Stratified proportional subdistribution hazards model with covariate‐adjusted censoring weight for case‐cohort studies

Efficient estimation for left-truncated competing risks regression for case-cohort studies

The case-cohort study design provides a cost-effective study design for a large cohort study with competing risk outcomes. The proportional subdistribution hazards model is widely used to estimate direct covariate effects on the cumulative incidence function for competing risk data. In biomedical studies, left truncation often occurs and brings extra challenges to the analysis. Existing inverse probability weighting methods for case-cohort studies with competing risk data not only have not addressed left truncation, but also are inefficient in regression parameter estimation for fully observed covariates. We propose an augmented inverse probability-weighted estimating equation for left-truncated competing risk data to address these limitations of the current literature. We further propose a more efficient estimator when extra information from the other causes is available. The proposed estimators are consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator is unbiased and leads to estimation efficiency gain in the regression parameter estimation. We analyze the Atherosclerosis Risk in Communities study data using the proposed methods.

Additive subdistribution hazards regression for competing risks data in case-cohort studies

In survival data analysis, a competing risk is an event whose occurrence precludes or alters the chance of the occurrence of the primary event of interest. In large cohort studies with long-term follow-up, there are often competing risks. Further, if the event of interest is rare in such large studies, the case-cohort study design is widely used to reduce the cost and achieve the same efficiency as a cohort study. The conventional additive hazards modeling for competing risks data in case-cohort studies involves the cause-specific hazard function, under which direct assessment of covariate effects on the cumulative incidence function, or the subdistribution, is not possible. In this paper, we consider an additive hazard model for the subdistribution of a competing risk in case-cohort studies. We propose estimating equations based on inverse probability weighting methods for the estimation of the model parameters. Consistency and asymptotic normality of the proposed estimators are established. The performance of the proposed methods in finite samples is examined through simulation studies and the proposed approach is applied to a case-cohort dataset from the Sister Study.

The analysis of multiple outcomes, multiple variables and variables selection in hematopoietic cell transplantation studies

It is common to study time-to-event data in cancer research such as hematopoietic cell transplantation (HCT) for leukemia. The extensive work has been done for the univariate survival outcome, that is, one event type. However, in practice a subject is often exposed to multiple types of outcomes. In this article, we review various types of right-censored data with multiple outcome types including competing risks data, recurrent event data, and composite endpoints. We also provide hematopoietic cell transplantation data examples.

The Case for Case-Cohort: An Applied Epidemiologist's Guide to Reframing Case-Cohort Studies to Improve Usability and Flexibility

When research questions require the use of precious samples, expensive assays or equipment, or labor-intensive data collection or analysis, nested case-control or case-cohort sampling of observational cohort study participants can often reduce costs. These study designs have similar statistical precision for addressing a singular research question, but case-cohort studies have broader efficiency and superior flexibility. Despite this, case-cohort designs are comparatively underutilized in the epidemiologic literature. Recent advances in statistical methods and software have made analyses of case-cohort data easier to implement, and advances from casual inference, such as inverse probability of sampling weights, have allowed the case-cohort design to be used with a variety of target parameters and populations. To provide an accessible link to this technical literature, we give a conceptual overview of case-cohort study analysis with inverse probability of sampling weights. We show how this general analytic approach can be leveraged to more efficiently study subgroups of interest or disease subtypes or to examine associations independent of case status. A brief discussion of how this framework could be extended to incorporate other related methodologic applications further demonstrates the broad cost-effectiveness and adaptability of case-cohort methods for a variety of modern epidemiologic applications in resource-limited settings.

Competing risks regression models with covariates-adjusted censoring weight under the generalized case-cohort design

A generalized case-cohort design has been used when measuring exposures is expensive and events are not rare in the full cohort. This design collects expensive exposure information from a (stratified) randomly selected subset from the full cohort, called the subcohort, and a fraction of cases outside the subcohort. For the full cohort study with competing risks, He et al. (Scand J Stat 43:103-122, 2016) studied the non-stratified proportional subdistribution hazards model with covariate-dependent censoring to directly evaluate covariate effects on the cumulative incidence function. In this paper, we propose a stratified proportional subdistribution hazards model with covariate-adjusted censoring weights for competing risks data under the generalized case-cohort design. We consider a general class of weight functions to account for the generalized case-cohort design. Then, we derive the optimal weight function which minimizes the asymptotic variance of parameter estimates within the general class of weight functions. The proposed estimator is shown to be consistent and asymptotically normally distributed. The simulation studies show (i) the proposed estimator with covariate-adjusted weight is unbiased when the censoring distribution depends on covariates; and (ii) the proposed estimator with the optimal weight function gains parameter estimation efficiency. We apply the proposed method to stem cell transplantation and diabetes data sets.

Case-cohort design in hematopoietic cell transplant studies

SERIES EDITORS- NOTE

Imagine you and your colleagues have done 1000 transplants in persons with acute myeloid leukaemia (AML) in 1st remission. 5 percent of the 20 percent of recipients relapsing posttransplant have an isolated central nervous system relapse. You are curious and want to know whether there is anything special about this 5 percent, specifically whether this risk corelates with any pretransplant clinical and laboratory co-variates. You have extensive clinical data and some typical laboratory data on all 1000 but you suspect the culprit is mutation topography. What to do? Fortunately you have bio-banked DNA from the 1000. If resources and monies are not limiting you can do targeted or next generation sequencing on all 1000 DNA samples and off you go. However, most of us lack unlimited resources and monies. How can you sensibly and efficiently tackle this research problem? The answer is a case-cohort design study. In the typescript which follows Profs. Cai and Kim explain how to accomplish this. If you follow their advice you may need only to analyze samples from < 300 recipients rather than 1000 to test your hypothesis. They explain how to design such a study and provide references to estimate sample size.Sadly, their typescript will not tell you how to get funding for the study, whish poor devil who will have to write the protocol, worse, who will shepherd it though endless committees for approval and the like. Help on these issues is outside the scope of our statistics series. In this context we suggest advice from Woody Allen's article in the New Yorker: The Kugelmass Episode (April 24, 1977). When Prof. Kugelmass (English, City College) tells his analyst Dr. Mandel he has fallen in love with Emma Bovary who died of arsenic poisoning near Rouen, France 120 years earlier the analyst says: After all, I'm an analyst, not a magician. Kugelmass' reply: Then perhaps what I need is a magician and is off to Coney Island to find one. Good luck, the magician may still be there! (Note: This typescript is R-rated. It contains an equation.)Robert Peter Gale, Imperial College London, and Mei-Jie Zhang, Medical College of Wisconsin and CIBMTR.