A method for determining groups in cumulative incidence curves in competing risk data.

The cumulative incidence function is the standard method for estimating the marginal probability of a given event in the presence of competing risks. One basic but important goal in the analysis of competing risk data is the comparison of these curves, for which limited literature exists. We proposed a new procedure that lets us not only test the equality of these curves but also group them if they are not equal. The proposed method allows determining the composition of the groups as well as an automatic selection of their number. Simulation studies show the good numerical behavior of the proposed methods for finite sample size. The applicability of the proposed method is illustrated using real data.

Anxiety and/or depression: which symptoms contribute to adverse clinical outcomes after amputation?

BACKGROUND: One of the most serious complications of diabetes mellitus (DM) is a diabetic foot ulcer (DFU), with lower extremity amputation (LEA). AIMS: This study aims to explore the role of anxiety and depression on mortality, reamputation and healing, after a LEA due to DFU. METHODS: A sample of 149 patients with DFU who underwent LEA answered the Hospital Anxiety and Depression Scale and a sociodemographic and clinical questionnaire. This is a longitudinal and multicenter study with four assessment moments that used Cox proportional hazards models adjusted for demographic and clinical variables. RESULTS: Rate of mortality, reamputation and healing, 10 months after LEA were 9.4%, 27.5% and 61.7%, respectively. Anxiety, at baseline, was negatively associated with healing. However, depression was not an independent predictor of mortality. None of the psychological factors was associated with reamputation. CONCLUSION: Results highlight the significant contribution of anxiety symptoms at pre-surgery, to healing after a LEA. Suggestions for psychological interventions are made.

Estimation in the progressive illness-death model: A nonexhaustive review.

Multistate models can be successfully used for describing complex event history data, for example, describing stages in the disease progression of a patient. The so-called "illness-death" model plays a central role in the theory and practice of these models. Many time-to-event datasets from medical studies with multiple end points can be reduced to this generic structure. In these models one important goal is the modeling of transition rates but biomedical researchers are also interested in reporting interpretable results in a simple and summarized manner. These include estimates of predictive probabilities, such as the transition probabilities, occupation probabilities, cumulative incidence functions, and the sojourn time distributions. We will give a review of some of the available methods for estimating such quantities in the progressive illness-death model conditionally (or not) on covariate measures. For some of these quantities estimators based on subsampling are employed. Subsampling, also referred to as landmarking, leads to small sample sizes and usually to heavily censored data leading to estimators with higher variability. To overcome this issue estimators based on a preliminary estimation (presmoothing) of the probability of censoring may be used. Among these, the presmoothed estimators for the cumulative incidences are new. We also introduce feasible estimation methods for the cumulative incidence function conditionally on covariate measures. The proposed methods are illustrated using real data. A comparative simulation study of several estimation approaches is performed and existing software in the form of R packages is discussed.

A method for determining groups in multiple survival curves.

Survival analysis includes a wide variety of methods for analyzing time-to-event data. One basic but important goal in survival analysis is the comparison of survival curves between groups. Several nonparametric methods have been proposed in the literature to test for the equality of survival curves for censored data. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, it can be interesting to ascertain whether curves can be grouped or if all these curves are different from each other. A method is proposed that allows determining groups with an automatic selection of their number. The validity and behavior of the proposed method was evaluated through simulation studies. The applicability of the proposed method is illustrated using real data. Software in the form of an R package has been developed implementing the proposed method.

A Multistate Model for Analyzing Transitions Between Body Mass Index Categories During Childhood: The Generation XXI Birth Cohort Study.

Prevalences of overweight and obesity in young children have risen dramatically in the last several decades in most developed countries. Childhood overweight and obesity are known to have immediate and long-term health consequences and are now recognized as important public health concerns. We used a Markov 4-state model with states defined by 4 body mass index (BMI; weight (kg)/height (m)2) categories (underweight (<-2 standard deviations (SDs) of BMI z score), normal weight (-2 ≤ SD ≤ 1), overweight (1 < SD ≤ 2), and obese (>2 SDs of BMI z score)) to study the rates of transition to higher or lower BMI categories among children aged 4-10 years. We also used this model to study the relationships between explanatory variables and their transition rates. The participants consisted of 4,887 children from the Generation XXI Birth Cohort Study (Porto, Portugal; 2005-2017) who underwent anthropometric evaluation at age 4 years and in at least 1 of the subsequent follow-up waves (ages 7 and 10 years). Children who were normal weight were more likely to move to higher BMI categories than to lower categories, whereas overweight children had similar rates of transition to the 2 adjacent categories. We evaluated the associations of maternal age and education, type of delivery, sex, and birth weight with childhood overweight and obesity, but we observed statistically significant results only for sex and maternal education with regard to the progressive transitions.

Nonparametric estimation of time-dependent ROC curves conditional on a continuous covariate.

The receiver-operating characteristic (ROC) curve is the most widely used measure for evaluating the performance of a diagnostic biomarker when predicting a binary disease outcome. The ROC curve displays the true positive rate (or sensitivity) and the false positive rate (or 1-specificity) for different cut-off values used to classify an individual as healthy or diseased. In time-to-event studies, however, the disease status (e.g. death or alive) of an individual is not a fixed characteristic, and it varies along the study. In such cases, when evaluating the performance of the biomarker, several issues should be taken into account: first, the time-dependent nature of the disease status; and second, the presence of incomplete data (e.g. censored data typically present in survival studies). Accordingly, to assess the discrimination power of continuous biomarkers for time-dependent disease outcomes, time-dependent extensions of true positive rate, false positive rate, and ROC curve have been recently proposed. In this work, we present new nonparametric estimators of the cumulative/dynamic time-dependent ROC curve that allow accounting for the possible modifying effect of current or past covariate measures on the discriminatory power of the biomarker. The proposed estimators can accommodate right-censored data, as well as covariate-dependent censoring. The behavior of the estimators proposed in this study will be explored through simulations and illustrated using data from a cohort of patients who suffered from acute coronary syndrome.

Nonparametric estimation of the survival function for ordered multivariate failure time data: A comparative study.

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions, and the conditional distribution of gap times. In this work, we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a dataset from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study.

Multi-state models are often used for modeling complex event history data. In these models the estimation of the transition probabilities is of particular interest, since they allow for long-term predictions of the process. These quantities have been traditionally estimated by the Aalen-Johansen estimator, which is consistent if the process is Markov. Several non-Markov estimators have been proposed in the recent literature, and their superiority with respect to the Aalen-Johansen estimator has been proved in situations in which the Markov condition is strongly violated. However, the existing estimators have the drawback of requiring that the support of the censoring distribution contains the support of the lifetime distribution, which is not often the case. In this article, we propose two new methods for estimating the transition probabilities in the progressive illness-death model. Some asymptotic results are derived. The proposed estimators are consistent regardless the Markov condition and the referred assumption about the censoring support. We explore the finite sample behavior of the estimators through simulations. The main conclusion of this piece of research is that the proposed estimators are much more efficient than the existing non-Markov estimators in most cases. An application to a clinical trial on colon cancer is included. Extensions to progressive processes beyond the three-state illness-death model are discussed.

smoothHR: an R package for pointwise nonparametric estimation of hazard ratio curves of continuous predictors.

The Cox proportional hazards regression model has become the traditional choice for modeling survival data in medical studies. To introduce flexibility into the Cox model, several smoothing methods may be applied, and approaches based on splines are the most frequently considered in this context. To better understand the effects that each continuous covariate has on the outcome, results can be expressed in terms of splines-based hazard ratio (HR) curves, taking a specific covariate value as reference. Despite the potential advantages of using spline smoothing methods in survival analysis, there is currently no analytical method in the R software to choose the optimal degrees of freedom in multivariable Cox models (with two or more nonlinear covariate effects). This paper describes an R package, called smoothHR, that allows the computation of pointwise estimates of the HRs--and their corresponding confidence limits--of continuous predictors introduced nonlinearly. In addition the package provides functions for choosing automatically the degrees of freedom in multivariable Cox models. The package is available from the R homepage. We illustrate the use of the key functions of the smoothHR package using data from a study on breast cancer and data on acute coronary syndrome, from Galicia, Spain.

Multi-state models for the analysis of time-to-event data.

The experience of a patient in a survival study may be modelled as a process with two states and one possible transition from an "alive" state to a "dead" state. In some studies, however, the "alive" state may be partitioned into two or more intermediate (transient) states, each of which corresponding to a particular stage of the illness. In such studies, multi-state models can be used to model the movement of patients among the various states. In these models issues, of interest include the estimation of progression rates, assessing the effects of individual risk factors, survival rates or prognostic forecasting. In this article, we review modelling approaches for multi-state models, and we focus on the estimation of quantities such as the transition probabilities and survival probabilities. Differences between these approaches are discussed, focussing on possible advantages and disadvantages for each method. We also review the existing software currently available to fit the various models and present new software developed in the form of an R library to analyse such models. Different approaches and software are illustrated using data from the Stanford heart transplant study and data from a study on breast cancer conducted in Galicia, Spain.

tdc.msm: an R library for the analysis of multi-state survival data.

The aim of this paper is to present an R library, called tdc.msm, developed to analyze multi-state survival data. In this library, the time-dependent regression model and multi-state models are included as two possible approaches for such data. For the multi-state modelling five different models are considered, allowing the user to choose between Markov and semi-Markov property, as well as to use homogeneous or non-homogeneous models. Specifically, the following multi-state models in continuous time were implemented: Cox Markov model; Cox semi-Markov model; homogeneous Markov model; non-homogeneous piecewise model and non-parametric Markov model. This software can be used to fit multi-state models with one initial state (e.g., illness diagnosis), a finite number of intermediate states, representing, for example, a change of treatment, and one absorbing state corresponding to a terminal event of interest. Graphical output includes survival estimates, transition probabilities estimates and smooth log hazard for continuous covariates.

Nonparametric estimation of transition probabilities in a non-Markov illness-death model.

In this paper we consider nonparametric estimation of transition probabilities for multi-state models. Specifically, we focus on the illness-death or disability model. The main novelty of the proposed estimators is that they do not rely on the Markov assumption, typically assumed to hold in a multi-state model. We investigate the asymptotic properties of the introduced estimators, such as their consistency and their convergence to a normal law. Simulations demonstrate that the new estimators may outperform Aalen-Johansen estimators (the classical nonparametric tool for estimating the transition probabilities) in non-Markov situation. An illustration through real data analysis is included.