Building Prediction Models for Dementia: The Need to Account for Interval Censoring and the Competing Risk of Death

Indiana University-Purdue University Indianapolis (IUPUI)Context. Prediction models for dementia are crucial for informing clinical decision making in older adults. Previous models have used genotype and age to obtain risk scores to determine risk of Alzheimer’s Disease, one of the most common forms of dementia (Desikan et al., 2017). However, previous prediction models do not account for the fact that the time to dementia onset is unknown, lying between the last negative and the first positive dementia diagnosis time (interval censoring). Instead, these models use time to diagnosis, which is greater than or equal to the true dementia onset time. Furthermore, these models do not account for the competing risk of death which is quite frequent among elder adults. Objectives. To develop a prediction model for dementia that accounts for interval censoring and the competing risk of death. To compare the predictions from this model with the predictions from a naïve analysis that ignores interval censoring and the competing risk of death. Methods. We apply the semiparametric sieve maximum likelihood (SML) approach to simultaneously model the cumulative incidence function (CIF) of dementia and death while accounting for interval censoring (Bakoyannis, Yu, & Yiannoutsos, 2017). The SML is implemented using the R package intccr. The CIF curves of dementia are compared for the SML and the naïve approach using a dataset from the Indianapolis Ibadan Dementia Project. Results. The CIF from the SML and the naïve approach illustrated that for healthier individuals at baseline, the naïve approach underestimated the incidence of dementia compared to the SML, as a result of interval censoring. Individuals with a poorer health condition at baseline have a CIF that appears to be overestimated in the naïve approach. This is due to older individuals with poor health conditions having an elevated risk of death. Conclusions. The SML method that accounts for the competing risk of death along with interval censoring should be used for fitting prediction/prognostic models of dementia to inform clinical decision making in older adults. Without controlling for the competing risk of death and interval censoring, the current models can provide invalid predictions of the CIF of dementia

Semiparametric regression on cumulative incidence function with interval-censored competing risks data and missing event types

Competing risk data are frequently interval-censored, that is, the exact event time is not observed but only known to lie between two examination time points such as clinic visits. In addition to interval censoring, another common complication is that the event type is missing for some study participants. In this article, we propose an augmented inverse probability weighted sieve maximum likelihood estimator for the analysis of interval-censored competing risk data in the presence of missing event types. The estimator imposes weaker than usual missing at random assumptions by allowing for the inclusion of auxiliary variables that are potentially associated with the probability of missingness. The proposed estimator is shown to be doubly robust, in the sense that it is consistent even if either the model for the probability of missingness or the model for the probability of the event type is misspecified. Extensive Monte Carlo simulation studies show good performance of the proposed method even under a large amount of missing event types. The method is illustrated using data from an HIV cohort study in sub-Saharan Africa, where a significant portion of events types is missing. The proposed method can be readily implemented using the new function ciregic_aipw in the R package intccr

Semiparametric regression on cumulative incidence function with interval-censored competing risks data

Many biomedical and clinical studies with time-to-event outcomes involve competing risks data. These data are frequently subject to interval censoring. This means that the failure time is not precisely observed but is only known to lie between two observation times such as clinical visits in a cohort study. Not taking into account the interval censoring may result in biased estimation of the cause-specific cumulative incidence function, an important quantity in the competing risks framework, used for evaluating interventions in populations, for studying the prognosis of various diseases, and for prediction and implementation science purposes. In this work, we consider the class of semiparametric generalized odds rate transformation models in the context of sieve maximum likelihood estimation based on B-splines. This large class of models includes both the proportional odds and the proportional subdistribution hazard models (i.e., the Fine-Gray model) as special cases. The estimator for the regression parameter is shown to be consistent, asymptotically normal and semiparametrically efficient. Simulation studies suggest that the method performs well even with small sample sizes. As an illustration, we use the proposed method to analyze data from HIV-infected individuals obtained from a large cohort study in sub-Saharan Africa. We also provide the R function ciregic that implements the proposed method and present an illustrative example

Crude incidence in two-phase designs in the presence of competing risks.

BackgroundIn many studies, some information might not be available for the whole cohort, some covariates, or even the outcome, might be ascertained in selected subsamples. These studies are part of a broad category termed two-phase studies. Common examples include the nested case-control and the case-cohort designs. For two-phase studies, appropriate weighted survival estimates have been derived; however, no estimator of cumulative incidence accounting for competing events has been proposed. This is relevant in the presence of multiple types of events, where estimation of event type specific quantities are needed for evaluating outcome.MethodsWe develop a non parametric estimator of the cumulative incidence function of events accounting for possible competing events. It handles a general sampling design by weights derived from the sampling probabilities. The variance is derived from the influence function of the subdistribution hazard.ResultsThe proposed method shows good performance in simulations. It is applied to estimate the crude incidence of relapse in childhood acute lymphoblastic leukemia in groups defined by a genotype not available for everyone in a cohort of nearly 2000 patients, where death due to toxicity acted as a competing event. In a second example the aim was to estimate engagement in care of a cohort of HIV patients in resource limited setting, where for some patients the outcome itself was missing due to lost to follow-up. A sampling based approach was used to identify outcome in a subsample of lost patients and to obtain a valid estimate of connection to care.ConclusionsA valid estimator for cumulative incidence of events accounting for competing risks under a general sampling design from an infinite target population is derived

Semiparametric Competing Risks Regression Under Interval Censoring Using the R Package intccr

Background and objective: Competing risk data are frequently interval-censored in real-world applications, that is, the exact event time is not precisely observed but is only known to lie between two time points such as clinic visits. This type of data requires special handling because the actual event times are unknown. To deal with this problem we have developed an easy-to-use open-source statistical software. Methods: An approach to perform semiparametric regression analysis of the cumulative incidence function with interval-censored competing risks data is the sieve maximum likelihood method based on B-splines. An important feature of this approach is that it does not impose restrictive parametric assumptions. Also, this methodology provides semiparametrically efficient estimates. Implementation of this methodology can be easily performed using our new R package intccr. Results: The R package intccr performs semiparametric regression analysis of the cumulative incidence function based on interval-censored competing risks data. It supports a large class of models including the proportional odds and the Fine-Gray proportional subdistribution hazards model as special cases. It also provides the estimated cumulative incidence functions for a particular combination of covariate values. The package also provides some data management functionality to handle data sets which are in a long format involving multiple lines of data per subject. Conclusions: The R package intccr provides a convenient and flexible software for the analysis of the cumulative incidence function based on interval-censored competing risks data

Flexible Models for Competing Risks and Weighted Analyses of Composite Endpoints

In many clinical studies the occurrence of different types of disease events over time is of interest. For example, in cardiovascular studies, disease events such as death, stroke or myocardial infarction are of interest. As another example, in central nervous system infections such as cryptococcal meningitis, unfavourable events such as death or neurological events and favourable events such as coma or fungal clearance are relevant. In statistical terminology, competing risks refer to data where the time and type of the first disease event are analysed. Such data arise naturally if a nonfatal disease event is of interest but is precluded by death in a substantial proportion of subjects. Competing risks are the topic of the first four chapters of this thesis. An alternative approach used in many randomized controlled clinical trials is to combine different harmful events to a single composite endpoint. The analysis of trials with a composite endpoints is the topic of the fifth chapter. This thesis is organised as follows: Chapters 1 and 2 are introductory chapters and provide an overview of statistical approaches to competing risks and semi-nonparametric (SNP) density estimation. Two concepts that form the basis for the work in Chapters 3 and 4 are introduced here: the cumulative incidence function (CIF) and SNP densities. For competing risks data, the CIF describes the absolute risk of different event types depending on time and is the most important quantity for data description, prognostic modelling, and medical decision making. SNP densities are densities that can be expressed as the product of a squared polynomial (of variable degree) and a base density which is chosen as the standard normal or the exponential density in this work. Chapter 3 presents a novel approach to CIF-estimation. The underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and time and the time to event distributions conditional on the event type are modelled using SNP densities. One key strength of the approach is that it can handle arbitrary censoring and truncation. A stepwise forward algorithm for model estimation and adaptive selection of SNP polynomial degrees is presented, implemented in the statistical software R, evaluated in a sequence of simulation studies, and applied to data sets from clinical trials in central nervous system infections. The simulations demonstrate that the SNP approach frequently outperforms both parametric and nonparametric alternatives. They also support the use of “ad hoc” asymptotic inference to derive confidence intervals despite a lack of a formal mathematical verification for the relevant asymptotic properties. Chapter 4 extends the work of Chapter 3 to regression modelling, i.e. the quantification of cov-ariate effects on the CIF. A careful discussion of interpretational and identifiability issues which are intrinsic to models based on the mixture factorization is provided and the usage of the model is only recommended in settings with sufficient follow-up relative to the timing of the events. A simulation study demonstrates that the proposed approach is competitive compared to common statistical models for competing risks in terms of accuracy of parameter estimates and predictions. However, it also shows that “ad hoc” asymptotic inference is only valid if sample size is large. The chapter also provides a suggestion for model diagnostics of the proposed model, an area that has been somewhat neglected for competing risks data. Chapter 5 discusses the analysis of composite endpoints. A common critique of traditional analyses of composite endpoints is that all disease events are equally weighted whereas their clinical relevance may differ substantially. This chapter addresses this by introducing a framework for the weighted analysis of composite endpoints that handles both binary and time-to-event data. To address the difficulty in selecting an exact set of weights, it proposes a method for constructing simultaneous confidence intervals and tests that protect the familywise type I error in the strong sense across families of weights which satisfy flexible inequality and order constraints based on the theory of χ-2-distributions. It is then demonstrated in several simulation scenarios as well as applications that the proposed method achieves the nominal simultaneous overall coverage rate with lower efficiency loss compared to the standard Scheffe’s procedure. Final remarks are given in Chapter 6 together with an outlook for potential future research directions