Copula-based semiparametric regression method for bivariate data under general interval censoring

Abstract

This research is motivated by discovering and underpinning genetic causes for the progression of a bilateral eye disease, Age-related Macular Degeneration (AMD), of which the primary outcomes, progression times to late-AMD, are bivariate and interval-censored due to intermittent assessment times. We propose a novel class of copula-based semiparametric transformation models for bivariate data under general interval censoring, which includes the case 1 interval censoring (current status data) and case 2 interval censoring. Specifically, the joint likelihood is modeled through a two-parameter Archimedean copula, which can flexibly characterize the dependence between the two margins in both tails. The marginal distributions are modeled through semiparametric transformation models using sieves, with the proportional hazards or odds model being a special case. We develop a computationally efficient sieve maximum likelihood estimation procedure for the unknown parameters, together with a generalized score test for the regression parameter(s).For the proposed sieve estimators of finite-dimensional parameters, we establish their asymptotic normality and efficiency. Extensive simulations are conducted to evaluate the performance of the 2 T. SUN and Y. DING proposed method in finite samples. Finally, we apply our method to a genome-wide analysis of AMD progression using the Age-Related Eye Disease Study (AREDS) data, to successfully identify novel risk variants associated with the disease progression. We also produce predicted joint and conditional progression-free probabilities, for patients with different genetic characteristics.

Genome‐wide association study‐based deep learning for survival prediction

“…Ideally one should take the correlation into account when constructing the prediction model. One possible extension includes using a copula model to account for the dependence between the two eyes from the same subject 48,49 and predicting the joint progression profiles of the two eyes through a DNN. We are investigating some of these extensions.…”

Identification and inference for subgroups with differential treatment efficacy from randomized controlled trials with survival outcomes through multiple testing

“…10 Many genetic studies have shown that the development or the progression of AMD is associated with various genetic regions and variants. [10][11][12][13][14] Specifically, in two recent genomewide association studies (GWAS) for AMD progression using the AREDS data where time-to-late-AMD is the outcome, multiple variants from ARMS2-HTRA1 and CFH regions have been discovered to be associated with AMD progression. 12,13 Besides association analyses where no treatment is involved, multiple research groups also investigated whether variants from these two gene regions are associated with differential treatment responses.…”

“…[10][11][12][13][14] Specifically, in two recent genomewide association studies (GWAS) for AMD progression using the AREDS data where time-to-late-AMD is the outcome, multiple variants from ARMS2-HTRA1 and CFH regions have been discovered to be associated with AMD progression. 12,13 Besides association analyses where no treatment is involved, multiple research groups also investigated whether variants from these two gene regions are associated with differential treatment responses. Research groups such as Klein et al 15 and Seddon et al 16 reported that genetic variants from CFH and ARMS2 regions were found to be associated with differential responses to the antioxidants plus zinc treatment.…”

Multivariate conditional transformation models

“…Analogous to GAMLSS, bivariate copula models with parametric marginal distributions, one‐parameter copulas, as well as joint semiparametric specifications for the predictors of all parameters of both marginal and copula models have been developed by Marra and Radice (2017) in a penalized likelihood framework and by Klein and Kneib (2016) using a Bayesian approach. Following these lines, Marra and Radice (2020) recently extended the framework to copula link‐based survival models, while Sun and Ding (2019) develop a copula‐based semiparametric regression method for bivariate data under general interval censoring. Alternatives to simultaneous estimation are two‐step procedures that first estimate the marginals and then the copula given the marginals and have been proposed by, for example, Vatter and Chavez‐Demoulin (2015) and Yee (2015) for parametric marginal distributions and bivariate one‐parameter and copulas.…”