Measurement Error Case Series Models with Application to Infection-Cardiovascular Risk in OlderPatients on Dialysis

Spatiotemporal multilevel joint modeling of longitudinal and survival outcomes in end-stage kidney disease

Individuals with end-stage kidney disease (ESKD) on dialysis experience high mortality and excessive burden of hospitalizations over time relative to comparable Medicare patient cohorts without kidney failure. A key interest in this population is to understand the time-dynamic effects of multilevel risk factors that contribute to the correlated outcomes of longitudinal hospitalization and mortality. For this we utilize multilevel data from the United States Renal Data System (USRDS), a national database that includes nearly all patients with ESKD, where repeated measurements/hospitalizations over time are nested in patients and patients are nested within (health service) regions across the contiguous U.S. We develop a novel spatiotemporal multilevel joint model (STM-JM) that accounts for the aforementioned hierarchical structure of the data while considering the spatiotemporal variations in both outcomes across regions. The proposed STM-JM includes time-varying effects of multilevel (patient- and region-level) risk factors on hospitalization trajectories and mortality and incorporates spatial correlations across the spatial regions via a multivariate conditional autoregressive correlation structure. Efficient estimation and inference are performed via a Bayesian framework, where multilevel varying coefficient functions are targeted via thin-plate splines. The finite sample performance of the proposed method is assessed through simulation studies. An application of the proposed method to the USRDS data highlights significant time-varying effects of patient- and region-level risk factors on hospitalization and mortality and identifies specific time periods on dialysis and spatial locations across the U.S. with elevated hospitalization and mortality risks.

Bias and estimation under misspecification of the risk period in self-controlled case series studies

The self-controlled case series (SCCS) method is useful for estimating the relative incidence (RI) of acute events, such as adverse events (AEs) during a specified risk period following an exposure (e.g., 6-week period after vaccinations or 30-day period after infection-related hospitalizations). In practice, the "optimal" risk period is unknown and must be specified. To date, two approaches are available to guide the specification of the risk period. Both methods do not fully utilize the nature of the bias due to misspecification, which to date has not been characterized. Thus, we elucidate the bias of SCCS estimate of the RI when the risk period is misspecified. We then propose a novel method that more effectively estimates the optimal risk period and the associated RI of AEs. The new method incorporates information on the functional form of the bias. Efficacy of the proposed approach is illustrated with substantial reduction in bias and variance in simulation studies. The proposed method is illustrated with two SCCS studies to determine the (1) risk of idiopathic thrombocytopenic purpura after measles-mumps-rubella vaccination in children and (2) risk of cardiovascular events after infection-related hospitalizations in older patients on dialysis.

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

Recent studies found that infection-related hospitalization was associated with increased risk of cardiovascular (CV) events, such as myocardial infarction and stroke in the dialysis population. In this work, we develop time-varying effects modeling tools in order to examine the CV outcome risk trajectories during the time periods before and after an initial infection-related hospitalization. For this, we propose partly conditional and fully conditional partially linear generalized varying coefficient models (PL-GVCMs) for modeling time-varying effects in longitudinal data with substantial follow-up truncation by death. Unconditional models that implicitly target an immortal population is not a relevant target of inference in applications involving a population with high mortality, like the dialysis population. A partly conditional model characterizes the outcome trajectory for the dynamic cohort of survivors, where each point in the longitudinal trajectory represents a snapshot of the population relationships among subjects who are alive at that time point. In contrast, a fully conditional approach models the time-varying effects of the population stratified by the actual time of death, where the mean response characterizes individual trends in each cohort stratum. We compare and contrast partly and fully conditional PL-GVCMs in our aforementioned application using hospitalization data from the United States Renal Data System. For inference, we develop generalized likelihood ratio tests. Simulation studies examine the efficacy of estimation and inference procedures.

Weighted hurdle regression method for joint modeling of cardiovascular events likelihood and rate in the US dialysis population

We propose a new weighted hurdle regression method for modeling count data, with particular interest in modeling cardiovascular events in patients on dialysis. Cardiovascular disease remains one of the leading causes of hospitalization and death in this population. Our aim is to jointly model the relationship/association between covariates and (i) the probability of cardiovascular events, a binary process, and (ii) the rate of events once the realization is positive-when the 'hurdle' is crossed-using a zero-truncated Poisson distribution. When the observation period or follow-up time, from the start of dialysis, varies among individuals, the estimated probability of positive cardiovascular events during the study period will be biased. Furthermore, when the model contains covariates, then the estimated relationship between the covariates and the probability of cardiovascular events will also be biased. These challenges are addressed with the proposed weighted hurdle regression method. Estimation for the weighted hurdle regression model is a weighted likelihood approach, where standard maximum likelihood estimation can be utilized. The method is illustrated with data from the United States Renal Data System. Simulation studies show the ability of proposed method to successfully adjust for differential follow-up times and incorporate the effects of covariates in the weighting.

Cardiovascular event risk dynamics over time in older patients on dialysis: a generalized multiple-index varying coefficient model approach

Among patients on dialysis, cardiovascular disease and infection are leading causes of hospitalization and death. Although recent studies have found that the risk of cardiovascular events is higher after an infection-related hospitalization, studies have not fully elucidated how the risk of cardiovascular events changes over time for patients on dialysis. In this work, we characterize the dynamics of cardiovascular event risk trajectories for patients on dialysis while conditioning on survival status via multiple time indices: (1) time since the start of dialysis, (2) time since the pivotal initial infection-related hospitalization, and (3) the patient's age at the start of dialysis. This is achieved by using a new class of generalized multiple-index varying coefficient (GM-IVC) models. The proposed GM-IVC models utilize a multiplicative structure and one-dimensional varying coefficient functions along each time and age index to capture the cardiovascular risk dynamics before and after the initial infection-related hospitalization among the dynamic cohort of survivors. We develop a two-step estimation procedure for the GM-IVC models based on local maximum likelihood. We report new insights on the dynamics of cardiovascular events risk using the United States Renal Data System database, which collects data on nearly all patients with end-stage renal disease in the United States. Finally, simulation studies assess the performance of the proposed estimation procedures.

Naive hypothesis testing for case series analysis with time-varying exposure onset measurement error: inference for infection-cardiovascular risk in patients on dialysis

The case series method is useful in studying the relationship between time-varying exposures, such as infections, and acute events observed during the observation periods of individuals. It provides estimates of the relative incidences of events in risk periods (e.g., 30-day period after infections) relative to the baseline periods. When the times of exposure onsets are not known precisely, application of the case series model ignoring exposure onset measurement error leads to biased estimates. Bias-correction is necessary in order to understand the true directions and effect sizes associated with exposure risk periods, although uncorrected estimators have smaller variance. Thus, inference via hypothesis testing based on uncorrected test statistics, if valid, is potentially more powerful. Furthermore, the tests can be implemented in standard software and do not require additional auxiliary data. In this work, we examine the validity and power of naive hypothesis testing, based on applying the case series analysis to the imprecise data without correcting for the error. Based on simulation studies and theoretical calculations, we determine the validity and relative power of common hypothesis tests of interest in case series analysis. In particular, we illustrate that the tests for the global null hypothesis, the overall null hypotheses associated with all risk periods or all age effects are valid. However, tests of individual risk period parameters are not generally valid. Practical guidelines are provided and illustrated with data from patients on dialysis.