Survival analysis under the Cox proportional hazards model with pooled covariates

Abstract

For a continuous time‐to‐event outcome and an expensive‐to‐measure exposure, we develop a pooling design and propose a likelihood‐based approach to estimate the hazard ratios (HRs) of a Cox proportional hazards (PH) model. Our proposed approach fits a PH model based on pooled exposures with individually observed time‐to‐event outcomes. The design and estimation exploits the equivalence of the conditional logistic likelihood functions arising from a matched case‐control study and the partial likelihood function of a riskset‐matched, nested case‐control (NCC) subset of a cohort study. To create the pools, we first focus on an NCC subcohort. Pools are formed at random while keeping the matching intact. Pool‐level exposure and confounders are then evaluated and used in the likelihood to estimate the HR and the standard error of the estimates. The estimators are MLEs, provide consistent estimates of the individual‐level HRs, and are asymptotically normal. Our simulation results indicate that the pooled estimates are comparable to the estimates obtained from the NCC subcohort. The units of analysis for the pooled design are the pools and not the individual participants. Hence the effective sample size is reduced. Therefore, the variance of the HR estimate increases with increasing poolsize. However, this variance inflation in small samples can be offset by including more matched controls per case within the NCC subcohort. An application is demonstrated with the Second Manifestations of ARTerial disease (SMART) study.

Privacy-preserving analysis of time-to-event data under nested case-control sampling

“…In this article, we propose a privacy-preserving analysis technique for time-to-event data within the NCC sampling framework. The technique leverages the pooling scheme introduced by Weinberg and others 16 , 18 , 31 to randomly aggregate individual records across matched sets within the same NCC subcohorts, stratified by the outcome status. Only the aggregated covariate levels of the NCC subcohorts are shared with the analytical site.…”

“…As it would be shown later, equation (3) is of the same form as the conditional logistic likelihood for a 1 : m matched case-control subcohort. 33,31 Hence, model parameters and standard errors (SEs) could be estimated with standard statistical programs available for conditional logistic regression, for example, monospaceclogit function in the monospacesurvival package. 34 The link between the two likelihoods is outlined in Section 2.1.3.…”

“…NCC subcohort sampling provides an attractive alternative to full cohort analysis, particularly when the analysis is constraint by the amount of available resources 30 or the amount of information that could be released. 31 This idea provides a key motivation for the proposed method where aggregate values of NCC subcohorts are utilized to preserve individual records during Cox regression modeling. NCC sampling is also sometimes referred to as riskset sampling or incidence density sampling.…”

“…Upon reducing the Cox partial likelihood in ( 2 ) to the NCC subcohort likelihood given in equation ( 3 ), the nodes set out to follow the outcome dependent aggregation scheme described by Saha-Chaudhuri and Weinberg 18 and Saha-Chaudhuri and Juwara. 31 …”

A Importância Da Análise De Sobrevida Para Os Estudos Epidemiológicos E De Saúde

“…A modelagem estatística pelo método semiparamétrico de Cox gera uma curva logarítmica para cada variável, enquanto o método paramétrico de Weibull resulta em uma função exponencial capaz de estimar a ocorrência do desfecho no tempo com as covariáveis selecionadas (Mittal et al, 2014). Assim é possível identificar fatores preditivos e, simultaneamente, excluir confundidores (ElHafeez et al, 2012;Saha-Chaudhuri & Juwara, 2021).…”