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Panel data arises when transitions between different states are interval-censored in multi-state data. The analysis of such data using non-parametric multi-state models was not possible until recently, but is very desirable as it allows for more flexibility than its parametric counterparts. The single available result to date has some unique drawbacks. We propose a non-parametric estimator of the transition intensities for panel data using an Expectation Maximisation algorithm. The method allows for a mix of interval-censored and right-censored (exactly observed) transitions. A condition to check for the convergence of the algorithm to the non-parametric maximum likelihood estimator is given. A simulation study comparing the proposed estimator to a consistent estimator is performed, and shown to yield near identical estimates at smaller computational cost. A data set on the emergence of teeth in children is analysed. Code to perform the analyses is publicly available., Comment: 32 pages, 17 figures. Software in the form of an R package for the proposed method can be found on GitHub: https://github.com/d-gomon/icmstate

In the presence of unmeasured heterogeneity, the hazard ratio for exposure has a complex causal interpretation. To address this, accelerated failure time (AFT) models, which assess the effect on the survival time ratio scale, are often suggested as a better alternative. AFT models also allow for straightforward confounder adjustment. In this work, we formalize the causal interpretation of the acceleration factor in AFT models using structural causal models and data under independent censoring. We prove that the acceleration factor is a valid causal effect measure, even in the presence of frailty and treatment effect heterogeneity. Through simulations, we show that the acceleration factor better captures the causal effect than the hazard ratio when both AFT and proportional hazards models apply. Additionally, we extend the interpretation to systems with time-dependent acceleration factors, revealing the challenge of distinguishing between a time-varying homogeneous effect and unmeasured heterogeneity. While the causal interpretation of acceleration factors is promising, we caution practitioners about potential challenges in estimating these factors in the presence of effect heterogeneity.

Competing risks models can involve more than one time scale. A relevant example is the study of mortality after a cancer diagnosis, where time since diagnosis but also age may jointly determine the hazards of death due to different causes. Multiple time scales have rarely been explored in the context of competing events. Here, we propose a model in which the cause-specific hazards vary smoothly over two times scales. It is estimated by two-dimensional $P$-splines, exploiting the equivalence between hazard smoothing and Poisson regression. The data are arranged on a grid so that we can make use of generalized linear array models for efficient computations. The R-package TwoTimeScales implements the model. As a motivating example we analyse mortality after diagnosis of breast cancer and we distinguish between death due to breast cancer and all other causes of death. The time scales are age and time since diagnosis. We use data from the Surveillance, Epidemiology and End Results (SEER) program. In the SEER data, age at diagnosis is provided with a last open-ended category, leading to coarsely grouped data. We use the two-dimensional penalised composite link model to ungroup the data before applying the competing risks model with two time scales., Comment: 36 pages, 9 figures, 2 tables

The Fine-Gray model for the subdistribution hazard is commonly used for estimating associations between covariates and competing risks outcomes. When there are missing values in the covariates included in a given model, researchers may wish to multiply impute them. Assuming interest lies in estimating the risk of only one of the competing events, this paper develops a substantive-model-compatible multiple imputation approach that exploits the parallels between the Fine-Gray model and the standard (single-event) Cox model. In the presence of right-censoring, this involves first imputing the potential censoring times for those failing from competing events, and thereafter imputing the missing covariates by leveraging methodology previously developed for the Cox model in the setting without competing risks. In a simulation study, we compared the proposed approach to alternative methods, such as imputing compatibly with cause-specific Cox models. The proposed method performed well (in terms of estimation of both subdistribution log hazard ratios and cumulative incidences) when data were generated assuming proportional subdistribution hazards, and performed satisfactorily when this assumption was not satisfied. The gain in efficiency compared to a complete-case analysis was demonstrated in both the simulation study and in an applied data example on competing outcomes following an allogeneic stem cell transplantation. For individual-specific cumulative incidence estimation, assuming proportionality on the correct scale at the analysis phase appears to be more important than correctly specifying the imputation procedure used to impute the missing covariates.

Objective Hospitals register information in the electronic health records (EHR) continuously until discharge or death. As such, there is no censoring for in-hospital outcomes. We aimed to compare different dynamic regression modeling approaches to predict central line-associated bloodstream infections (CLABSI) in EHR while accounting for competing events precluding CLABSI. Materials and Methods We analyzed data from 30,862 catheter episodes at University Hospitals Leuven from 2012 and 2013 to predict 7-day risk of CLABSI. Competing events are discharge and death. Static models at catheter onset included logistic, multinomial logistic, Cox, cause-specific hazard, and Fine-Gray regression. Dynamic models updated predictions daily up to 30 days after catheter onset (i.e. landmarks 0 to 30 days), and included landmark supermodel extensions of the static models, separate Fine-Gray models per landmark time, and regularized multi-task learning (RMTL). Model performance was assessed using 100 random 2:1 train-test splits. Results The Cox model performed worst of all static models in terms of area under the receiver operating characteristic curve (AUC) and calibration. Dynamic landmark supermodels reached peak AUCs between 0.741-0.747 at landmark 5. The Cox landmark supermodel had the worst AUCs (<=0.731) and calibration up to landmark 7. Separate Fine-Gray models per landmark performed worst for later landmarks, when the number of patients at risk was low. Discussion and Conclusion Categorical and time-to-event approaches had similar performance in the static and dynamic settings, except Cox models. Ignoring competing risks caused problems for risk prediction in the time-to-event framework (Cox), but not in the categorical framework (logistic regression)., Comment: 3388 words; 3 figures; 4 tables

Covariate imbalance between treatment groups makes it difficult to compare cumulative incidence curves in competing risk analyses. In this paper we discuss different methods to estimate adjusted cumulative incidence curves including inverse probability of treatment weighting and outcome regression modeling. For these methods to work, correct specification of the propensity score model or outcome regression model, respectively, is needed. We introduce a new doubly robust estimator, which requires correct specification of only one of the two models. We conduct a simulation study to assess the performance of these three methods, including scenarios with model misspecification of the relationship between covariates and treatment and/or outcome. We illustrate their usage in a cohort study of breast cancer patients estimating covariate-adjusted marginal cumulative incidence curves for recurrence, second primary tumour development and death after undergoing mastectomy treatment or breast-conserving therapy. Our study points out the advantages and disadvantages of each covariate adjustment method when applied in competing risk analysis.

Prediction models are increasingly proposed for guiding treatment decisions, but most fail to address the special role of treatments, leading to inappropriate use. This paper highlights the limitations of using standard prediction models for treatment decision support. We identify `causal blind spots' in three common approaches to handling treatments in prediction modelling: including treatment as a predictor, restricting data based on treatment status and ignoring treatments. When predictions are used to inform treatment decisions, confounders, colliders and mediators, as well as changes in treatment protocols over time may lead to misinformed decision-making. We illustrate potential harmful consequences in several medical applications. We advocate for an extension of guidelines for development, reporting and evaluation of prediction models to ensure that the intended use of the model is matched to an appropriate risk estimand. When prediction models are intended to inform treatment decisions, prediction models should specify upfront the treatment decisions they aim to support and target a prediction estimand in line with that goal. This requires a shift towards developing predictions under the specific treatment options under consideration (`predictions under interventions'). Predictions under interventions need causal reasoning and inference techniques during development and validation. We argue that this will improve the efficacy of prediction models in guiding treatment decisions and prevent potential negative effects on patient outcomes.

Hazard models are the most commonly used tool to analyse time-to-event data. If more than one time scale is relevant for the event under study, models are required that can incorporate the dependence of a hazard along two (or more) time scales. Such models should be flexible to capture the joint influence of several times scales and nonparametric smoothing techniques are obvious candidates. P-splines offer a flexible way to specify such hazard surfaces, and estimation is achieved by maximizing a penalized Poisson likelihood. Standard observations schemes, such as right-censoring and left-truncation, can be accommodated in a straightforward manner. The model can be extended to proportional hazards regression with a baseline hazard varying over two scales. Generalized linear array model (GLAM) algorithms allow efficient computations, which are implemented in a companion R-package.

Monitoring the quality of statistical processes has been of great importance, mostly in industrial applications. Control charts are widely used for this purpose, but often lack the possibility to monitor survival outcomes. Recently, inspecting survival outcomes has become of interest, especially in medical settings where outcomes often depend on risk factors of patients. For this reason many new survival control charts have been devised and existing ones have been extended to incorporate survival outcomes. The R package success allows users to construct risk-adjusted control charts for survival data. Functions to determine control chart parameters are included, which can be used even without expert knowledge on the subject of control charts. The package allows to create static as well as interactive charts, which are built using ggplot2 (Wickham 2016) and plotly (Sievert 2020)., Comment: 29 pages, 10 figures, guide for the R package success, see https://cran.r-project.org/package=success Published version of the article

Hazard ratios are prone to selection bias, compromising their use as causal estimands. On the other hand, the hazard difference has been shown to remain unaffected by the selection of frailty factors over time. Therefore, observed hazard differences can be used as an unbiased estimator for the causal hazard differences in the absence of confounding. However, in the presence of effect (on the hazard) heterogeneity, the hazard difference is also affected by selection. In this work, we formalize how the observed hazard difference (from a randomized controlled trial) evolves by selecting favourable levels of effect modifiers in the exposed group and thus deviates from the causal hazard difference of interest. Such selection may result in a non-linear integrated hazard difference curve even when the individual causal effects are time-invariant. Therefore, a homogeneous time-varying causal additive effect on the hazard can not be distinguished from a constant but heterogeneous causal effect. We illustrate this causal issue by studying the effect of chemotherapy on the survival time of patients suffering from carcinoma of the oropharynx using data from a clinical trial. The hazard difference can thus not be used as an appropriate measure of the causal effect without making untestable assumptions.

It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from built-in selection bias as, over time, the individuals at risk in the exposed and unexposed are no longer exchangeable. In this work, we formalize how the observed hazard ratio evolves and deviates from the causal hazard ratio of interest in the presence of heterogeneity of the hazard of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty, and categorical (harming, beneficial or neutral) effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio can not be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands such as contrasts of the survival probabilities.

Rapidly detecting problems in the quality of care is of utmost importance for the well-being of patients. Without proper inspection schemes, such problems can go undetected for years. Cumulative sum (CUSUM) charts have proven to be useful for quality control, yet available methodology for survival outcomes is limited. The few available continuous time inspection charts usually require the researcher to specify an expected increase in the failure rate in advance, thereby requiring prior knowledge about the problem at hand. Misspecifying parameters can lead to false positive alerts and large detection delays. To solve this problem, we take a more general approach to derive the new Continuous time Generalized Rapid response CUSUM (CGR-CUSUM) chart. We find an expression for the approximate average run length (average time to detection) and illustrate the possible gain in detection speed by using the CGR-CUSUM over other commonly used monitoring schemes on a real life data set from the Dutch Arthroplasty Register as well as in simulation studies. Besides the inspection of medical procedures, the CGR-CUSUM can also be used for other real time inspection schemes such as industrial production lines and quality control of services., Comment: 24 pages, 3 figures - The methods described in the article have been implemented in the R package success on CRAN, see https://cran.r-project.org/package=success

Benchmarking is commonly used in many healthcare settings to monitor clinical performance, with the aim of increasing cost-effectiveness and safe care of patients. The funnel plot is a popular tool in visualizing the performance of a healthcare center in relation to other centers and to a target, taking into account statistical uncertainty. In this paper we develop methodology for constructing funnel plots for survival data. The method takes into account censoring and can deal with differences in censoring distributions across centers. Practical issues in implementing the methodology are discussed, particularly in the setting of benchmarking clinical outcomes for hematopoietic stem cell transplantation. A simulation study is performed to assess the performance of the funnel plots under several scenarios. Our methodology is illustrated using data from the EBMT benchmarking project., Comment: 24 pages, 4 figures, 1 table

The problem of dynamic prediction with time-dependent covariates, given by biomarkers, repeatedly measured over time, has received much attention over the last decades. Two contrasting approaches have become in widespread use. The first is joint modelling, which attempts to jointly model the longitudinal markers and the event time. The second is landmarking, a more pragmatic approach that avoids modelling the marker process. Landmarking has been shown to be less efficient than correctly specified joint models in simulation studies, when data are generated from the joint model. When the mean model is misspecified, however, simulation has shown that joint models may be inferior to landmarking. The objective of this paper is to develop methods that improve the predictive accuracy of landmarking, while retaining its relative simplicity and robustness. We start by fitting a working longitudinal model for the biomarker, including a temporal correlation structure. Based on that model, we derive a predictable time-dependent process representing the expected value of the biomarker after the landmark time, and we fit a time-dependent Cox model based on the predictable time-dependent covariate. Dynamic predictions based on this approach for new patients can be obtained by first deriving the expected values of the biomarker, given the measured values before the landmark time point, and then calculating the predicted probabilities based on the time-dependent Cox model. We illustrate the approach in predicting overall survival in liver cirrhosis patients based on prothrombin index., Comment: 24 pages, 6 figures, 4 tables

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, the samples are often selected at a later time, which results in delayed entry. Thus, only individuals who have not yet experienced the terminal event will be included in the study. We propose a method for estimating the joint frailty model from such left-truncated data. The frailty distribution among the selected survivors differs from the frailty distribution in the underlying population if the recurrence process and the terminal event are associated. The correctly adjusted marginal likelihood can be expressed as a ratio of two integrals over the frailty distribution, which may be approximated using Gaussian quadrature. The baseline rates are specified as piecewise constant functions, and the covariates are assumed to have multiplicative effects on the event rates. We assess the performance of the estimation procedure in a simulation study, and apply the method to estimate age-specific rates of recurrent urinary tract infections and mortality in an older population., Comment: Added reference to final publication. This preprint was last edited March 26, 2021, and has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Lifetime Data Analysis, and is available online at https://doi.org/10.1007/s10985-022-09587-z

In this paper we study approaches for dealing with treatment when developing a clinical prediction model. Analogous to the estimand framework recently proposed by the European Medicines Agency for clinical trials, we propose a `predictimand' framework of different questions that may be of interest when predicting risk in relation to treatment started after baseline. We provide a formal definition of the estimands matching these questions, give examples of settings in which each is useful and discuss appropriate estimators including their assumptions. We illustrate the impact of the predictimand choice in a dataset of patients with end-stage kidney disease. We argue that clearly defining the estimand is equally important in prediction research as in causal inference., Comment: under review

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We describe an efficient algorithm to find the maximum likelihood estimator. The method is contrasted with the ordinary least squares approach in a simulation study, and the method is illustrated on a realistic data set.

The decrease in the increase in death rates at old ages is a phenomenon that has repeatedly been discussed in demographic research. While mortality deceleration can be explained in the gamma-Gompertz model as an effect of selection in heterogeneous populations, this phenomenon can be difficult to assess statistically because it relates to the tail of the distribution of the ages at death. By using a focused information criterion (FIC) for model selection, we can directly target model performance at those advanced ages. The gamma-Gompertz model is reduced to the competing Gompertz model without mortality deceleration if the variance parameter lies on the boundary of the parameter space. We develop a new version of the FIC that is adapted to this non-standard condition. In a simulation study, the new FIC is shown to outperform other methods in detecting mortality deceleration. The application of the FIC to extinct French-Canadian birth cohorts demonstrates that focused model selection can be used to rebut previous assertions about mortality deceleration.

The public health impact of a harmful exposure can be quantified by the population-attributable fraction (PAF). The PAF describes the attributable risk due to an exposure and is often interpreted as the proportion of preventable cases if the exposure could be extinct. Difficulties in the definition and interpretation of the PAF arise when the exposure of interest depends on time. Then, the definition of exposed and unexposed individuals is not straightforward. We propose dynamic prediction and landmarking to define and estimate a PAF in this data situation. Two estimands are discussed which are based on two hypothetical interventions that could prevent the exposure in different ways. Considering the first estimand, at each landmark the estimation problem is reduced to a time-independent setting. Then, estimation is simply performed by using a generalized-linear model accounting for the current exposure state and further (time-varying) covariates. The second estimand is based on counterfactual outcomes, estimation can be performed using pseudo-values or inverse-probability weights. The approach is explored in a simulation study and applied on two data examples. First, we study a large French database of intensive care unit patients to estimate the population-benefit of a pathogen-specific intervention that could prevent ventilator-associated pneumonia caused by the pathogen Pseudomonas aeruginosa. Moreover, we quantify the population-attributable burden of locoregional and distant recurrence in breast cancer patients., Comment: A revised version has been submitted