Predicting time-to-intubation after critical care admission using machine learning and cured fraction information.

Intubation for mechanical ventilation (MV) is one of the most common high-risk procedures performed in Intensive Care Units (ICUs). Early prediction of intubation may have a positive impact by providing timely alerts to clinicians and consequently avoiding high-risk late intubations. In this work, we propose a new machine learning method to predict the time to intubation during the first five days of ICU admission, based on the concept of cure survival models. Our approach combines classification and survival analysis, to effectively accommodate the fraction of patients not at risk of intubation, and provide a better estimate of time to intubation, for patients at risk. We tested our approach and compared it to other predictive models on a dataset collected from a secondary care hospital (AZ Groeninge, Kortrijk, Belgium) from 2015 to 2021, consisting of 3425 ICU stays. Furthermore, we utilised SHAP for feature importance analysis, extracting key insights into the relative significance of variables such as vital signs, blood gases, and patient characteristics in predicting intubation in ICU settings. The results corroborate that our approach improves the prediction of time to intubation in critically ill patients, by using routinely collected data within the first hours of admission in the ICU. Early warning of the need for intubation may be used to help clinicians predict the risk of intubation and rank patients according to their expected time to intubation.

On variable selection in a semiparametric AFT mixture cure model.

In clinical studies, one often encounters time-to-event data that are subject to right censoring and for which a fraction of the patients under study never experience the event of interest. Such data can be modeled using cure models in survival analysis. In the presence of cure fraction, the mixture cure model is popular, since it allows to model probability to be cured (called the incidence) and the survival function of the uncured individuals (called the latency). In this paper, we develop a variable selection procedure for the incidence and latency parts of a mixture cure model, consisting of a logistic model for the incidence and a semiparametric accelerated failure time model for the latency. We use a penalized likelihood approach, based on adaptive LASSO penalties for each part of the model, and we consider two algorithms for optimizing the criterion function. Extensive simulations are carried out to assess the accuracy of the proposed selection procedure. Finally, we employ the proposed method to a real dataset regarding heart failure patients with left ventricular systolic dysfunction.

An information-theoretic approach for the assessment of a continuous outcome as a surrogate for a binary true endpoint based on causal inference: Application to vaccine evaluation.

Within the causal association paradigm, a method is proposed to assess the validity of a continuous outcome as a surrogate for a binary true endpoint. The methodology is based on a previously introduced information-theoretic definition of surrogacy and has two main steps. In the first step, a new model is proposed to describe the joint distribution of the potential outcomes associated with the putative surrogate and the true endpoint of interest. The identifiability issues inherent to this type of models are handled via sensitivity analysis. In the second step, a metric of surrogacy new to this setting, the so-called individual causal association is presented. The methodology is studied in detail using theoretical considerations, some simulations, and data from a randomized clinical trial evaluating an inactivated quadrivalent influenza vaccine. A user-friendly R package Surrogate is provided to carry out the evaluation exercise.

A nonparametric instrumental approach to confounding in competing risks models.

This paper discusses nonparametric identification and estimation of the causal effect of a treatment in the presence of confounding, competing risks and random right-censoring. Our identification strategy is based on an instrumental variable. We show that the competing risks model generates a nonparametric quantile instrumental regression problem. Quantile treatment effects on the subdistribution function can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment.

Goodness-of-fit tests in proportional hazards models with random effects.

This paper deals with testing the functional form of the covariate effects in a Cox proportional hazards model with random effects. We assume that the responses are clustered and incomplete due to right censoring. The estimation of the model under the null (parametric covariate effect) and the alternative (nonparametric effect) is performed using the full marginal likelihood. Under the alternative, the nonparametric covariate effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using a bootstrap method. The performance of the proposed testing procedure is studied through simulations. The method is also applied on two real data sets one from biomedical research and one from veterinary medicine.

Discussion on "Instrumented difference-in-differences" by Ting Ye, Ashkan Ertefaie, James Flory, Sean Hennessy, and Dylan S. Small.

We discuss Ye et al. 2022, which combines instrumental variables methods with difference in differences. First, we compare the paper to other works in the difference in differences literatures and argue that the main contribution lies in the multiply robust estimation approach. Then, we reformulate the causal assumptions in Ye et al. 2022 in the usual theoretical framework of the instrumental variables literature. This clarifies in which sense the difference in differences design can weaken the standard instrumental variable conditions.

Semiparametric estimation of the nonmixture cure model with auxiliary survival information.

With rapidly increasing data sources, statistical methods that make use of external information are gradually becoming popular tools in medical research. In this article, we efficiently synthesize the auxiliary survival information and propose a semiparametric estimation method for the combined empirical likelihood in the framework of the nonmixture cure model, to enhance inference about the associations between exposures and disease outcomes. The auxiliary survival probabilities from external sources are first summarized as unbiased estimation equations, which help produce more efficient estimates of the effects of interest and improve the prediction accuracy for the risk of the event. Then we develop a Bernstein-based sieve empirical likelihood method to estimate the parametric and nonparametric components simultaneously. Such an estimation procedure allows us to reduce the computation burden while preserving the shape constraint on the baseline distribution function. The resulting estimators for the true associations are strongly consistent and asymptotically normal. Instead of collecting substantial exposure data, the auxiliary survival information at multiple time points is incorporated, which further reduces the mean squared error of the estimators. This contributes to biomarker evaluation and treatment effect analysis within smaller studies. We show how to choose the number of auxiliary survival probabilities appropriately and provide a guideline for practical applications. Simulation studies demonstrate that the estimators enjoy large gains in efficiency. A melanoma dataset is analyzed for illustrating the methodology.

Infectious diseases epidemiology, quantitative methodology, and clinical research in the midst of the COVID-19 pandemic: Perspective from a European country.

Starting from historic reflections, the current SARS-CoV-2 induced COVID-19 pandemic is examined from various perspectives, in terms of what it implies for the implementation of non-pharmaceutical interventions, the modeling and monitoring of the epidemic, the development of early-warning systems, the study of mortality, prevalence estimation, diagnostic and serological testing, vaccine development, and ultimately clinical trials. Emphasis is placed on how the pandemic had led to unprecedented speed in methodological and clinical development, the pitfalls thereof, but also the opportunities that it engenders for national and international collaboration, and how it has simplified and sped up procedures. We also study the impact of the pandemic on clinical trials in other indications. We note that it has placed biostatistics, epidemiology, virology, infectiology, and vaccinology, and related fields in the spotlight in an unprecedented way, implying great opportunities, but also the need to communicate effectively, often amidst controversy.

Nonparametric covariate hypothesis tests for the cure rate in mixture cure models.

In lifetime data, like cancer studies, there may be long term survivors, which lead to heavy censoring at the end of the follow-up period. Since a standard survival model is not appropriate to handle these data, a cure model is needed. In the literature, covariate hypothesis tests for cure models are limited to parametric and semiparametric methods. We fill this important gap by proposing a nonparametric covariate hypothesis test for the probability of cure in mixture cure models. A bootstrap method is proposed to approximate the null distribution of the test statistic. The procedure can be applied to any type of covariate, and could be extended to the multivariate setting. Its efficiency is evaluated in a Monte Carlo simulation study. Finally, the method is applied to a colorectal cancer dataset.

Flexible parametric model for survival data subject to dependent censoring.

When modeling survival data, it is common to assume that the (log-transformed) survival time (T) is conditionally independent of the (log-transformed) censoring time (C) given a set of covariates. There are numerous situations in which this assumption is not realistic, and a number of correction procedures have been developed for different models. However, in most cases, either some prior knowledge about the association between T and C is required, or some auxiliary information or data is/are supposed to be available. When this is not the case, the application of many existing methods turns out to be limited. The goal of this paper is to overcome this problem by developing a flexible parametric model, that is a type of transformed linear model. We show that the association between T and C is identifiable in this model. The performance of the proposed method is investigated both in an asymptotic way and through finite sample simulations. We also develop a formal goodness-of-fit test approach to assess the quality of the fitted model. Finally, the approach is applied to data coming from a study on liver transplants.

Flexible parametric approach to classical measurement error variance estimation without auxiliary data.

Measurement error in the continuous covariates of a model generally yields bias in the estimators. It is a frequent problem in practice, and many correction procedures have been developed for different classes of models. However, in most cases, some information about the measurement error distribution is required. When neither validation nor auxiliary data (e.g., replicated measurements) are available, this specification turns out to be tricky. In this article, we develop a flexible likelihood-based procedure to estimate the variance of classical additive error of Gaussian distribution, without additional information, when the covariate has compact support. The performance of this estimator is investigated both in an asymptotic way and through finite sample simulations. The usefulness of the obtained estimator when using the simulation extrapolation (SIMEX) algorithm, a widely used correction method, is then analyzed in the Cox proportional hazards model through other simulations. Finally, the whole procedure is illustrated on real data.

The single-index/Cox mixture cure model.

In survival analysis, it often happens that a certain fraction of the subjects under study never experience the event of interest, that is, they are considered "cured." In the presence of covariates, a common model for this type of data is the mixture cure model, which assumes that the population consists of two subpopulations, namely the cured and the non-cured ones, and it writes the survival function of the whole population given a set of covariates as a mixture of the survival function of the cured subjects (which equals one), and the survival function of the non-cured ones. In the literature, one usually assumes that the mixing probabilities follow a logistic model. This is, however, a strong modeling assumption, which might not be met in practice. Therefore, in order to have a flexible model which at the same time does not suffer from curse-of-dimensionality problems, we propose in this paper a single-index model for the mixing probabilities. For the survival function of the non-cured subjects we assume a Cox proportional hazards model. We estimate this model using a maximum likelihood approach. We also carry out a simulation study, in which we compare the estimators under the single-index model and under the logistic model for various model settings, and we apply the new model and estimation method on a breast cancer data set.

Hybrid combinations of parametric and empirical likelihoods.

This paper develops a hybrid likelihood (HL) method based on a compromise between parametric and nonparametric likelihoods. Consider the setting of a parametric model for the distribution of an observation Y with parameter θ. Suppose there is also an estimating function m(·, µ) identifying another parameter µ via Em(Y, µ) = 0, at the outset defined independently of the parametric model. To borrow strength from the parametric model while obtaining a degree of robustness from the empirical likelihood method, we formulate inference about θ in terms of the hybrid likelihood function Hn (θ) = Ln (θ)1-a Rn (µ(θ)) a . Here a ∈ [0,1) represents the extent of the compromise, Ln is the ordinary parametric likelihood for θ, Rn is the empirical likelihood function, and µ is considered through the lens of the parametric model. We establish asymptotic normality of the corresponding HL estimator and a version of the Wilks theorem. We also examine extensions of these results under misspecification of the parametric model, and propose methods for selecting the balance parameter a.

Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach.

In many situations in survival analysis, it may happen that a fraction of individuals will never experience the event of interest: they are considered to be cured. The promotion time cure model takes this into account. We consider the case where one or more explanatory variables in the model are subject to measurement error, which should be taken into account to avoid biased estimators. A general approach is the simulation-extrapolation algorithm, a method based on simulations which allows one to estimate the effect of measurement error on the bias of the estimators and to reduce this bias. We extend this approach to the promotion time cure model. We explain how the algorithm works, and we show that the proposed estimator is approximately consistent and asymptotically normally distributed, and that it performs well in finite samples. Finally, we analyse a database in cardiology: among the explanatory variables of interest is the ejection fraction, which is known to be measured with error.

Robust estimation for homoscedastic regression in the secondary analysis of case-control data.

Primary analysis of case-control studies focuses on the relationship between disease D and a set of covariates of interest (Y, X). A secondary application of the case-control study, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated owing to the case-control sampling, where the regression of Y on X is different from what it is in the population. Previous work has assumed a parametric distribution for Y given X and derived semiparametric efficient estimation and inference without any distributional assumptions about X. We take up the issue of estimation of a regression function when Y given X follows a homoscedastic regression model, but otherwise the distribution of Y is unspecified. The semiparametric efficient approaches can be used to construct semiparametric efficient estimates, but they suffer from a lack of robustness to the assumed model for Y given X. We take an entirely different approach. We show how to estimate the regression parameters consistently even if the assumed model for Y given X is incorrect, and thus the estimates are model robust. For this we make the assumption that the disease rate is known or well estimated. The assumption can be dropped when the disease is rare, which is typically so for most case-control studies, and the estimation algorithm simplifies. Simulations and empirical examples are used to illustrate the approach.

A simulation procedure based on copulas to generate clustered multi-state survival data.

Generating survival data with a clustered and multi-state structure is useful to study finite sample properties of multi-state models, competing risks models and frailty models. We propose a simulation procedure based on a copula model for each competing events block, allowing to introduce dependence between times of different transitions and between those of grouped subjects. The effect of simulated frailties and covariates can be added in a proportional hazards way. In order to mimic information from real data, we also propose a method for the tuning of parameters via numerical minimization of a criterion function based on the ratios of target and observed values of median times and of probabilities of competing events. An example is provided on simulation of data mimicking those from a multicenter study on head and neck cancer, where the interest is in studying both time to local relapses and to distant metastases before death. The results demonstrated that data simulated according to our proposed method have characteristics very close to the target values.