The Cox proportional hazards model is typically used to analyze time‐to‐event data. If the event of interest is rare and covariates are difficult or expensive to collect, the nested case‐control (NCC) design provides consistent estimates at reduced costs with minimal impact on precision if the model is specified correctly. If our scientific goal is to conduct inference regarding an association of interest, it is essential that we specify the model a priori to avoid multiple testing bias. We cannot, however, be certain that all assumptions will be satisfied so it is important to consider robustness of the NCC design under model misspecification. In this manuscript, we show that in finite sample settings where the functional form of a covariate of interest is misspecified, the estimates resulting from the partial likelihood estimator under the NCC design depend on the number of controls sampled at each event time. To account for this dependency, we propose an estimator that recovers the results obtained using using the full cohort, where full covariate information is available for all study participants. We present the utility of our estimator using simulation studies and show the theoretical properties. We end by applying our estimator to motivating data from the Alzheimer's Disease Neuroimaging Initiative.
We consider a functional linear Cox regression model for characterizing the association between time-to-event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high-dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time-to-event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high-dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer's disease. Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu).
more » « less- NSF-PAR ID:
- 10485958
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 74
- Issue:
- 1
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 109-117
- Size(s):
- p. 109-117
- Sponsoring Org:
- National Science Foundation
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