Comparison of the results of Cox proportional hazards model and parametric models in the study of length of stay in a tertiary teaching hospital in Tehran, Iran

Survival analysis is a set of methods used for analysis of the data which exist until the occurrence of an event. This study aimed to compare the results of the use of the semi-parametric Cox model with parametric models to determine the factors influencing the length of stay of patients in the inpatient units of Women Hospital in Tehran, Iran. In this historical cohort study all 3421 charts of the patients admitted to Obstetrics, Surgery and Oncology units in 2008 were reviewed and the required patient data such as medical insurance coverage types, admission months, days and times, inpatient units, final diagnoses, the number of diagnostic tests, admission types were collected. The patient length of stay in hospital 'leading to recovery' was considered as a survival variable. To compare the semi-parametric Cox model and parametric (including exponential, Weibull, Gompertz, log-normal, log-logistic and gamma) models and find the best model fitted to studied data, Akaike's Information Criterion (AIC) and Cox-Snell residual were used. P<0.05 was considered as statistically significant. AIC and Cox-Snell residual graph showed that the gamma model had the lowest AIC (4288.598) and the closest graph to the bisector. The results of the gamma model showed that factors affecting the patient length of stay were admission day, inpatient unit, related physician specialty, emergent admission, final diagnosis and the number of laboratory tests, radiographies and sonographies (P<0.05). The results showed that the gamma model provided a better fit to the studied data than the Cox proportional hazards model. Therefore, it is better for researchers of healthcare field to consider this model in their researches about the patient length of stay (LOS) if the assumption of proportional hazards is not fulfilled.     

Assessment of skewed exposure in case-control studies with pooling

Pooling-based strategies that combine samples from multiple participants for laboratory assays have been proposed for epidemiologic investigations of biomarkers to address issues including cost, efficiency, detection, and when minimal sample volume is available. A modification of the standard logistic regression model has been previously described to allow use with pooled data; however, this model makes assumptions regarding exposure distribution and logit-linearity of risk (i.e., constant odds ratio) that can be violated in practice. We were motivated by a nested case-control study of miscarriage and inflammatory factors with highly skewed distributions to develop a more flexible model for analysis of pooled data. Using characteristics of the gamma distribution and the relation between models of binary outcome conditional on exposure and of exposure conditional on outcome, we use a modified logistic regression to accommodate nonlinearity because of unequal shape parameters in gamma distributed exposure for cases and controls. Using simulations, we compare our approach with existing methods for logistic regression for pooled data considering: (1) constant and dose-dependent effects; (2) gamma and log-normal distributed exposure; (3) effect size; and (4) the proportions of biospecimens pooled. We show that our approach allows estimation of odds ratios that vary with exposure level, yet has minimal loss of efficiency compared with existing approaches when exposure effects are dose-invariant. Our model performed similarly to a maximum likelihood estimation approach in terms of bias and efficiency, and provides an easily implemented approach for estimation with pooled biomarker data when effects may not be constant across exposure. Copyright ? 2012 John Wiley & Sons, Ltd.     

Comparing alternative models: log vs Cox proportional hazard?

Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y|x) using the Cox model.     

Selecting a separable parametric spatiotemporal covariance structure for longitudinal imaging data

Longitudinal imaging studies allow great insight into how the structure and function of a subject's internal anatomy changes over time. Unfortunately, the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation: the temporal from the repeated measures and the spatial from the outcomes of interest being observed at multiple points in a patient's body. We propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data. The model makes use of spatial (exponential, spherical, and Matérn) and temporal (compound symmetric, autoregressive‐1, Toeplitz, and unstructured) parametric correlation functions. A simulation study, inspired by a longitudinal cardiac imaging study on mitral regurgitation patients, compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on types I and II error rates for inference on fixed effects when the specified model is incorrect. Information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures. Misspecification of the covariance structure was found to have the ability to inflate the type I error or have an overly conservative test size, which corresponded to decreased power. An example with clinical data is given illustrating how the covariance structure procedure can be performed in practice, as well as how covariance structure choice can change inferences about fixed effects. Copyright © 2014 John Wiley & Sons, Ltd.     

Capture-recapture using multiple data sources: estimating the prevalence of diabetes

Objective: To examine the potential for using multiple list sources and capture‐recapture methods for estimating the prevalence of diagnosed diabetes. Method: A model‐averaging procedure using an adjusted Akaike's Information Criterion (QAICc) was used to combine capture‐recapture estimates from log‐linear models obtained from simultaneously analysing four sources of data. The method was illustrated using four separate lists of patients with diabetes, resident in Otago, New Zealand. Results: Eighteen candidate models with a QAICc weight of more than 0.01 were obtained. A total of 5,716 individuals were enrolled on one or more of the four lists, of whom 379 (6.6%) appeared on all four lists and 1,670 (29.2%) appeared on one list only. The model‐averaged estimate of the total number of people with diagnosed diabetes was 6,721 (95% CI: 6,097, 7,346). The age‐standardised prevalence was 3.70% (95% CI: 3.36–4.04%) for the total population and 4.45% (95% CI: 4.03–4.86) for adults aged 15+ years. Conclusions: Estimated diabetes prevalence was consistent with national survey results. Capture‐recapture methods, combined with model averaging, are a cheap, efficient tool to estimate the prevalence of diagnosed diabetes. Implications: This method provides a relatively easy way to estimate the prevalence of diagnosed diabetes using routinely collected diabetes information, thus providing the opportunity to monitor the diabetes epidemic and inform planning decisions and resource allocation.     

Analysis of rubella antibody distribution from newborn dried blood spots using finite mixture models

Eluted dried blood spot specimens from newborn screening, collected in 2004 in North Thames and anonymously linked to birth registration data, were tested for maternally acquired rubella IgG antibody as a proxy for maternal antibody concentration using an enzyme-linked immunosorbent assay. Finite mixture regression models were fitted to the antibody concentrations from 1964 specimens. The Bayesian Information Criterion (BIC) was used as a model selection criterion to avoid over-fitting the number of mixture model components. This allowed investigation of the independent effect of maternal age and maternal country of birth on rubella antibody concentration without dichotomizing the outcome variable using cut-off values set a priori. Mixture models are a highly useful method of analysis in seroprevalence studies of vaccine-preventable infections in which preset cut-off values may overestimate the size of the seronegative population.     

Parametric modelling of cost data in medical studies

The cost of medical resources used is often recorded for each patient in clinical studies in order to inform decision-making. Although cost data are generally skewed to the right, interest is in making inferences about the population mean cost. Common methods for non-normal data, such as data transformation, assuming asymptotic normality of the sample mean or non-parametric bootstrapping, are not ideal. This paper describes possible parametric models for analysing cost data.Four example data sets are considered, which have different sample sizes and degrees of skewness. Normal, gamma, log-normal, and log-logistic distributions are fitted, together with three-parameter versions of the latter three distributions. Maximum likelihood estimates of the population mean are found; confidence intervals are derived by a parametric BC(a) bootstrap and checked by MCMC methods. Differences between model fits and inferences are explored.Skewed parametric distributions fit cost data better than the normal distribution, and should in principle be preferred for estimating the population mean cost. However for some data sets, we find that models that fit badly can give similar inferences to those that fit well. Conversely, particularly when sample sizes are not large, different parametric models that fit the data equally well can lead to substantially different inferences. We conclude that inferences are sensitive to choice of statistical model, which itself can remain uncertain unless there is enough data to model the tail of the distribution accurately. Investigating the sensitivity of conclusions to choice of model should thus be an essential component of analysing cost data in practice.     

Boosting for detection of gene–environment interactions

In genetic association studies, it is typically thought that genetic variants and environmental variables jointly will explain more of the inheritance of a phenotype than either of these two components separately. Traditional methods to identify gene–environment interactions typically consider only one measured environmental variable at a time. However, in practice, multiple environmental factors may each be imprecise surrogates for the underlying physiological process that actually interacts with the genetic factors. In this paper, we develop a variant of L₂ boosting that is specifically designed to identify combinations of environmental variables that jointly modify the effect of a gene on a phenotype. Because the effect modifiers might have a small signal compared with the main effects, working in a space that is orthogonal to the main predictors allows us to focus on the interaction space. In a simulation study that investigates some plausible underlying model assumptions, our method outperforms the least absolute shrinkage and selection and Akaike Information Criterion and Bayesian Information Criterion model selection procedures as having the lowest test error. In an example for the Women's Health Initiative‐Population Architecture using Genomics and Epidemiology study, the dedicated boosting method was able to pick out two single‐nucleotide polymorphisms for which effect modification appears present. The performance was evaluated on an independent test set, and the results are promising. Copyright © 2012 John Wiley & Sons, Ltd.     

A multiparameter regression model for interval-censored survival data

We develop flexible multiparameter regression (MPR) survival models for interval-censored survival data arising in longitudinal prospective studies and longitudinal randomised controlled clinical trials. A multiparameter Weibull regression survival model, which is wholly parametric, and has nonproportional hazards, is the main focus of the article. We describe the basic model, develop the interval-censored likelihood, and extend the model to include gamma frailty and a dispersion model. We evaluate the models by means of a simulation study and a detailed reanalysis of data from the Signal Tandmobiel study. The results demonstrate that the MPR model with frailty is computationally efficient and provides an excellent fit to the data.     

A determinant‐based criterion for working correlation structure selection in generalized estimating equations

In generalized estimating equations (GEE), the correlation between the repeated observations on a subject is specified with a working correlation matrix. Correct specification of the working correlation structure ensures efficient estimators of the regression coefficients. Among the criteria used, in practice, for selecting working correlation structure, Rotnitzky‐Jewell, Quasi Information Criterion (QIC) and Correlation Information Criterion (CIC) are based on the fact that if the assumed working correlation structure is correct then the model‐based (naive) and the sandwich (robust) covariance estimators of the regression coefficient estimators should be close to each other. The sandwich covariance estimator, used in defining the Rotnitzky‐Jewell, QIC and CIC criteria, is biased downward and has a larger variability than the corresponding model‐based covariance estimator. Motivated by this fact, a new criterion is proposed in this paper based on the bias‐corrected sandwich covariance estimator for selecting an appropriate working correlation structure in GEE. A comparison of the proposed and the competing criteria is shown using simulation studies with correlated binary responses. The results revealed that the proposed criterion generally performs better than the competing criteria. An example of selecting the appropriate working correlation structure has also been shown using the data from Madras Schizophrenia Study. Copyright © 2015 John Wiley & Sons, Ltd.     

Non-Hodgkin's lymphoma and agricultural use of the insecticide lindane

Data from population-based case-control studies of non-Hodgkin's lymphoma among white men from Kansas, Nebraska, Iowa, and Minnesota were pooled to evaluate potential risks from environmental exposures in more detail, while controlling for potential confounding factors. These data provided the opportunity to evaluate the risk of non-Hodgkin's lymphoma from potential exposures to lindane, a pesticide that causes cancer in laboratory animals and has been associated with human cancer in a few epidemiologic investigations. This pooled data set includes 987 individuals with non-Hodgkin's lymphoma and 2,895 population-based controls. Information was obtained by telephone or in person interviews, which included detailed questions on farm practices and agricultural use of chemicals. Logistic regression was used to calculate odds ratios (ORs) adjusted for age, state of residence, and subject or proxy interviews. Reported use of lindane significantly increased the risk of non-Hodgkin's's lymphoma by 50%. Some use characteristics were suggestive of an association. ORs were greater among persons who first used the pesticide 20 years before diagnosis (OR = 1.7) than more recently (OR = 1.3), among those who reported more frequent use (OR = 2.0 for use 5 or more days per year versus 1.6 for fewer than five days per year), and from use on crops (OR = 1.9), rather than from use on animals (OR = 1.3), although these differences were not statistically significant. On the other hand, ORs were lower when based on direct interviews (OR = 1.3) than on data from proxy respondents (OR = 2.1) and adjustment for potential confounding by use of 2,4-D and diazinon reduced the ORs associated with lindane use from 1.5 to 1.2 and 1.3, respectively. Lindane does not appear to be a major etiologic factor in the development of non-Hodgkin's's lymphoma, although a small role cannot be ruled out. Am. J. Ind. Med. 33:82–87, 1998. Published 1998 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

The use of asymmetric distributions in average bioequivalence

Generic drugs have been commercialized in numerous countries. Most of these countries approve the commercialization of a generic drug when there is evidence of bioequivalence between the generic drug and the reference drug. Generally, the pharmaceutical industry is responsible for the bioequivalence test under the supervision of a regulatory agency. This procedure is concluded after a statistical data analysis. Several agencies adopt a standard statistical analysis based on procedures that were previously established. In practice, we face situations in which this standard model does not fit to some sets of bioequivalence data. In this study, we propose an evaluation of bioequivalence using univariate and bivariate models based on an extended generalized gamma distribution and a skew‐t distribution, under a Bayesian perspective. We introduce a study of the empirical power of hypothesis tests for univariate models, showing advantages in the use of an extended generalized gamma distribution. Three sets of bioequivalence data were analyzed under these new procedures and compared with the standard model proposed by the majority of regulatory agencies. In order to verify that the asymmetrical distributions are usually better fitted for the data, when compared with the standard model, model discrimination methods were used, such as the Deviance Information Criterion (DIC) and quantile–quantile plots. The research concluded that, in general, the use of the extended generalized gamma distribution may be more appropriate to model bioequivalence data in the original scale. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust network-based regularization and variable selection for high-dimensional genomic data in cancer prognosis

In cancer genomic studies, an important objective is to identify prognostic markers associated with patients' survival. Network-based regularization has achieved success in variable selections for high-dimensional cancer genomic data, because of its ability to incorporate the correlations among genomic features. However, as survival time data usually follow skewed distributions, and are contaminated by outliers, network-constrained regularization that does not take the robustness into account leads to false identifications of network structure and biased estimation of patients' survival. In this study, we develop a novel robust network-based variable selection method under the accelerated failure time model. Extensive simulation studies show the advantage of the proposed method over the alternative methods. Two case studies of lung cancer datasets with high-dimensional gene expression measurements demonstrate that the proposed approach has identified markers with important implications.     

Segmental modeling of viral load changes for HIV longitudinal data with skewness and detection limits

Although it is a common practice to analyze complex HIV longitudinal data using nonlinear mixed‐effects or nonparametric mixed‐effects models in literature, the following issues may standout. (i) In clinical practice, the profile of each subject's viral response may follow a ‘broken‐stick’‐like trajectory, indicating multiple phases of decline and increase in response. Such multiple phases (change points) may be an important indicator to help quantify treatment effect and improve management of patient care. To estimate change points, nonlinear mixed‐effects or nonparametric mixed‐effects models become a challenge because of complicated structures of model formulations. (ii) The commonly assumed distribution for model random errors is normal, but this assumption may unrealistically obscure important features of subject variations. (iii) The response observations (viral load) may be subject to left censoring due to a limit of detection. Inferential procedures can be complicated dramatically when data with asymmetric (skewed) characteristics and left censoring are observed in conjunction with change points as unknown parameters into models. There is relatively little work concerning all these features simultaneously. This article proposes segmental mixed‐effects models with skew distributions for the response process (with left censoring) under a Bayesian framework. A real data example is used to illustrate the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

How sensitive are cost-effectiveness analyses to choice of parametric distributions?

BACKGROUND: Cost-effectiveness analyses of clinical trial data are based on assumptions about the distributions of costs and effects. Cost data usually have very skewed distributions and can be difficult to model. The authors investigate whether choice of distribution can make a difference to the conclusions drawn. METHODS: The authors compare 3 distributions for cost data-normal, gamma, and lognormal-using similar parametric models for the cost-effectiveness analyses. Inferences on the cost-effectiveness plane are derived, together with cost-effectiveness acceptability curves. These methods are applied to data from a trial of rapid magnetic resonance imaging (rMRI) investigation in patients with low back pain. RESULTS: The gamma and lognormal distributions fitted the cost data much better than the normal distribution. However, in terms of inferences about cost-effectiveness, it was the normal and gamma distributions that gave similar results. Using the lognormal distribution led to the conclusion that rMRI was cost-effective for a range of willingness-to-pay values where assuming a gamma or normal distribution did not. CONCLUSIONS: Conclusions from cost-effectiveness analyses are sensitive to choice of distribution and, in particular, to how the upper tail of the cost distribution beyond the observed data is modeled. How well a distribution fits the data is an insufficient guide to model choice. A sensitivity analysis is therefore necessary to address uncertainty about choice of distribution.     

Logistic regression analysis of biomarker data subject to pooling and dichotomization

There is growing interest in pooling specimens across subjects in epidemiologic studies, especially those involving biomarkers. This paper is concerned with regression analysis of epidemiologic data where a binary exposure is subject to pooling and the pooled measurement is dichotomized to indicate either that no subjects in the pool are exposed or that some are exposed, without revealing further information about the exposed subjects in the latter case. The pooling process may be stratified on the disease status (a binary outcome) and possibly other variables but is otherwise assumed random. We propose methods for estimating parameters in a prospective logistic regression model and illustrate these with data from a population-based case-control study of colorectal cancer. Simulation results show that the proposed methods perform reasonably well in realistic settings and that pooling can lead to sizable gains in cost efficiency. We make recommendations with regard to the choice of design for pooled epidemiologic studies.     

住院患儿医院感染发生率ARIMA时间序列模型

目的初步探索和评价儿童患者医院感染发生率的自回归滑动平均混合模型(ARIMA)预测模型。方法以某院2011年1月—2014年12月4年医院感染发生率数据建立ARIMA模型,依据信息量准则,确定最优模型;以2015年医院感染发生率数据作为验证样本,评价模型的可行性。结果 ARIMA(0,1,1)为医院感染率最优预测模型,其最小信息量准则(AIC)、贝叶斯信息准则(BIC)值分别为66.61、70.76,模型残差序列的LjungBox统计量Q=14.14,差异无统计学意义(P=0.658),提示残差为白噪声序列,模型拟合良好。医院感染率实际值与预测值的平均绝对百分误差值(MAPE)为22.4,实际值均在预测值95%可信区间内,未见超出点。结论 ARIMA时间序列模型拟合医院感染率效果良好,具有预测住院患儿医院感染发生情况的实际价值。     

Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method

Experimental studies in biomedical research frequently pose analytical problems related to small sample size. In such studies, there are conflicting findings regarding the choice of parametric and nonparametric analysis, especially with non‐normal data. In such instances, some methodologists questioned the validity of parametric tests and suggested nonparametric tests. In contrast, other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests. Some researchers have recommended using a bootstrap test; however, this method also has small sample size limitation. We used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing. The present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric, nonparametric, and permutation tests through extensive simulations under various conditions and using real data examples. The nonparametric pooled bootstrap t‐test provided equal or greater power for comparing two means as compared with unpaired t‐test, Welch t‐test, Wilcoxon rank sum test, and permutation test while maintaining type I error probability for any conditions except for Cauchy and extreme variable lognormal distributions. In such cases, we suggest using an exact Wilcoxon rank sum test. Nonparametric bootstrap paired t‐test also provided better performance than other alternatives. Nonparametric bootstrap test provided benefit over exact Kruskal–Wallis test. We suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non‐normal data in small sample size studies. Copyright © 2017 John Wiley & Sons, Ltd.     

Clearance of young parasite forms following treatment of falciparum malaria in humans: comparison of three simple mathematical models.

To characterize post-treatment clearance of young forms of Plasmodium falciparum from the blood, three differential equation models, a linear decline, a linear then logarithmic decline, and the Michaelis-Menten (MM) kinetic equation, were fitted to log-transformed serial parasite counts from 30 semi-immune patients with synchronous parasitaemias allocated one of six antimalarial drug regimens. The first two equations were solved analytically. The MM equation was solved numerically using a fifth-order Runge-Kutta method. For each equation, parasite clearance was assumed stochastic and log-transformed parasite counts were assumed to be normally distributed at each time-point. Comparisons between models were by Minimum Akaike Information Criterion Estimate. A constrained MM equation fitted the data at least as well as the other two models in 5 of 6 drug groups and also when pooled data were analysed, providing a single index which could be used in drug efficacy studies in similar situations or as part of more complex models that encompass asynchronous, complicated infections.     

Hierarchical Bayesian spatial models for alcohol availability, drug "hot spots" and violent crime

Background  

Ecologic studies have shown a relationship between alcohol outlet densities, illicit drug use and violence. The present study examined this relationship in the City of Houston, Texas, using a sample of 439 census tracts. Neighborhood sociostructural covariates, alcohol outlet density, drug crime density and violent crime data were collected for the year 2000, and analyzed using hierarchical Bayesian models. Model selection was accomplished by applying the Deviance Information Criterion.