Time-varying effect modeling with longitudinal data truncated by death: conditional models, interpretations, and inference

Kürüm

et al. 2020

Biometrics

Self Cite

For patients on dialysis, hospitalizations remain a major risk factor for mortality and morbidity. We use data from a large national database, United States Renal Data System, to model time‐varying effects of hospitalization risk factors as functions of time since initiation of dialysis. To account for the three‐level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities, we propose a multilevel mixed effects varying coefficient model (MME‐VCM) where multilevel (patient‐ and facility‐level) random effects are used to model the dependence structure of the data. The proposed MME‐VCM also includes multilevel covariates, where baseline demographics and comorbidities are among the patient‐level factors, and staffing composition and facility size are among the facility‐level risk factors. To address the challenge of high‐dimensional integrals due to the hierarchical structure of the random effects, we propose a novel two‐step approximate EM algorithm based on the fully exponential Laplace approximation. Inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions. The finite sample performance of the proposed estimation procedure is studied through simulations.

Section: Model Specificationmentioning

confidence: 99%

A multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis

Kürüm

et al. 2020

Biometrics

Self Cite

“…Partly conditional models study the dynamic cohort of survivors and have been considered in the context of generalized linear models for longitudinal data where missingness is primarily due to truncation by death. 20 Estes et al 8,21 considered partly conditional target of inference for varying coefficient models.…”

Section: Varying Coefficient Model For Multilevel Risk Factorsmentioning

confidence: 99%

Modeling time‐varying effects of multilevel risk factors of hospitalizations in patients on dialysis

Chen

et al. 2018

Statistics in Medicine

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For chronic dialysis patients, a unique population requiring continuous medical care, methodologies to monitor patient outcomes, such as hospitalizations, over time, after initiation of dialysis, are of particular interest. Contributing to patient hospitalizations is a number of multilevel covariates such as demographics and comorbidities at the patient level and staffing composition at the dialysis facility level. We propose a varying coefficient model for multilevel risk factors (VCM-MR) to study the time-varying effects of covariates on patient hospitalization risk as a function of time on dialysis. The proposed VCM-MR also includes subject-specific random effects to account for within-subject correlation and dialysis facility-specific fixed effect varying coefficient functions to allow for the modeling of flexible time-varying facility-specific risk trajectories. An approximate EM algorithm and an iterative Newton-Raphson approach are proposed to address the challenge of estimation of high-dimensional parameters (varying coefficient functions) for thousands of dialysis facilities in the United States. The proposed modeling allows for comparisons between time-varying effects of multilevel risk factors as well as testing of facility-specific fixed effects. The method is applied to model hospitalization risk using the rich hierarchical data available on dialysis patients initiating dialysis between January 1, 2006 and December 31, 2008 from the United States Renal Data System, a large national database, where 331 443 hospitalizations over time are nested within patients, and 89 889 patients are nested within 2201 dialysis facilities. Patients are followed-up until December 31, 2013, where the follow-up time is truncated five years after the initiation of dialysis. Finite sample properties are studied through extensive simulations.

“…To achieve the above goals we propose the generalized (logistic) MVCM

g false[E {Y_{ij} false(t false) ∣ Z_{ij}, b_{ij}, t < S_{ij}} false] = g {p_{ij} false(t false)} = γ_{i} false(t false) + b_{ij} + Z_{ij}^{T} β, i = 1, \dots, I,

where g is the logit link function, t denotes the time after initiation of dialysis,

S_{ij}

denotes death time of subject j , the functions

γ_{i} false(t false)

correspond to the fixed time‐varying facility‐level effects,

b_{i} = {false(b_{i 1}, \dots, b_{{iN}_{i}} false)}^{T}

correspond to subject‐specific random effects (REs) within the i th facility with variance

σ_{b}^{2}

β = {false(β_{1}, \dots, β_{r} false)}^{T}

is a vector of regression parameters, and

p_{ij} false(t false) \equiv E {Y_{ij} false(t false) ∣ Z_{ij}, b_{ij}, t < S_{ij}} = g^{- 1} {γ_{i} false(t false) + b_{ij} + Z_{ij}^{T} β}

denotes the ‘partly conditional’ target of inference, conditional on being alive

t < S_{ij}

. The partly conditional target of inference has been considered before in modeling longitudinal data (Kurland and Heagerty ) and more recently in the context of varying coefficient models (Estes et al ; ) to model time‐varying regression effects in the dynamic cohort of survivors. We alert the reader here that model…”

Section: Multilevel Varying Coefficient Model For Time‐dynamic Profilingmentioning

confidence: 99%

Time-Dynamic Profiling with Application to Hospital Readmission Among Patients on Dialysis

Estes

Chen³

et al. 2018

Biometrics

Self Cite

Standard profiling analysis aims to evaluate medical providers, such as hospitals, nursing homes, or dialysis facilities, with respect to a patient outcome. The outcome, for instance, may be mortality, medical complications, or 30-day (unplanned) hospital readmission. Profiling analysis involves regression modeling of a patient outcome, adjusting for patient health status at baseline, and comparing each provider's outcome rate (e.g., 30-day readmission rate) to a normative standard (e.g., national "average"). Profiling methods exist mostly for non time-varying patient outcomes. However, for patients on dialysis, a unique population which requires continuous medical care, methodologies to monitor patient outcomes continuously over time are particularly relevant. Thus, we introduce a novel time-dynamic profiling (TDP) approach to assess the time-varying 30-day readmission rate. TDP is used to estimate, for the first time, the risk-standardized time-dynamic 30-day hospital readmission rate, throughout the time period that patients are on dialysis. We develop the framework for TDP by introducing the standardized dynamic readmission ratio as a function of time and a multilevel varying coefficient model with facility-specific time-varying effects. We propose estimation and inference procedures tailored to the problem of TDP and to overcome the challenge of high-dimensional parameters when examining thousands of dialysis facilities.