Comparing methods for modeling longitudinal and survival data, with consideration of mediation analysis

Joint modeling of longitudinal and survival data has received much attention and is becoming increasingly useful. In clinical studies, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for longitudinal data and a survival model is applied to event outcomes. The argument in favor of a joint model has been the efficient use of the data as the survival information goes into modeling the longitudinal process and vice versa. In this thesis, we present joint maximum likelihood methods, a two stage approach and time dependent covariate methods that link longitudinal data to survival data. First, we use simulation studies to explore and assess the performance of these methods with bias, accuracy and coverage probabilities. Then, we focus on four time dependent methods considering models that are unadjusted and adjusted for time. Finally, we consider mediation analysis for longitudinal and survival data. Mediation analysis is introduced and applied in a research framework based on genetic variants, longitudinal measures and disease risk. We implement accelerated failure time regression using the joint maximum likelihood approach (AFT-joint) and an accelerated failure time regression model using the observed longitudinal measures as time dependent covariates (AFT-observed) to assess the mediated effect. We found that the two stage approach (TSA) performed best at estimating the link parameter. The joint maximum likelihood methods that used the predicted values of the longitudinal measures, similar to the TSA, provided larger estimates. The time dependent covariate methods that used the observed longitudinal measures in the survival analysis underestimated the true estimates. The mediation results showed that the AFT-joint and the AFT-observed underestimated the mediated effect. Comparison of the methods in Framingham Heart Study data revealed similar patterns. We recommend adjusting for time when estimating the association parameter in time dependent Cox and logistic models. Additional work is needed for estimating the mediated effect with longitudinal and survival data

Data Analysis and Experimental Design for Accelerated Life Testing with Heterogeneous Group Effects

abstract: In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects. Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship. The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

A Review on Joint Models in Biometrical Research

In some fields of biometrical research joint modelling of longitudinal measures and event time data has become very popular. This article reviews the work in that area of recent fruitful research by classifying approaches on joint models in three categories: approaches with focus on serial trends, approaches with focus on event time data and approaches with equal focus on both outcomes. Typically longitudinal measures and event time data are modelled jointly by introducing shared random effects or by considering conditional distributions together with marginal distributions. We present the approaches in an uniform nomenclature, comment on sub-models applied to longitudinal measures and event time data outcomes individually and exemplify applications in biometrical research

Freeze-Thaw Durability and Long-Term Performance Evaluation of Shotcrete in Cold Regions

This study’s aim was to evaluate the freeze-thaw durability of shotcrete in cold regions and predict its long-term performance. One benchmark mix design from the WSDOT was chosen to prepare samples for performance evaluation. Shotcrete specimens were conditioned in accordance with ASTM C666. The long-term freeze-thaw performance after certain cycles was evaluated using the dynamic modulus of elasticity test (ASTM C215), fracture energy test (RILEM 50-FMC), and X-ray CT microstructure imaging analysis. Probabilistic damage analysis was conducted to establish the relation between the durability life and the damage parameter for different probabilities of reliability using the three-parameter Weibull distribution model. The fracture energy test was found to be a more sensitive test method than the dynamic modulus of elasticity for screening material deterioration over time and for capturing accumulative material damage caused by rapid freeze-thaw action, because of smaller durability factors (degradation ratios) obtained from the fracture energy test. X-ray CT imaging analysis is capable of detecting microcracks that form and pore evolution in the aggregate and interface transition zone of conditioned samples. Moreover, the continuum damage mechanic-based model shows potential in predicting long-term material degradation and the service life of shotcrete

Research-based versus clinical serum creatinine measurements and the association of acute kidney injury with subsequent kidney function: findings from the Chronic Renal Insufficiency Cohort study.

Background:Observational studies relying on clinically obtained data have shown that acute kidney injury (AKI) is linked to accelerated chronic kidney disease (CKD) progression. However, prior reports lacked uniform collection of important confounders such as proteinuria and pre-AKI kidney function trajectory, and may be susceptible to ascertainment bias, as patients may be more likely to undergo kidney function testing after AKI. Methods:We studied 444 adults with CKD who participated in the prospective Chronic Renal Insufficiency Cohort (CRIC) Study and were concurrent members of a large integrated healthcare delivery system. We estimated glomerular filtration rate (eGFR) trajectories using serum creatinine measurements from (i) the CRIC research protocol (yearly) and (ii) routine clinical care. We used linear mixed effects models to evaluate the associations of AKI with acute absolute change in eGFR and post-AKI eGFR slope, and explored whether these varied by source of creatinine results. Models were adjusted for demographic characteristics, diabetes status and albuminuria. Results:During median follow-up of 8.5 years, mean rate of eGFR loss was -0.31 mL/min/1.73 m2/year overall, and 73 individuals experienced AKI (55% Stage 1). A significant interaction existed between AKI and source of serum creatinine for acute absolute change in eGFR level after discharge; in contrast, AKI was independently associated with a faster rate of eGFR decline (mean additional loss of -0.67 mL/min/1.73 m2/year), which was not impacted by source of serum creatinine. Conclusions:AKI is independently associated with subsequent steeper eGFR decline regardless of the serum creatinine source used, but the strength of association is smaller than observed in prior studies after taking into account key confounders such as pre-AKI eGFR slope and albuminuria

The Association Between Rate and Severity of Exacerbations in Chronic Obstructive Pulmonary Disease: An Application of a Joint Frailty-Logistic Model.

Exacerbations are a hallmark of chronic obstructive pulmonary disease (COPD). Evidence suggests the presence of substantial between-individual variability (heterogeneity) in exacerbation rates. The question of whether individuals vary in their tendency towards experiencing severe (versus mild) exacerbations, or whether there is an association between exacerbation rate and severity, has not yet been studied. We used data from the MACRO Study, a 1-year randomized trial of the use of azithromycin for prevention of COPD exacerbations (United States and Canada, 2006-2010; n = 1,107, mean age = 65.2 years, 59.1% male). A parametric frailty model was combined with a logistic regression model, with bivariate random effects capturing heterogeneity in rate and severity. The average rate of exacerbation was 1.53 episodes/year, with 95% of subjects having a model-estimated rate of 0.47-4.22 episodes/year. The overall ratio of severe exacerbations to total exacerbations was 0.22, with 95% of subjects having a model-estimated ratio of 0.04-0.60. We did not confirm an association between exacerbation rate and severity (P = 0.099). A unified model, implemented in standard software, could estimate joint heterogeneity in COPD exacerbation rate and severity and can have applications in similar contexts where inference on event time and intensity is considered. We provide SAS code (SAS Institute, Inc., Cary, North Carolina) and a simulated data set to facilitate further uses of this method