Adjusted-crude-incidence analysis of multiple treatments and unbalanced samples on competing risks (original) (raw)
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Revisiting the Cumulative Incidence Function With Competing Risks Data
arXiv (Cornell University), 2022
We consider estimation of the cumulative incidence function (CIF) in the competing risks Cox model. We study three methods. Methods 1 and 2 are existing methods while Method 3 is a newly-proposed method. Method 3 is constructed so that the sum of the CIF's across all event types at the last observed event time is guaranteed, assuming no ties, to be equal to 1. The performance of the methods is examined in a simulation study, and the methods are illustrated on a data example from the field of computer code comprehension. The newly-proposed Method 3 exhibits performance comparable to that of Methods 1 and 2 in terms of bias, variance, and confidence interval coverage rates. Thus, with our newly-proposed estimator, the advantage of having the end-of-study total CIF equal to 1 is achieved with no price to be paid in terms of performance.
Impact of and Correction for Outcome Misclassification in Cumulative Incidence Estimation
PLOS ONE, 2015
Cohort studies and clinical trials may involve multiple events. When occurrence of one of these events prevents the observance of another, the situation is called "competing risks". A useful measure in such studies is the cumulative incidence of an event, which is useful in evaluating interventions or assessing disease prognosis. When outcomes in such studies are subject to misclassification, the resulting cumulative incidence estimates may be biased. In this work, we study the mechanism of bias in cumulative incidence estimation due to outcome misclassification. We show that even moderate levels of misclassification can lead to seriously biased estimates in a frequently unpredictable manner. We propose an easy to use estimator for correcting this bias that is uniformly consistent. Extensive simulations suggest that this method leads to unbiased estimates in practical settings. The proposed method is useful, both in settings where misclassification probabilities are known by historical data or can be estimated by other means, and for performing sensitivity analyses when the misclassification probabilities are not precisely known.
Crude incidence in two-phase designs in the presence of competing risks
BMC Medical Research Methodology, 2016
Background: In 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. Methods: We 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. Results: The 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. Conclusions: A valid estimator for cumulative incidence of events accounting for competing risks under a general sampling design from an infinite target population is derived.
Assessing cumulative incidence functions under the semiparametric additive risk model
Statistics in Medicine, 2009
In analyzing competing risks data, a quantity of considerable interest is the cumulative incidence function. Often the effect of covariates on the cumulative incidence function is modeled via the proportional hazards model for the cause-specific hazard function. As the proportionality assumption may be too restrictive in practice, we consider an alternative more flexible semiparametric additive hazards model of [1] for the cause-specific hazard. This model specifies the effect of covariates on the cause-specific hazard to be additive as well as allows the effect of some covariates to be fixed and that of others to be time-varying. We present an approach for constructing confidence intervals as well as confidence bands for the cause-specific cumulative incidence function of subjects with given values of the covariates. Furthermore, we also present an approach for constructing confidence intervals and confidence bands for comparing two cumulative incidence functions given values of the covariates. The finite sample property of the proposed estimators is investigated through simulations. We conclude our paper with an analysis of the well-known malignant melanoma data using our method.
arXiv (Cornell University), 2024
Regression analyses based on transformations of cumulative incidence functions are often adopted when modeling and testing for treatment effects in clinical trial settings involving competing and semi-competing risks. Common frameworks include the Fine-Gray model and models based on direct binomial regression. Using large sample theory we derive the limiting values of treatment effect estimators based on such models when the data are generated according to multiplicative intensity-based models, and show that the estimand is sensitive to several process features. The rejection rates of hypothesis tests based on cumulative incidence function regression models are also examined for null hypotheses of different types, based on which a robustness property is established. In such settings supportive secondary analyses of treatment effects are essential to ensure a full understanding of the nature of treatment effects. An application to a palliative study of individuals with breast cancer metastatic to bone is provided for illustration.
Estimating risk and rate levels, ratios and differences in case‐control studies
2002
Abstract Classic (or 'cumulative') case-control sampling designs do not admit inferences about quantities of interest other than risk ratios, and then only by making the rare events assumption. Probabilities, risk differences and other quantities cannot be computed without knowledge of the population incidence fraction. Similarly, density (or 'risk set') case-control sampling designs do not allow inferences about quantities other than the rate ratio.
Exposure stratified case-cohort designs
1998
A variant of the case-cohort design is proposed for the situation in which a correlate of the exposure (or prognostic factor) of interest is available for all cohort members, and exposure information is to be collected for a case-cohort sample. The cohort is stratified according to the correlate, and the subcohort is selected by stratified random sampling. A number of possible methods for the analysis of such exposure stratified case-cohort samples are presented and some of their statistical properties developed. The bias and efficiency of the methods are compared to each other, and to randomly sampled case-cohort studies, in a limited computer simulation study. We found that all of the proposed analysis methods performed reasonably well and were more efficient than a randomly sampled case-cohort sample. We conclude that these methods are well suited for the "clinical trials setting" in which subjects enter the study at time zero (at diagnosis or treatment) and a correlate of an expensive prognostic factor is collected for all study subjects at the time of entry to the study. In such studies, a correlate stratified subcohort can be much more cost-efficient for investigation of the expensive prognostic factor than a randomly sampled subcohort.
Cumulative risk regression in case–cohort studies using pseudo-observations
Lifetime Data Analysis, 2020
Case-cohort studies are useful when information on certain risk factors is difficult or costly to ascertain. Particularly, a case-cohort study may be well suited in situations where several case series are of interest, e.g. in studies with competing risks, because the same sub-cohort may serve as a comparison group for all case series. Previous analyses of this kind of sampled cohort data most often involved estimation of rate ratios based on a Cox regression model. However, with competing risks this method will not provide parameters that directly describe the association between covariates and cumulative risks. In this paper, we study regression analysis of cause-specific cumulative risks in case-cohort studies using pseudo-observations. We focus mainly on the situation with competing risks. However, as a by-product, we also develop a method by which absolute mortality risks may be analyzed directly from casecohort survival data. We adjust for the case-cohort sampling by inverse sampling probabilities applied to a generalized estimation equation. The large-sample properties of the proposed estimator are developed and small-sample properties are evaluated in a simulation study. We apply the methodology to study the effect of a specific diet component and a specific gene on the absolute risk of atrial fibrillation.