Review and comparison of ROC curve estimators for a time‐dependent outcome with marker‐dependent censoring

To quantify the ability of a marker to predict the onset of a clinical outcome in the future, time‐dependent estimators of sensitivity, specificity, and ROC curve have been proposed accounting for censoring of the outcome. In this paper, we review these estimators, recall their assumptions about the censoring mechanism and highlight their relationships and properties. A simulation study shows that marker‐dependent censoring can lead to important biases for the ROC estimators not adapted to this case. A slight modification of the inverse probability of censoring weighting estimators proposed by Uno et al. (2007) and Hung and Chiang (2010a) performs as well as the nearest neighbor estimator of Heagerty et al. (2000) in the simulation study and has interesting practical properties. Finally, the estimators were used to evaluate abilities of a marker combining age and a cognitive test to predict dementia in the elderly. Data were obtained from the French PAQUID cohort. The censoring appears clearly marker‐dependent leading to appreciable differences between ROC curves estimated with the different methods.     

Time‐to‐event continual reassessment method incorporating treatment cycle information with application to an oncology phase I trial

Delayed dose limiting toxicities (i.e. beyond first cycle of treatment) is a challenge for phase I trials. The time‐to‐event continual reassessment method (TITE‐CRM) is a Bayesian dose‐finding design to address the issue of long observation time and early patient drop‐out. It uses a weighted binomial likelihood with weights assigned to observations by the unknown time‐to‐toxicity distribution, and is open to accrual continually. To avoid dosing at overly toxic levels while retaining accuracy and efficiency for DLT evaluation that involves multiple cycles, we propose an adaptive weight function by incorporating cyclical data of the experimental treatment with parameters updated continually. This provides a reasonable estimate for the time‐to‐toxicity distribution by accounting for inter‐cycle variability and maintains the statistical properties of consistency and coherence. A case study of a First‐in‐Human trial in cancer for an experimental biologic is presented using the proposed design. Design calibrations for the clinical and statistical parameters are conducted to ensure good operating characteristics. Simulation results show that the proposed TITE‐CRM design with adaptive weight function yields significantly shorter trial duration, does not expose patients to additional risk, is competitive against the existing weighting methods, and possesses some desirable properties.     

Outcome-dependent sampling from existing cohorts with longitudinal binary response data: study planning and analysis

When novel scientific questions arise after longitudinal binary data have been collected, the subsequent selection of subjects from the cohort for whom further detailed assessment will be undertaken is often necessary to efficiently collect new information. Key examples of additional data collection include retrospective questionnaire data, novel data linkage, or evaluation of stored biological specimens. In such cases, all data required for the new analyses are available except for the new target predictor or exposure. We propose a class of longitudinal outcome-dependent sampling schemes and detail a design corrected conditional maximum likelihood analysis for highly efficient estimation of time-varying and time-invariant covariate coefficients when resource limitations prohibit exposure ascertainment on all participants. Additionally, we detail an important study planning phase that exploits available cohort data to proactively examine the feasibility of any proposed substudy as well as to inform decisions regarding the most desirable study design. The proposed designs and associated analyses are discussed in the context of a study that seeks to examine the modifying effect of an interleukin-10 cytokine single nucleotide polymorphism on asthma symptom regression in adolescents participating Childhood Asthma Management Program Continuation Study. Using this example we assume that all data necessary to conduct the study are available except subject-specific genotype data. We also assume that these data would be ascertained by analyzing stored blood samples, the cost of which limits the sample size.     

Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time‐Varying Covariates

Summary Neuroimaging data collected at repeated occasions are gaining increasing attention in the neuroimaging community due to their potential in answering questions regarding brain development, aging, and neurodegeneration. These datasets are large and complicated, characterized by the intricate spatial dependence structure of each response image, multiple response images per subject, and covariates that may vary with time. We propose a multiscale adaptive generalized method of moments (MA‐GMM) approach to estimate marginal regression models for imaging datasets that contain time‐varying, spatially related responses and some time‐varying covariates. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. Further, instead of assuming independence of voxels (the components that make up each subject’s response image at each time point) as many current neuroimaging analysis techniques do, this method “adaptively smoothes” neuroimaging response data, computing parameter estimates by iteratively building spheres around each voxel and combining observations within the spheres with weights. MA‐GMM’s development adds to the few available modeling approaches intended for longitudinal imaging data analysis. Simulation studies and an analysis of a real longitudinal imaging dataset from the Alzheimer’s Disease Neuroimaging Initiative are used to assess the performance of MA‐GMM. Martha Skup, Hongtu Zhu, and Heping Zhang for the Alzheimer’s Disease Neuroimaging Initiative.     

Bayesian Estimation of the Time‐Varying Sensitivity of a Diagnostic Test with Application to Mother‐to‐Child Transmission of HIV

Summary We present a Bayesian model to estimate the time‐varying sensitivity of a diagnostic assay when the assay is given repeatedly over time, disease status is changing, and the gold standard is only partially observed. The model relies on parametric assumptions for the distribution of the latent time of disease onset and the time‐varying sensitivity. Additionally, we illustrate the incorporation of historical data for constructing prior distributions. We apply the new methods to data collected in a study of mother‐to‐child transmission of HIV and include a covariate for sensitivity to assess whether two different assays have different sensitivity profiles.     

Cox proportional hazards models with left truncation and time‐varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time‐to‐event cohort data, two different ways of choosing a time scale have been discussed in the literature: time‐on‐study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time‐varying coefficient for left‐truncated and right‐censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well‐established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.     

On the validity of time‐dependent AUC estimation in the presence of cure fraction

During the last decades, several approaches have been proposed to estimate the time‐dependent area under the receiver operating characteristic curve (AUC) of risk tools derived from survival data. The validity of these estimators relies on some regularity assumptions among which a survival function being proper. In practice, this assumption is not always satisfied because a fraction of the population may not be susceptible to experience the event of interest even for long follow‐up. Studying the sensitivity of the proposed estimators to the violation of this assumption is of substantial interest. In this paper, we investigate the performance of a nonparametric simple estimator, developed for classical survival data, in the case when the population exhibits a cure fraction. Motivated from the current practice of deriving risk tools in oncology and cardiovascular disease prevention, we also assess the loss, in terms of predictive performance, when deriving risk tools from survival models that do not acknowledge the presence of cure. The simulation results show that the investigated method is valid even under the presence of cure. They also show that risk tools derived from survival models that ignore the presence of cure have smaller AUC compared to those derived from survival models that acknowledge the presence of cure. This was also attested with a real data analysis from a breast cancer study.     

Time‐Varying Latent Effect Model for Longitudinal Data with Informative Observation Times

Summary In analysis of longitudinal data, it is not uncommon that observation times of repeated measurements are subject‐specific and correlated with underlying longitudinal outcomes. Taking account of the dependence between observation times and longitudinal outcomes is critical under these situations to assure the validity of statistical inference. In this article, we propose a flexible joint model for longitudinal data analysis in the presence of informative observation times. In particular, the new procedure considers the shared random‐effect model and assumes a time‐varying coefficient for the latent variable, allowing a flexible way of modeling longitudinal outcomes while adjusting their association with observation times. Estimating equations are developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, with variance–covariance matrix that has a closed form and can be consistently estimated by the usual plug‐in method. One additional advantage of the procedure is that it provides a unified framework to test whether the effect of the latent variable is zero, constant, or time‐varying. Simulation studies show that the proposed approach is appropriate for practical use. An application to a bladder cancer data is also given to illustrate the methodology.     

Semiparametric Transformation Models with Time‐Varying Coefficients for Recurrent and Terminal Events

Summary In this article, we propose a family of semiparametric transformation models with time‐varying coefficients for recurrent event data in the presence of a terminal event such as death. The new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time. For the inference on the proposed models, a class of estimating equations is developed and asymptotic properties of the resulting estimators are established. In addition, a lack‐of‐fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite‐sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is also illustrated.     

Dose–response relationship from longitudinal data with response‐dependent dose modification using likelihood methods

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose–response relationship. In this study, we consider the dose–response relationship under these situations. We show that maximum‐likelihood estimates are consistent without modeling the dose‐modification mechanisms when the selection of the dose as a time‐dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose‐modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose–response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum‐likelihood estimates of the dose–response relationship are consistent under the dose modification based only on observed responses.     

Wrong,but useful: regional species distribution models may not be improved by range‐wide data under biased sampling

Species distribution modeling (SDM) is an essential method in ecology and conservation. SDMs are often calibrated within one country's borders, typically along a limited environmental gradient with biased and incomplete data, making the quality of these models questionable. In this study, we evaluated how adequate are national presence‐only data for calibrating regional SDMs. We trained SDMs for Egyptian bat species at two different scales: only within Egypt and at a species‐specific global extent. We used two modeling algorithms: Maxent and elastic net, both under the point‐process modeling framework. For each modeling algorithm, we measured the congruence of the predictions of global and regional models for Egypt, assuming that the lower the congruence, the lower the appropriateness of the Egyptian dataset to describe the species' niche. We inspected the effect of incorporating predictions from global models as additional predictor (“prior”) to regional models, and quantified the improvement in terms of AUC and the congruence between regional models run with and without priors. Moreover, we analyzed predictive performance improvements after correction for sampling bias at both scales. On average, predictions from global and regional models in Egypt only weakly concur. Collectively, the use of priors did not lead to much improvement: similar AUC and high congruence between regional models calibrated with and without priors. Correction for sampling bias led to higher model performance, whatever prior used, making the use of priors less pronounced. Under biased and incomplete sampling, the use of global bats data did not improve regional model performance. Without enough bias‐free regional data, we cannot objectively identify the actual improvement of regional models after incorporating information from the global niche. However, we still believe in great potential for global model predictions to guide future surveys and improve regional sampling in data‐poor regions.