Proportional hazards models and age–period–cohort analysis of cancer rates

Age–period–cohort (APC) analysis is widely used in cancer epidemiology to model trends in cancer rates. We develop methods for comparative APC analysis of two independent cause‐specific hazard rates assuming that an APC model holds for each one. We construct linear hypothesis tests to determine whether the two hazards are absolutely proportional or proportional after stratification by cohort, period, or age. When a given proportional hazards model appears adequate, we derive simple expressions for the relative hazards using identifiable APC parameters. To demonstrate the utility of these new methods, we analyze cancer incidence rates in the United States in blacks versus whites for selected cancers, using data from the National Cancer Institute's Surveillance, Epidemiology, and End Results Program. The examples illustrate that each type of proportionality may be encountered in practice. Published in 2010 by John Wiley & Sons, Ltd.     

A Bayesian generalized age–period–cohort power model for cancer projections

Age–period–cohort (APC) models are the state of art in cancer projections, assessing past and recent trends and extrapolating mortality or incidence data into the future. Nordpred is a well‐established software, assuming a Poisson distribution for the counts and a log‐link or power‐link function with fixed power; however, its predictive performance is poor for sparse data. Bayesian models with log‐link function have been applied, but they can lead to extreme estimates. In this paper, we address criticisms of the aforementioned models by providing Bayesian formulations based on a power‐link and develop a generalized APC power‐link model, which assumes a random rather than fixed power parameter. In addition, a power model with a fixed power parameter of five was formulated in the Bayesian framework. The predictive performance of the new models was evaluated on Swiss lung cancer mortality data using model‐based estimates of observed periods. Results indicated that the generalized APC power‐link model provides best estimates for male and female lung cancer mortality. The gender‐specific models were further applied to project lung cancer mortality in Switzerland during the periods 2009–2013 and 2014–2018. Copyright © 2014 John Wiley & Sons, Ltd.     

Age‐period‐cohort models using smoothing splines: a generalized additive model approach

Age‐period‐cohort (APC) models are used to analyze temporal trends in disease or mortality rates, dealing with linear dependency among associated effects of age, period, and cohort. However, the nature of sparseness in such data has severely limited the use of APC models. To deal with these practical limitations and issues, we advocate cubic smoothing splines. We show that the methods of estimable functions proposed in the framework of generalized linear models can still be considered to solve the non‐identifiability problem when the model fitting is within the framework of generalized additive models with cubic smoothing splines. Through simulation studies, we evaluate the performance of the cubic smoothing splines in terms of the mean squared errors of estimable functions. Our results support the use of cubic smoothing splines for APC modeling with sparse but unaggregated data from a Lexis diagram. Copyright © 2013 John Wiley & Sons, Ltd.     

Using full‐cohort data in nested case–control and case–cohort studies by multiple imputation

In many large prospective cohorts, expensive exposure measurements cannot be obtained for all individuals. Exposure–disease association studies are therefore often based on nested case–control or case–cohort studies in which complete information is obtained only for sampled individuals. However, in the full cohort, there may be a large amount of information on cheaply available covariates and possibly a surrogate of the main exposure(s), which typically goes unused. We view the nested case–control or case–cohort study plus the remainder of the cohort as a full‐cohort study with missing data. Hence, we propose using multiple imputation (MI) to utilise information in the full cohort when data from the sub‐studies are analysed. We use the fully observed data to fit the imputation models. We consider using approximate imputation models and also using rejection sampling to draw imputed values from the true distribution of the missing values given the observed data. Simulation studies show that using MI to utilise full‐cohort information in the analysis of nested case–control and case–cohort studies can result in important gains in efficiency, particularly when a surrogate of the main exposure is available in the full cohort. In simulations, this method outperforms counter‐matching in nested case–control studies and a weighted analysis for case–cohort studies, both of which use some full‐cohort information. Approximate imputation models perform well except when there are interactions or non‐linear terms in the outcome model, where imputation using rejection sampling works well. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling exposure–lag–response associations with distributed lag non‐linear models

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non‐linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross‐basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure‐responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.     

Assessing risk prediction models in case–control studies using semiparametric and nonparametric methods

The predictiveness curve is a graphical tool that characterizes the population distribution of Risk(Y)=P(D=1|Y), where D denotes a binary outcome such as occurrence of an event within a specified time period and Y denotes predictors. A wider distribution of Risk(Y) indicates better performance of a risk model in the sense that making treatment recommendations is easier for more subjects. Decisions are more straightforward when a subject's risk is deemed to be high or low. Methods have been developed to estimate predictiveness curves from cohort studies. However, early phase studies to evaluate novel risk prediction markers typically employ case–control designs. Here, we present semiparametric and nonparametric methods for evaluating a continuous risk prediction marker that accommodates case–control data. Small sample properties are investigated through simulation studies. The semiparametric methods are substantially more efficient than their nonparametric counterparts under a correctly specified model. We generalize them to settings where multiple prediction markers are involved. Applications to prostate cancer risk prediction markers illustrate methods for comparing the risk prediction capacities of markers and for evaluating the increment in performance gained by adding a marker to a baseline risk model. We propose a modified Hosmer–Lemeshow test for case–control study data to assess calibration of the risk model that is a natural complement to this graphical tool. Copyright © 2010 John Wiley & Sons, Ltd.     

Age,period and cohort effects on body mass index in New Zealand, 1997–2038

Objective: To estimate the effects of age, period and birth cohort on observed trends, and to provide short‐ to medium‐term projections of population BMI in New Zealand. Methods: Data were obtained from New Zealand national health surveys covering the period 1997 to 2015 (n=76,294 individuals). A Hierarchical Age‐Period‐Cohort (HAPC) model and an Age‐Period model with interaction terms were specified for population groups defined by ethnicity and sex. Observed trends were extrapolated to estimate group‐specific BMI projections for the period 2015–2038; these were weighted by projected population sizes to calculate population‐wide BMI projections. Results: Population mean BMI increased from 26.4 kg/m² (95%CI 26.2–26.5) in 1997 to 28.3 kg/m² (95%CI 28.2–28.5) in 2015. Both models identified substantial, approximately linear, period trends behind this increase, with no significant cohort effects. Mean BMI was projected to reach 30.6 kg/m² (95%CI 29.4–31.7; HAPC model) to 30.8 kg/m² (95%CI 30.2–31.4; Age‐Period model) by 2038. Conclusions: BMI continues to increase in New Zealand. On current trends, population mean BMI will exceed 30 kg/m² – the clinical cut‐off for obesity – by the early 2030s. Implications for public health: Unless prevented by comprehensive public health policy changes, increasing population obesity is likely to result in unfavourable economic and health impacts.     

Random‐effects meta‐regression models for studying nonlinear dose–response relationship,with an application to alcohol and esophageal squamous cell carcinoma

A fundamental challenge in meta‐analyses of published epidemiological dose–response data is the estimate of the function describing how the risk of disease varies across different levels of a given exposure. Issues in trend estimate include within studies variability, between studies heterogeneity, and nonlinear trend components. We present a method, based on a two‐step process, that addresses simultaneously these issues. First, two‐term fractional polynomial models are fitted within each study included in the meta‐analysis, taking into account the correlation between the reported estimates for different exposure levels. Second, the pooled dose–response relationship is estimated considering the between studies heterogeneity, using a bivariate random‐effects model. This method is illustrated by a meta‐analysis aimed to estimate the shape of the dose–response curve between alcohol consumption and esophageal squamous cell carcinoma (SCC). Overall, 14 case–control studies and one cohort study, including 3000 cases of esophageal SCC, were included. The meta‐analysis provided evidence that ethanol intake was related to esophageal SCC risk in a nonlinear fashion. High levels of alcohol consumption resulted in a substantial risk of esophageal SCC as compared to nondrinkers. However, a statistically significant excess risk for moderate and intermediate doses of alcohol was also observed, with no evidence of a threshold effect. Copyright © 2010 John Wiley & Sons, Ltd.     

Mixture models for undiagnosed prevalent disease and interval‐censored incident disease: applications to a cohort assembled from electronic health records

For cost‐effectiveness and efficiency, many large‐scale general‐purpose cohort studies are being assembled within large health‐care providers who use electronic health records. Two key features of such data are that incident disease is interval‐censored between irregular visits and there can be pre‐existing (prevalent) disease. Because prevalent disease is not always immediately diagnosed, some disease diagnosed at later visits are actually undiagnosed prevalent disease. We consider prevalent disease as a point mass at time zero for clinical applications where there is no interest in time of prevalent disease onset. We demonstrate that the naive Kaplan–Meier cumulative risk estimator underestimates risks at early time points and overestimates later risks. We propose a general family of mixture models for undiagnosed prevalent disease and interval‐censored incident disease that we call prevalence–incidence models. Parameters for parametric prevalence–incidence models, such as the logistic regression and Weibull survival (logistic–Weibull) model, are estimated by direct likelihood maximization or by EM algorithm. Non‐parametric methods are proposed to calculate cumulative risks for cases without covariates. We compare naive Kaplan–Meier, logistic–Weibull, and non‐parametric estimates of cumulative risk in the cervical cancer screening program at Kaiser Permanente Northern California. Kaplan–Meier provided poor estimates while the logistic–Weibull model was a close fit to the non‐parametric. Our findings support our use of logistic–Weibull models to develop the risk estimates that underlie current US risk‐based cervical cancer screening guidelines. Published 2017. This article has been contributed to by US Government employees and their work is in the public domain in the USA.     

Mixed models,linear dependency,and identification in age‐period‐cohort models

This paper examines the identification problem in age‐period‐cohort models that use either linear or categorically coded ages, periods, and cohorts or combinations of these parameterizations. These models are not identified using the traditional fixed effect regression model approach because of a linear dependency between the ages, periods, and cohorts. However, these models can be identified if the researcher introduces a single just identifying constraint on the model coefficients. The problem with such constraints is that the results can differ substantially depending on the constraint chosen. Somewhat surprisingly, age‐period‐cohort models that specify one or more of ages and/or periods and/or cohorts as random effects are identified. This is the case without introducing an additional constraint. I label this identification as statistical model identification and show how statistical model identification comes about in mixed models and why which effects are treated as fixed and which are treated as random can substantially change the estimates of the age, period, and cohort effects. Copyright © 2017 John Wiley & Sons, Ltd.     

Latent variable models for gene–environment interactions in longitudinal studies with multiple correlated exposures

Many existing cohort studies designed to investigate health effects of environmental exposures also collect data on genetic markers. The Early Life Exposures in Mexico to Environmental Toxicants project, for instance, has been genotyping single nucleotide polymorphisms on candidate genes involved in mental and nutrient metabolism and also in potentially shared metabolic pathways with the environmental exposures. Given the longitudinal nature of these cohort studies, rich exposure and outcome data are available to address novel questions regarding gene–environment interaction (G × E). Latent variable (LV) models have been effectively used for dimension reduction, helping with multiple testing and multicollinearity issues in the presence of correlated multivariate exposures and outcomes. In this paper, we first propose a modeling strategy, based on LV models, to examine the association between repeated outcome measures (e.g., child weight) and a set of correlated exposure biomarkers (e.g., prenatal lead exposure). We then construct novel tests for G × E effects within the LV framework to examine effect modification of outcome–exposure association by genetic factors (e.g., the hemochromatosis gene). We consider two scenarios: one allowing dependence of the LV models on genes and the other assuming independence between the LV models and genes. We combine the two sets of estimates by shrinkage estimation to trade off bias and efficiency in a data‐adaptive way. Using simulations, we evaluate the properties of the shrinkage estimates, and in particular, we demonstrate the need for this data‐adaptive shrinkage given repeated outcome measures, exposure measures possibly repeated and time‐varying gene–environment association. Copyright © 2014 John Wiley & Sons, Ltd.     

Exposure enriched outcome dependent designs for longitudinal studies of gene–environment interaction

Joint effects of genetic and environmental factors have been increasingly recognized in the development of many complex human diseases. Despite the popularity of case‐control and case‐only designs, longitudinal cohort studies that can capture time‐varying outcome and exposure information have long been recommended for gene–environment (G × E) interactions. To date, literature on sampling designs for longitudinal studies of G × E interaction is quite limited. We therefore consider designs that can prioritize a subsample of the existing cohort for retrospective genotyping on the basis of currently available outcome, exposure, and covariate data. In this work, we propose stratified sampling based on summaries of individual exposures and outcome trajectories and develop a full conditional likelihood approach for estimation that adjusts for the biased sample. We compare the performance of our proposed design and analysis with combinations of different sampling designs and estimation approaches via simulation. We observe that the full conditional likelihood provides improved estimates for the G × E interaction and joint exposure effects over uncorrected complete‐case analysis, and the exposure enriched outcome trajectory dependent design outperforms other designs in terms of estimation efficiency and power for detection of the G × E interaction. We also illustrate our design and analysis using data from the Normative Aging Study, an ongoing longitudinal cohort study initiated by the Veterans Administration in 1963. Copyright © 2017 John Wiley & Sons, Ltd.     

慢性病趋势预测瓶颈剖析及优化模式构建分析

目的 基于对中国疾病预测研究的发展沿革、预测方法及研究瓶颈分析,旨在通过优化慢性病趋势预测模式为中国慢性病防治提供一定的理论依据。方法 通过文献荟萃分析,系统梳理中国慢性病预测发展现状及瓶颈,分析优化预测模式。结果 中国慢性病预测重视度不足,人群发病率预测较匮乏,方法学应用仍停留在线性或多元回归层面。从人口、经济、社会3个范畴筛选出影响因素变量构建状态空间模型,该优化模式比其他的时间序列自回归模型的拟合优度更高。结论 状态空间模型用于构建特定区域的慢性病趋势预测模型,可大大提高长期预测的精度和灵敏性,为循证决策提供强有力支撑。     

The Wilcoxon–Mann–Whitney test under scrutiny

The Wilcoxon–Mann–Whitney (WMW) test is often used to compare the means or medians of two independent, possibly nonnormal distributions. For this problem, the true significance level of the large sample approximate version of the WMW test is known to be sensitive to differences in the shapes of the distributions. Based on a wide ranging simulation study, our paper shows that the problem of lack of robustness of this test is more serious than is thought to be the case. In particular, small differences in variances and moderate degrees of skewness can produce large deviations from the nominal type I error rate. This is further exacerbated when the two distributions have different degrees of skewness. Other rank‐based methods like the Fligner–Policello (FP) test and the Brunner–Munzel (BM) test perform similarly, although the BM test is generally better. By considering the WMW test as a two‐sample T test on ranks, we explain the results by noting some undesirable properties of the rank transformation. In practice, the ranked samples should be examined and found to sufficiently satisfy reasonable symmetry and variance homogeneity before the test results are interpreted. Copyright © 2009 John Wiley & Sons, Ltd.     

Weighted Kaplan–Meier estimators for two‐stage treatment regimes

In two‐stage randomization designs, patients are randomized to one of the initial treatments, and at the end of the first stage, they are randomized to one of the second stage treatments depending on the outcome of the initial treatment. Statistical inference for survival data from these trials uses methods such as marginal mean models and weighted risk set estimates. In this article, we propose two forms of weighted Kaplan–Meier (WKM) estimators based on inverse‐probability weighting—one with fixed weights and the other with time‐dependent weights. We compare their properties with that of the standard Kaplan–Meier (SKM) estimator, marginal mean model‐based (MM) estimator and weighted risk set (WRS) estimator. Simulation study reveals that both forms of weighted Kaplan–Meier estimators are asymptotically unbiased, and provide coverage rates similar to that of MM and WRS estimators. The SKM estimator, however, is biased when the second randomization rates are not the same for the responders and non‐responders to initial treatment. The methods described are demonstrated by applying to a leukemia data set. Copyright © 2010 John Wiley & Sons, Ltd.     

Using accelerated drug stability results to inform long‐term studies in shelf life determination

In the pharmaceutical industry, the shelf life of a drug product is determined by data gathered from stability studies and is intended to provide consumers with a high degree of confidence that the drug retains its strength, quality, and purity under appropriate storage conditions. In this paper, we focus on liquid drug formulations and propose a Bayesian approach to estimate a drug product's shelf life, where prior knowledge gained from the accelerated study conducted during the drug development stage is used to inform the long‐term study. Classical and nonlinear Arrhenius regression models are considered for the accelerated conditions, and two examples are given where posterior results from the accelerated study are used to construct priors for a long‐term stability study.     

Bayesian inference for the stereotype regression model: Application to a case–control study of prostate cancer

The stereotype regression model for categorical outcomes, proposed by Anderson (J. Roy. Statist. Soc. B. 1984; 46 :1–30) is nested between the baseline‐category logits and adjacent category logits model with proportional odds structure. The stereotype model is more parsimonious than the ordinary baseline‐category (or multinomial logistic) model due to a product representation of the log‐odds‐ratios in terms of a common parameter corresponding to each predictor and category‐specific scores. The model could be used for both ordered and unordered outcomes. For ordered outcomes, the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable, but are inherently multi‐dimensional in nature. As pointed out by Greenland (Statist. Med. 1994; 13 :1665–1677), an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome‐stratified sampling as in case–control studies. In addition, for matched case–control studies, the stereotype model is amenable to classical conditional likelihood principle, whereas there is no reduction due to sufficiency under the proportional odds model. In spite of these attractive features, the model has been applied less, as there are issues with maximum likelihood estimation and likelihood‐based testing approaches due to non‐linearity and lack of identifiability of the parameters. We present comprehensive Bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach. We illustrate our methodology by analyzing data from The Flint Men's Health Study, a case–control study of prostate cancer in African‐American men aged 40–79 years. We use clinical staging of prostate cancer in terms of Tumors, Nodes and Metastasis as the categorical response of interest. Copyright © 2009 John Wiley & Sons, Ltd.     

Between–within models for survival analysis

A popular way to control for confounding in observational studies is to identify clusters of individuals (e.g., twin pairs), such that a large set of potential confounders are constant (shared) within each cluster. By studying the exposure–outcome association within clusters, we are in effect controlling for the whole set of shared confounders. An increasingly popular analysis tool is the between–within (BW) model, which decomposes the exposure–outcome association into a ‘within‐cluster effect’ and a ‘between‐cluster effect’. BW models are relatively common for nonsurvival outcomes and have been studied in the theoretical literature. Although it is straightforward to use BW models for survival outcomes, this has rarely been carried out in practice, and such models have not been studied in the theoretical literature. In this paper, we propose a gamma BW model for survival outcomes. We compare the properties of this model with the more standard stratified Cox regression model and use the proposed model to analyze data from a twin study of obesity and mortality. We find the following: (i) the gamma BW model often produces a more powerful test of the ‘within‐cluster effect’ than stratified Cox regression; and (ii) the gamma BW model is robust against model misspecification, although there are situations where it could give biased estimates. Copyright © 2013 John Wiley & Sons, Ltd.     

三种模型在江西省流感样病例预测中的应用与比较

目的 构建江西省流感流行趋势最优预测模型,为流感防控提供科学指导。 方法 从"中国流感监测信息系统"导出江西省2013-2017年每月流感哨点监测数据,并采用自回归（autoregressive,AR）、指数平滑（exponential smoothing,ES）和自回归积分滑动平均（autoregressive integrated moving average,ARIMA）等不同预测方法建模,并将2017年1~12月的预测值和实际比较。 结果 三种模型的R2分别为0.731、0.751和0.815;均方根误差（root mean square error,RMSE）分别为0.253、0.243和0.212;平均绝对误差（mean absolute error,MAE）分别为0.189、0.178和0.151;平均绝对百分误差（mean absolute percent error,MAPE）分别为10.092、9.523和8.124;平均相对误差（mean relative error,MRE）分别为11.45%、10.92%和8.96%。 结论 在进行江西省流感样病例就诊百分比趋势建模中,ARIMA是一个较好预测流感样病例就诊百分比的模型。