Readily available proxies for time of disease onset such as time of the first diagnostic code can lead to substantial risk prediction error if performing analyses based on poor proxies. Due to the lack of detailed documentation and labor intensiveness of manual annotation, it is often only feasible to ascertain for a small subset the current status of the disease by a follow up time rather than the exact time. In this paper, we aim to develop risk prediction models for the onset time efficiently leveraging both a small number of labels on current status and a large number of unlabeled observations on imperfect proxies. Under a semiparametric transformation model for onset and a highly flexible measurement error models for proxy onset time, we propose the semisupervised risk prediction method by combining information from proxies and limited labels efficiently. From an initial estimator solely based on the labelled subset, we perform a one-step correction with the full data augmenting against a mean zero rank correlation score derived from the proxies. We establish the consistency and asymptotic normality of the proposed semi-supervised estimator and provide a resampling procedure for interval estimation. Simulation studies demonstrate that the proposed estimator performs well in finite sample. We illustrate the proposed estimator by developing a genetic risk prediction model for obesity using data from Partners Biobank Electronic Health Records (EHR).
Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, p…
Databases derived from electronic health records (EHRs) are commonly subject to left truncation, a type of selection bias induced due to patients needing to survive long enough to satisfy certain entry criteria. Standard methods to adjust for left truncation bias rely on an assumption of marginal independence between entry and survival times, which may not always be satisfied in practice. In this work, we examine how a weaker assumption of conditional independence can result in unbiased estimation of common statistical parameters. In particular, we show the estimability of conditional paramete…
Probabilistic survival predictions from models trained with Maximum Likelihood Estimation (MLE) can have high, and sometimes unacceptably high variance. The field of meteorology, where the paradigm of maximizing sharpness subject to calibration is popular, has addressed this problem by using scoring rules beyond MLE, such as the Continuous Ranked Probability Score (CRPS). In this paper we present the \emph{Survival-CRPS}, a generalization of the CRPS to the survival prediction setting, with right-censored and interval-censored variants. We evaluate our ideas on the mortality prediction task us…
We are interested in survival analysis of hemodialysis patients for whom several biomarkers are recorded over time. Motivated by this challenging problem, we propose a general framework for multivariate joint longitudinal-survival modeling that can be used to examine the association between several longitudinally recorded covariates and a time-to-event endpoint. Our method allows for simultaneous modeling of longitudinal covariates by taking their correlation into account. This leads to a more efficient method for modeling their trajectories over time, and hence, it can better capture their re…
In medicine, researchers often seek to infer the effects of a given treatment on patients' outcomes. However, the standard methods for causal survival analysis make simplistic assumptions about the data-generating process and cannot capture complex interactions among patient covariates. We introduce the Dynamic Survival Transformer (DynST), a deep survival model that trains on electronic health records (EHRs). Unlike previous transformers used in survival analysis, DynST can make use of time-varying information to predict evolving survival probabilities. We derive a semi-synthetic EHR dataset …
De-biased Distribution Estimation for Locally Differential Private Survival Data
The State University of New York (SUNY) at Buffalo（纽约州立大学布法罗分校）；National Chengchi University（国立政治大学）；University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）
We use a combination of extreme value theory, survival analysis and computer-intensive methods to analyze the mortality of Italian and French semi-supercentenarians for whom there are validated records. After accounting for the effects of the sampling frame, there appears to be a constant rate of mortality beyond age 108 years and no difference between countries and cohorts. These findings are consistent with previous work based on the International Database on Longevity and suggest that any physical upper bound for humans is so large that it is unlikely to be approached. There is no evidence …
Dependent survival data arise in many contexts. One context is clustered survival data, where survival data are collected on clusters such as families or medical centers. Dependent survival data also arise when multiple survival times are recorded for each individual. Frailty models is one common approach to handle such data. In frailty models, the dependence is expressed in terms of a random effect, called the frailty. Frailty models have been used with both Cox proportional hazards model and the accelerated failure time model. This paper reviews recent developments in the area of frailty mod…
In survival studies it is important to record the values of key longitudinal covariates until the occurrence of event of a subject. For this reason, it is essential to study the association between longitudinal and time-to-event outcomes using the joint model. In this paper, profile likelihood approach has been used to estimate the cumulative hazard and regression parameters from the joint model of survival and longitudinal data. Moreover, we show the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the …
Increasingly, medical research is dependent on data collected for non-research purposes, such as electronic health records data (EHR). EHR data and other large databases can be prone to measurement error in key exposures, and unadjusted analyses of error-prone data can bias study results. Validating a subset of records is a cost-effective way of gaining information on the error structure, which in turn can be used to adjust analyses for this error and improve inference. We extend the mean score method for the two-phase analysis of discrete-time survival models, which uses the unvalidated covar…
Aalborg University Hospital（奥尔堡大学医院）；Aalborg University（奥尔堡大学）
Outcome regressed on class labels identified by unsupervised clustering is custom in many applications. However, it is common to ignore the misclassification of class labels caused by the learning algorithm, which potentially leads to serious bias of the estimated effect parameters. Due to its generality we suggest to redress the situation by use of the simulation and extrapolation method. Performance is illustrated by simulated data from Gaussian mixture models. Finally, we apply our method to a study which regressed overall survival on class labels derived from unsupervised clustering of gen…
Survival function estimation is used in many disciplines, but it is most common in medical analytics in the form of the Kaplan-Meier estimator. Sensitive data (patient records) is used in the estimation without any explicit control on the information leakage, which is a significant privacy concern. We propose a first differentially private estimator of the survival function and show that it can be easily extended to provide differentially private confidence intervals and test statistics without spending any extra privacy budget. We further provide extensions for differentially private estimati…
The electronic health record (EHR) provides an unprecedented opportunity to build actionable tools to support physicians at the point of care. In this paper, we investigate survival analysis in the context of EHR data. We introduce deep survival analysis, a hierarchical generative approach to survival analysis. It departs from previous approaches in two primary ways: (1) all observations, including covariates, are modeled jointly conditioned on a rich latent structure; and (2) the observations are aligned by their failure time, rather than by an arbitrary time zero as in traditional survival a…
Contrasting marginal counterfactual survival curves across treatment arms is an effective and popular approach for inferring the causal effect of an intervention on a right-censored time-to-event outcome. A key challenge to drawing such inferences in observational settings is the possible existence of unmeasured confounding, which may invalidate most commonly used methods that assume no hidden confounding bias. In this paper, rather than making the standard no unmeasured confounding assumption, we extend the recently proposed proximal causal inference framework of Miao et al. (2018), Tchetgen …
The timing of antiretroviral therapy (ART) initiation for HIV and tuberculosis (TB) co-infected patients needs to be considered carefully. CD4 cell count can be used to guide decision making about when to initiate ART. Evidence from recent randomized trials and observational studies generally supports early initiation but does not provide information about effects of initiation time on a continuous scale. In this paper, we develop and apply a highly flexible structural proportional hazards model for characterizing the effect of treatment initiation time on a survival distribution. The model ca…
The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In practice, however, observations are almost always tainted by errors and uncertainties. If the yardstick used to compare forecasts is imprecise, one can wonder whether such types of errors may or may not have a strong influence on decisions based on classical scoring rules. We propose a new scoring rule scheme in the context of models that incorporate errors of …
University Medical Center Göttingen（哥廷根大学医学中心）；University of Regensburg（雷根斯堡大学）；Kiel University（基尔大学）；University Medical Center Schleswig-Holstein（石勒苏益格-荷尔斯泰因大学医学中心）
Estimating the effects of interventions on patient outcome is one of the key aspects of personalized medicine. Their inference is often challenged by the fact that the training data comprises only the outcome for the administered treatment, and not for alternative treatments (the so-called counterfactual outcomes). Several methods were suggested for this scenario based on observational data, i.e.~data where the intervention was not applied randomly, for both continuous and binary outcome variables. However, patient outcome is often recorded in terms of time-to-event data, comprising right-cens…
