Presence Of Time-varying Covariates Research Articles

Dynamic Prediction Using Landmark Historical Functional Cox Regression

Dynamic prediction of survival data in the presence of time-varying covariates is an area of active research. Two common analytic approaches for this type of data are joint modeling of the longitudinal and survival processes and landmarking. However, there has been little work dedicated to densely measured time-varying covariates using either approach. Moreover, the software for joint modeling is slow, especially for large datasets, and rather limited for landmarking. We propose a landmark approach for dynamic prediction of survival outcomes using densely measured longitudinal predictors, which treats the past of the time-varying covariate at each landmark point as a functional predictor. This approach is orders of magnitude faster than existing software for simpler joint models. Our extensive comparative simulation study required 8.4 computation-years, over 99% of which was devoted to fitting and predicting from two joint models. Our landmark approach performs similarly to joint modeling when the joint model is correctly specified and substantially out-performs it when it is not. Methods are motivated by an application predicting time to recovery of Multiple Sclerosis lesions in a large neuroimaging dataset. Supplementary materials for this article are available online.

Parametric frailty model based analysis of survival data with time-varying risk factors

In the follow-up study, a covariate changing over time is known as a time-varying covariate. By using the frailty model, we can analyze the effect of such a variable on survival time. When heterogeneity is present, the statistical analysis of the survival data without considering frailty gives a less accurate estimate of parameters. The proportional hazard (PH) assumption of the Cox regression model for time-varying covariates does not hold. The PH assumption was tested using Schoenfeld residuals, and a p-value of less than 0.05 was deemed statistically significant. The covariates' p-value is less than 0.05, which suggests that they do not meet the PH assumption and shows that the covariate is time-varying. This article aims to illustrate how to carry out statistical analysis by using frailty models in the presence of time-varying covariates and to compare their performance. Two frailty models, namely the Gamma frailty model and the inverse-Gaussian frailty model with log-normal and Weibull as initial hazards, were used in this study. AIC and BIC were used to compare the performance of the models. An application to hospital readmission data for patients with colorectal cancer is illustrated.

Association Between Body Fat and Body Mass Index from Incomplete Longitudinal Proportion Data: Findings from the Fels Study

Obesity rates continue to exhibit an upward trajectory, particularly in the US, and is the underlying cause of several comorbidities, including but not limited to high blood pressure, high cholesterol, diabetes, heart disease, stroke, and cancers. To monitor obesity, body mass index (BMI) and proportion body fat (PBF) are two commonly used measurements. Although BMI and PBF changes over time in an individual’s lifespan and their relationship may also change dynamically, existing work has mostly remained cross-sectional, or separately modeling BMI and PBF. A combined longitudinal assessment is expected to be more effective in unravelling their complex interplay. To mitigate this, we consider Bayesian cross-domain latent growth curve models within a structural equation modeling framework, which simultaneously handles issues such as individually varying time metrics, proportion data, and potential missing not at random data for joint assessment of the longitudinal changes of BMI and PBF. Through simulation studies, we observe that our proposed models and estimation method yielded parameter estimates with small bias and mean squared error in general, however, a mis-specified missing data mechanism may cause inaccurate and inefficient parameter estimates. Furthermore, we demonstrate application of our method to a motivating longitudinal obesity study, controlling for both time-invariant (such as, sex), and time-varying (such as diastolic and systolic blood pressure, biceps skinfold, bioelectrical impedance, and waist circumference) covariates in separate models. Under time-invariance, we observe that the initial BMI level and the rate of change in BMI influenced PBF. However, in presence of time-varying covariates, only the initial BMI level influenced the initial PBF. The added-on selection model estimation indicated that observations with higher PBF values were less likely to be missing.

Ensemble methods for survival function estimation with time-varying covariates.

Survival data with time-varying covariates are common in practice. If relevant, they can improve on the estimation of a survival function. However, the traditional survival forests-conditional inference forest, relative risk forest and random survival forest-have accommodated only time-invariant covariates. We generalize the conditional inference and relative risk forests to allow time-varying covariates. We also propose a general framework for estimation of a survival function in the presence of time-varying covariates. We compare their performance with that of the Cox model and transformation forest, adapted here to accommodate time-varying covariates, through a comprehensive simulation study in which the Kaplan-Meier estimate serves as a benchmark, and performance is compared using the integrated difference between the true and estimated survival functions. In general, the performance of the two proposed forests substantially improves over the Kaplan-Meier estimate. Taking into account all other factors, under the proportional hazard setting, the best method is always one of the two proposed forests, while under the non-proportional hazard setting, it is the adapted transformation forest. -fold cross-validation is used as an effective tool to choose between the methods in practice.

THE BIDIRECTIONAL RELATIONSHIP BETWEEN AGING IN PLACE AND COGNITIVE FUNCTIONING OVER TIME

Residential stability (aging in place) in older adults may be either supportive or detrimental to cognitive aging, and may be dynamic over time. Using residential histories of 3608 older adults in the Cardiovascular Health Study, this study seeks to estimate the potentially bidirectional relationship between residential change and cognitive functioning. Residential data were recorded and georeferenced annually, and the Modified Mini-Mental State Examination assessed global cognitive functioning. Marginal structural models will be used to assess the effect of residential and cognitive exposures over time, in the presence of time-varying covariates that may act as confounders and mediators at different time points. We hypothesize that residential stability will have a bidirectional relationship with cognitive functioning over time. Aging in place will be associated with higher cognitive function during follow-up, and predict longer dementia-free survival. In turn, time to residential relocation during follow-up will be shorter among those with lower cognitive function.

Marginal structural Cox model to estimate the causal effect of clinical mastitis on Québec dairy cow culling risk

Health disorders, such as milk fever, displaced abomasum, or retained placenta, as well as poor reproductive performance, are known risk factors for culling in dairy cows. Clinical mastitis (CM) is one of the most influential culling risk factors. However the culling decision could be based either on the disease status or on the current milk yield, milk production being a significant confounder when modelling dairy cow culling risk. But milk yield (and somatic cell count) are time-varying confounders, which are also affected by prior CM and therefore lie on the causal pathway between the exposure of interest, CM, and the outcome, culling. Including these time-varying confounders could result in biased estimates. A marginal structural model (MSM) is a statistical technique allowing estimation of the causal effect of a time-varying exposure in the presence of time-varying covariates without conditioning on these covariates. The objective of this paper is to estimate the causal effect on culling of CM occurring between calving and 120 days in milk, using MSM to control for such time-varying confounders affected by previous exposure. A retrospective longitudinal study was conducted on data from dairy herds in the Province of Québec, Canada, by extracting health information events from the dairy herd health management software used by most Québec dairy producers and their veterinarians. The data were extracted for all lactations starting between January 1st and December 31st, 2010. A total of 3952 heifers and 8724 cows from 261 herds met the inclusion criteria and were used in the analysis.The estimated CM causal hazard ratios were 1.96 [1.57–2.44] and 1.47 [1.28–1.69] for heifers and cows, respectively, and as long as causal assumptions hold. Our findings confirm that CM was a risk factor for culling, but with a reduced effect compared to previous studies, which did not properly control for the presence of time-dependent confounders such as milk yield and somatic cell count. Cows experienced a lower risk for CM, with milk production having more influence on culling risk in cows than heifers.

Performance of growth mixture models in the presence of time-varying covariates.

Growth mixture modeling is often used to identify unobserved heterogeneity in populations. Despite the usefulness of growth mixture modeling in practice, little is known about the performance of this data analysis technique in the presence of time-varying covariates. In the present simulation study, we examined the impacts of five design factors: the proportion of the total variance of the outcome explained by the time-varying covariates, the number of time points, the error structure, the sample size, and the mixing ratio. More precisely, we examined the impact of these factors on the accuracy of parameter and standard error estimates, as well ason the class enumeration accuracy. Our results showed that the consistent Akaike information criterion (CAIC), thesample-size-adjusted CAIC(SCAIC), theBayesian information criterion (BIC), and the integrated completed likelihood criterion (ICL-BIC) proved to be highly reliable indicators of the true number of latent classes in the data, across design conditions, and that the sample-size-adjusted BIC (SBIC) also proved quite accurate, especially in larger samples. In contrast, the Akaike information criterion (AIC), theentropy, thenormalized entropy criterion(NEC), and the classification likelihood criterion (CLC) proved to be unreliable indicators of the true number of latent classes in the data. Our results also showed that substantial biases in the parameter and standard error estimates tended to be associated with growth mixture models that included only four time points.

Risk of attrition in a longitudinal study of skin cancer: logistic and survival models can give different results

ObjectivesLongitudinal studies are a major tool for public health research, but their value can be undermined by attrition. Identification of factors associated with attrition through modeling depends on the efficient use of data and is conditional on modeling assumptions being met. The primary aim of this study was to compare the performance of four models in analyzing attrition risk. Study Design and SettingData from participants who were lost to follow-up from The Nambour Skin Cancer Study between 1992 and 2000 were analyzed using logistic and survival models, for all-cause and nondeath attritions. ResultsDuring follow-up, 321 (19.8%) of 1,621 participants were lost to follow-up; 70 (4.3%) because of death and 251 (15.5%) for other reasons. Using survival models showed skin cancer diagnosis to be associated with increased all-cause attrition (hazard ratio: 2.3; 95% confidence interval [95% CI]: 1.5, 3.4) and nondeath attrition (subhazard ratio: 1.9; 95% CI: 1.0, 3.3). Using logistic regression resulted in inverse associations being observed for both all-cause attrition (odds ratio [OR]: 0.7; 95% CI: 0.5, 1.1) and nondeath attrition (OR: 0.5; 95% CI: 0.3, 1.0). ConclusionThese results demonstrate the relative inadequacy of a logistic as opposed to a survival approach when analyzing attrition risk in the presence of time-varying covariates and multiple timepoints.

Analyzing Complex Capture–Recapture Data in the Presence of Individual and Temporal Covariates and Model Uncertainty

We consider the issue of analyzing complex ecological data in the presence of covariate information and model uncertainty. Several issues can arise when analyzing such data, not least the need to take into account where there are missing covariate values. This is most acutely observed in the presence of time-varying covariates. We consider mark-recapture-recovery data, where the corresponding recapture probabilities are less than unity, so that individuals are not always observed at each capture event. This often leads to a large amount of missing time-varying individual covariate information, because the covariate cannot usually be recorded if an individual is not observed. In addition, we address the problem of model selection over these covariates with missing data. We consider a Bayesian approach, where we are able to deal with large amounts of missing data, by essentially treating the missing values as auxiliary variables. This approach also allows a quantitative comparison of different models via posterior model probabilities, obtained via the reversible jump Markov chain Monte Carlo algorithm. To demonstrate this approach we analyze data relating to Soay sheep, which pose several statistical challenges in fully describing the intricacies of the system.

Missing Covariates in Longitudinal Data with Informative Dropouts: Bias Analysis and Inference

We consider estimation in generalized linear mixed models (GLMM) for longitudinal data with informative dropouts. At the time a unit drops out, time-varying covariates are often unobserved in addition to the missing outcome. However, existing informative dropout models typically require covariates to be completely observed. This assumption is not realistic in the presence of time-varying covariates. In this article, we first study the asymptotic bias that would result from applying existing methods, where missing time-varying covariates are handled using naive approaches, which include: (1) using only baseline values; (2) carrying forward the last observation; and (3) assuming the missing data are ignorable. Our asymptotic bias analysis shows that these naive approaches yield inconsistent estimators of model parameters. We next propose a selection/transition model that allows covariates to be missing in addition to the outcome variable at the time of dropout. The EM algorithm is used for inference in the proposed model. Data from a longitudinal study of human immunodeficiency virus (HIV)-infected women are used to illustrate the methodology.

Monte Carlo Analysis of Score Test-Based Corrections in the Presence of Time-Varying Covariates within the Log-Hazard

Corrections based on the score test for neglected heterogeneity do not appear to have been used previously in the presence of time-varying covariates. This paper uses Monte Carlo analysis to evaluate, for a grouped hazard framework constructed for an empirical application, the efficacy of such corrections.

Analysis of incomplete multivariate data using linear models with structured covariance matrices.

Incomplete and unbalanced multivariate data often arise in longitudinal studies due to missing or unequally-timed repeated measurements and/or the presence of time-varying covariates. A general approach to analysing such data is through maximum likelihood analysis using a linear model for the expected responses, and structural models for the within-subject covariances. Two important advantages of this approach are: (1) the generality of the model allows the analyst to consider a wider range of models than were previously possible using classical methods developed for balanced and complete data, and (2) maximum likelihood estimates obtained from incomplete data are often preferable to other estimates such as those obtained from complete cases from the standpoint of bias and efficiency. A variety of applications of the model are discussed, including univariate and multivariate analysis of incomplete repeated measures data, analysis of growth curves with missing data using random effects and time-series models, and applications to unbalanced longitudinal data.