The performance of this test is compared to the other proposed tests in simulation analyses based on the characteristics of published controlled trials. When there is little or no between-trial heterogeneity, this modified test has a false-positive rate close to the nominal level while maintaining similar power to the original linear regression test ('Egger' test). When the degree of between-trial heterogeneity is large, none of the tests that have been proposed has uniformly good properties.     

山东省莒南县肾综合征出血热时空分布概率模型分析

目的探讨莒南县肾综合征出血热（HFRS）病例时空分布特点。方法对莒南县HFRS时空分布进行概率模型分析。结果莒南县HFRS病例的时间分布和空间分布皆不符合泊松分布（χ^2=38.44,P〈0.05;χ^2=138.58,P〈0.05）,而服从于负二项分布（χ^2=2.81,P〉0.05;χ^2=2.96,P〉0.05）,说明二者存在聚集性。高峰时点在4月21日,发病高峰期在2月10日至6月25日;空间分布主要集中在该县西部平原地带。结论要做好重点区域和关键季节HFRS的防治。     

Bayesian analysis of nonlinear mixed‐effects mixture models for longitudinal data with heterogeneity and skewness

It is a common practice to analyze complex longitudinal data using nonlinear mixed‐effects (NLME) models with normality assumption. The NLME models with normal distributions provide the most popular framework for modeling continuous longitudinal outcomes, assuming individuals are from a homogeneous population and relying on random‐effects to accommodate inter‐individual variation. However, the following two issues may standout: (i) normality assumption for model errors may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates, particularly, if the data exhibit skewness and (ii) a homogeneous population assumption may be unrealistically obscuring important features of between‐subject and within‐subject variations, which may result in unreliable modeling results. There has been relatively few studies concerning longitudinal data with both heterogeneity and skewness features. In the last two decades, the skew distributions have shown beneficial in dealing with asymmetric data in various applications. In this article, our objective is to address the simultaneous impact of both features arisen from longitudinal data by developing a flexible finite mixture of NLME models with skew distributions under Bayesian framework that allows estimates of both model parameters and class membership probabilities for longitudinal data. Simulation studies are conducted to assess the performance of the proposed models and methods, and a real example from an AIDS clinical trial illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported. Copyright © 2014 John Wiley & Sons, Ltd.     

深圳市龙岗区大气污染物与医院呼吸系统疾病门诊量的广义相加模型分析

目的 探讨深圳市龙岗区主要大气污染物(SO₂、NO₂、PM₁₀与PM_2.5)与医院呼吸系统疾病门诊量的关系。 方法 收集2013年1月1日－2015年12月31日深圳市龙岗区2家公立医院呼吸系统疾病逐日门诊量资料,深圳市龙岗区逐日大气污染物浓度及逐日气象资料分别来自深圳市环境监测站及气象局,运用时间序列分析广义相加模型对大气污染物日均浓度与呼吸系统疾病门诊量的关系及滞后效应进行分析。 结果 深圳市龙岗区2013－2015年SO₂ 、NO₂ 、PM₁₀ 与PM_2.5浓度中位数分别为8.08、38.08、46.05 μg/m³及31.04 μg/m³。2家医院三年呼吸系统门诊总量为549 169人次,日门诊量中位数为499人次/d。广义相加模型分析结果表明,除NO₂对呼吸系统疾病门诊量影响差异无统计学意义外,其余三种污染物对呼吸系统疾病门诊量影响均存在滞后效应,污染物每升高10 μg/m³,滞后2 d时SO₂对门诊量影响最强(相对危险度RR为1.030 7,95%CI:1.015 7~1.045 9),滞后3 d时PM₁₀与PM_2.5浓度对呼吸系统疾病门诊量影响最强(PM₁₀:RR=1.005 4,95%CI:1.002 8~1.008 0,PM_2.5:RR=1.006 0, 95%CI:1.002 7~1.009 4)。 结论 深圳市龙岗区大气SO₂、PM₁₀与PM_2.5浓度对医院呼吸系统疾病门诊量影响存在滞后效应。     

A comparison of regression trees, logistic regression, generalized additive models, and multivariate adaptive regression splines for predicting AMI mortality

Clinicians and health service researchers are frequently interested in predicting patient-specific probabilities of adverse events (e.g. death, disease recurrence, post-operative complications, hospital readmission). There is an increasing interest in the use of classification and regression trees (CART) for predicting outcomes in clinical studies. We compared the predictive accuracy of logistic regression with that of regression trees for predicting mortality after hospitalization with an acute myocardial infarction (AMI). We also examined the predictive ability of two other types of data-driven models: generalized additive models (GAMs) and multivariate adaptive regression splines (MARS). We used data on 9484 patients admitted to hospital with an AMI in Ontario. We used repeated split-sample validation: the data were randomly divided into derivation and validation samples. Predictive models were estimated using the derivation sample and the predictive accuracy of the resultant model was assessed using the area under the receiver operating characteristic (ROC) curve in the validation sample. This process was repeated 1000 times-the initial data set was randomly divided into derivation and validation samples 1000 times, and the predictive accuracy of each method was assessed each time. The mean ROC curve area for the regression tree models in the 1000 derivation samples was 0.762, while the mean ROC curve area of a simple logistic regression model was 0.845. The mean ROC curve areas for the other methods ranged from a low of 0.831 to a high of 0.851. Our study shows that regression trees do not perform as well as logistic regression for predicting mortality following AMI. However, the logistic regression model had performance comparable to that of more flexible, data-driven models such as GAMs and MARS.     

A polygenic model for integration of linkage and pathway information

We introduce an approximate model for linkage curves which accommodates the polygenic structure of complex diseases and accounts for the simultaneous action of closely located genes. The model is extended so that information on biological pathways can be integrated. Using data on rheumatoid arthritis, we describe some of the many applications which the model allows: it can be used to test for residual linkage in the presence of already established loci, to derive a global test for linkage, to test for the relevance of a gene list in terms of linkage and to help in candidate gene prioritization by integration of gene-pathway annotation data.     

A three-level model for binary time-series data: the effects of air pollution on school absences in the Southern California Children's Health Study

A three-level model is proposed to simultaneously examine the effects of daily exposure to air pollution and individual risk factors on health outcomes without aggregating over subjects or time. We used a logistic transition model with random effects to take into account heterogeneity and overdispersion of the observations. A distributed lag structure for pollution has been included, assuming that the event on day t for a subject depends on the levels of air pollution for several preceding days. We illustrate this proposed model via detailed analysis of the effect of air pollution on school absenteeism based on data from the Southern California Children's Health Study.     

A generalized partially linear mean‐covariance regression model for longitudinal proportional data,with applications to the analysis of quality of life data from cancer clinical trials

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean‐covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within‐subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd.