Left truncation arises frequently in observational cohort studies, in which subjects are sampled into substudies at some time during their follow-up, but the time origin of interest occurred prior to substudy sampling. For example, in the National Alzheimer's Coordinating Center (NACC) cumulative data set, many subjects experienced onset of cognitive impairment prior to their entry to the data set, and thus their time from impairment to Alzheimer's disease (AD) diagnosis is left truncated by their time to NACC entry. Standard methods of risk set adjustment can be used to adjust for this delayed entry, as long as the critical assumption of quasi-independence (i.e., factorization of the joint density over the observable region) between the entry time and time to AD diagnosis holds. However, this assumption often does not hold, and the simple adjusted analyses are biased. Truncated data, unlike purely censored data, enable identification of this requisite dependence due to joint observation of both the entry (truncation) time and the event time, and formal statistical tests are available. This proposal is motivated by our team's collective and extensive engagement in neurological disease studies, which display pervasive dependent truncation, and is supported by our expertise in survival analysis. This proposal adopts a range of analytical approaches to address dependent truncation that arises through any of several possible mechanisms. We accommodate unexplained dependence through inversion of transformation models and permutation null distributions, nonparametric bounds and estimation, and semi-parametric models, covariate-induced dependence through inverse probability weighting methods, and dependence that is induced by sequential truncating events through copula models. This project will establish a significantly enhanced collection of usable and robust methods for the analysis of dependently truncated data, which will strengthen the validity of research findings from studies of major public health problems, such as Alzheimer's disease. Each of our aims involves derivation of asymptotic results, extensive simulation, and application to our motivating neurologic disease studies.

Public Health Relevance

Delayed entry into studies complicates the analysis of these studies because it produces artificially inflated times to events of interest. This kind of sampling is prevalent in observational studies of neurological diseases, such as Azheimer's disease, other dementias, ALS and brain tumors, among many others. In this proposal, we develop novel statistical methods to optimally analyze data with this structure, and to support valid and robust scientific findings.

National Institute of Health (NIH)
National Institute of Neurological Disorders and Stroke (NINDS)
Research Project (R01)
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Biostatistical Methods and Research Design Study Section (BMRD)
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Vivalda, Joanna
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New York University
Biostatistics & Other Math Sci
Schools of Public Health
New York
United States
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Lee, Catherine; Betensky, Rebecca A; Alzheimer's Disease Neuroimaging Initiative (2018) Time-to-event data with time-varying biomarkers measured only at study entry, with applications to Alzheimer's disease. Stat Med 37:914-932
Chiou, Sy Han; Austin, Matthew D; Qian, Jing et al. (2018) Transformation model estimation of survival under dependent truncation and independent censoring. Stat Methods Med Res :962280218817573
Qian, Jing; Chiou, Sy Han; Maye, Jacqueline E et al. (2018) Threshold regression to accommodate a censored covariate. Biometrics :
Mandel, Micha; de Uña-Álvarez, Jacobo; Simon, David K et al. (2018) Inverse probability weighted Cox regression for doubly truncated data. Biometrics 74:481-487
Betensky, Rebecca A; Chiou, Sy Han (2017) Correlation among baseline variables yields non-uniformity of p-values. PLoS One 12:e0184531
Qian, Jing; Hyman, Bradley T; Betensky, Rebecca A (2017) Neurofibrillary Tangle Stage and the Rate of Progression of Alzheimer Symptoms: Modeling Using an Autopsy Cohort and Application to Clinical Trial Design. JAMA Neurol 74:540-548
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