Proportional Rate Model Research Articles

Clinical correlates and prognostic impact of cognitive decline in patients with heart failure and preserved ejection fraction: insights from PARAGON-HF

Abstract Background Cognitive decline is common in patients with heart failure (HF), but its clinical correlates and prognostic impact are not well understood in this population. Purpose To examine the baseline variables associated with cognitive decline and the associations between cognitive decline and HF outcomes in patients with heart failure and preserved ejection fraction (HFpEF). Methods We analyzed cognitive function, as measured by the Mini-Mental State Examination (MMSE), in 2895 patients with HFpEF enrolled in a pre-specified sub-study of PARAGON-HF. Logistic regression analysis was performed to determine the factors associated with cognitive decline i.e., a decrease in MMSE score of ≥3 points by 48 weeks. Time-updated Cox proportional hazards regressions and semiparametric proportional rates models were used to examine the subsequent risk of clinical outcomes after a decline in MMSE scores of ≥1-, 2- and 3-points during follow-up respectively, adjusted for known prognostic variables including NT-proBNP and baseline MMSE. Results A total of 450 (15.5% of the population) patients experienced a decrease in MMSE score of ≥3 points from baseline, at any follow-up visit. The corresponding number for a decrease in MMSE score of ≥2 points and ≥1 point was 755 (26.1%) and 1231 (42.5%), respectively. Independent predictors of cognitive decline at 48 weeks included older age, living in Latin America or the Asia/Pacific region, ischemic etiology, prior HF hospitalization, history of stroke/TIA, and lower serum albumin level (Figure 1). There was a graded relationship between the size of the decrease in MMSE score from baseline and the subsequent risk of mortality. Notably, a decrease of ≥3 points was associated with a 50% increase in the subsequent risk of death from any cause (adjusted HR 1.53, 95% CI 1.10-2.11) and a 90% elevation in risk of death from cardiovascular causes (1.89, 1.25-2.86), respectively, after extensive adjustment for known prognostic variables and baseline MMSE score. By contrast, cognitive decline during follow-up was not associated with a higher risk of HF hospitalization or the composite of HF hospitalization or CV death (Figure 2). Conclusions In patients with HFpEF, a decline in MMSE score during follow-up is independently associated with a graded increase in the risk for mortality, but not of HF hospitalization.The predictors for cognitive declineRisk of outcomes after a decline in MMSE

Clinical Correlates and Prognostic Impact of Cognitive Dysfunction in Patients With Heart Failure and Preserved Ejection Fraction: Insights From PARAGON-HF.

Cognitive impairment is common in patients with heart failure and preserved ejection fraction but its clinical correlates and prognostic associations are poorly understood. We analyzed cognitive function, using the Mini-Mental State Examination (MMSE), in patients with heart failure and preserved ejection fraction enrolled in a prespecified substudy of the PARAGON-HF trial (Prospective Comparison of Angiotensin Receptor Neprilysin Inhibitor With Angiotensin Receptor Blocker Global Outcomes in Heart Failure With Preserved Ejection Fraction). Logistic regression analyses were performed to determine the variables associated with lower MMSE scores at baseline and postbaseline decline in MMSE scores at 48 weeks. Cox proportional hazards regression and semiparametric proportional rates models were used to examine the risk of clinical outcomes related to baseline MMSE scores, and decline in MMSE scores during follow-up, adjusted for prognostic variables including NT-proBNP (N-terminal pro-B-type natriuretic peptide). At baseline, cognitive function was normal (MMSE score 28-30) in 1809 of 2895 patients (62.5%), borderline (score 24-27) in 794 (27.4%), and impaired (score <24) in 292 (10.1%). Variables associated with both a lower MMSE score at baseline and a decline in score from baseline included older age, a history of stroke or transient ischemia attack, and lower serum albumin. Compared with those with baseline MMSE scores of 28 to 30, patients in the lower MMSE score categories had a stepwise increase in the risk of the composite of time to first HF hospitalization or cardiovascular death, with an adjusted hazard ratio of 1.27 (95% CI, 1.06-1.53) for those with scores of 24 to 27 and 1.58 (95% CI, 1.21-2.06) for those with scores <24, respectively. These associations were also found for the individual components of the composite and all-cause death. Likewise, cognitive impairment was associated with a 50% higher risk of total (first and repeat) heart failure hospitalizations and cardiovascular deaths. Examining the change in MMSE score from baseline, a decrease in MMSE score during follow-up was associated with a higher risk of death. In patients with heart failure and preserved ejection fraction, even modest baseline impairment of cognitive function was associated with worse outcomes, including death. A decline in MMSE score during follow-up was a strong predictor of mortality, independent of other prognostic variables.

The influence of neighborhood income on healthcare utilization in pediatric liver transplant.

Neighborhood contextual factors are associated with liver transplant outcomes. We analyzed associations between neighborhood-level socioeconomic status and healthcare utilization for pediatric liver transplant recipients. We merged the Pediatric Health Information System and Scientific Registry of Transplant Recipients databases and included liver transplant recipients ≤21 years hospitalized between January 2004 and May 2022. Outcomes were annual inpatient bed-days, risk of hospitalizations, and risk of liver biopsies. The primary exposure was zip code-based neighborhood income at transplant. We applied causal inference for variable selection in multivariable analysis. We modeled annual inpatient bed-days with mixed-effect zero-inflated Poisson regression, and rates of hospitalization and liver biopsy with a Cox-type proportional rate model. We included 1006 participants from 29 institutions. Children from low-income neighborhoods were more likely to be publicly insured (67% vs. 46%), Black (20% vs. 12%), Hispanic (30% vs. 17%), and have higher model for end-stage liver disease/pediatric end-stage liver disease model scores at transplant (17 vs. 13) than the remaining cohort. We found no differences in inpatient bed-days or rates of hospitalization across neighborhood groups. In univariable analysis, low-income neighborhoods were associated with increased rates of liver biopsy (rate ratio [RR]: 1.57, 95% confidence interval [CI]: 1.04-2.34, p = 0.03). These findings persisted after adjusting for insurance, race, and ethnicity (RR: 1.86, 95% CI:1.23-2.83, p < 0.01). Children from low-income neighborhoods undergo more liver biopsies than other children. These procedures are invasive and potentially preventable. In addition to improving outcomes, interventions to mitigate health inequities among liver transplant recipients may reduce resource utilization.

Use of pancreatic endotherapy in patients with chronic pancreatitis: results from a multicenter cohort study in the United States

Background and AimsAlthough commonly used for treating complications of chronic pancreatitis (CP), data on the frequency and factors associated with the use of pancreatic endotherapy (PET) are limited. Our aim was to define the utilization and factors predictive for receiving PET in a well-characterized CP cohort. MethodsThis is a cross-sectional analysis of data from PROCEED, a multicenter US cohort study of CP. PET modalities primarily consisted of ERCP. A treatment course was defined as the number of sessions performed for a specific indication. A repeat course was defined as PET >1 year after completion of the last course. Multivariable logistic regression identified predictive factors for receiving PET, and proportional rates model assessed risk factors for repeat PET. ResultsOf a total of 681 subjects, 238 (34.9%) received PET. Factors associated with receiving PET included female sex (OR: 1.26, 95% CI: 1.03-1.53), lower education (OR: 1.30, 95% CI: 1.04-1.62), income ≤ $50,000 per year (OR: 1.35, 95% CI: 1.07-1.71) and prior acute pancreatitis (AP) (OR: 1.74, 95% CI: 1.31, 2.32). 103/238 subjects (43.3%) underwent repeat PET at a median duration of 2 years with 23.1% receiving 2 courses, 9.7% receiving 3 courses, and 10.4% receiving 4+ courses. ConclusionsNearly half of patients with CP who undergo PET received one or more repeat courses within 2-3 years. In addition to a prior history of AP, demographic and socioeconomic factors were associated with receiving PET.

Cardiovascular Outcomes in GRADE (Glycemia Reduction Approaches in Type 2 Diabetes: A Comparative Effectiveness Study).

Cardiovascular disease is a major cause of morbidity and mortality in patients with type 2 diabetes. The effects of glucose-lowering medications on cardiovascular outcomes in individuals with type 2 diabetes and low cardiovascular risk are unclear. We investigated cardiovascular outcomes by treatment group in participants randomly assigned to insulin glargine, glimepiride, liraglutide, or sitagliptin, added to baseline metformin, in GRADE (Glycemia Reduction Approaches in Type 2 Diabetes: A Comparative Effectiveness Study). A total of 5047 participants with a mean±SD age of 57.2±10.0 years, type 2 diabetes duration of 4.0±2.7 years, and low baseline prevalence of cardiovascular disease (myocardial infarction, 5.1%; cerebrovascular accident, 2.0%) were followed for a median of 5 years. Prespecified outcomes included between-group time-to-first event analyses of MACE-3 (composite of major adverse cardiovascular events: cardiovascular death, myocardial infarction, and stroke), MACE-4 (MACE-3+unstable angina requiring hospitalization or revascularization), MACE-5 (MACE-4+coronary revascularization), MACE-6 (MACE-5+hospitalization for heart failure), and the individual components. MACE outcomes and hospitalization for heart failure in the liraglutide-treated group were compared with the other groups combined using Cox proportional hazards models. MACE-6 was also analyzed as recurrent events using a proportional rate model to compare all treatment groups. We observed no statistically significant differences in the cumulative incidence of first MACE-3, MACE-4, MACE-5, or MACE-6, or their individual components, by randomized treatment group. However, when compared with the other treatment groups combined, the liraglutide-treated group had a significantly lower risk of MACE-5 (adjusted hazard ratio, 0.70 [95% CI, 0.54-0.91]; P=0.021), MACE-6 (adjusted hazard ratio, 0.70 [95% CI, 0.55-0.90]; P=0.021), and hospitalization for heart failure (adjusted hazard ratio, 0.49 [95% CI, 0.28-0.86]; P=0.022). Compared with the liraglutide group, significantly higher rates of recurrent MACE-6 events occurred in the groups treated with glimepiride (rate ratio, 1.61 [95% CI, 1.13-2.29]) or sitagliptin (rate ratio 1.75; [95% CI, 1.24-2.48]). This comparative effectiveness study of a contemporary cohort of adults with type 2 diabetes, largely without established cardiovascular disease, suggests that liraglutide treatment may reduce the risk of cardiovascular events in patients at relatively low risk compared with other commonly used glucose-lowering medications. URL: https://www.clinicaltrials.gov; Unique identifier: NCT01794143.

Proportional rates models for multivariate panel count data.

Multivariate panel count data arise when there are multiple types of recurrent events, and the observation for each study subject consists of the number of recurrent events of each type between two successive examinations. We formulate the effects of potentially time-dependent covariates on multiple types of recurrent events through proportional rates models, while leaving the dependence structures of the related recurrent events completely unspecified. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process, and we develop a simple and stable EM-type algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. In addition, we develop a class of graphical and numerical methods for checking the adequacy of the fitted model. Finally, we evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial.

A proportional incidence rate model for aggregated data to study the vaccine effectiveness against COVID-19 hospital and ICU admissions.

We develop a proportional incidence model that estimates vaccine effectiveness (VE) at the population level using conditional likelihood for aggregated data. Our model assumes that the population counts of clinical outcomes for an infectious disease arise from a superposition of Poisson processes with different vaccination statuses. The intensity function in the model is calculated as the product of per capita incidence rate and the at-risk population size, both of which are time-dependent. We formulate a log-linear regression model with respect to the relative risk, defined as the ratio between the per capita incidence rates of vaccinated and unvaccinated individuals. In the regression analysis, we treat the baseline incidence rate as a nuisance parameter, similar to the Cox proportional hazard model in survival analysis. We then apply the proposed models and methods to age-stratified weekly counts of COVID-19-related hospital and ICU admissions among adults in Ontario, Canada. The data spanned from 2021 to February 2022, encompassing the Omicron era and the rollout of booster vaccine doses. We also discuss the limitations and confounding effects while advocating for the necessity of more comprehensive and up-to-date individual-level data that document the clinical outcomes and measure potentialconfounders.

Stable visually guided reaching does not require an internal feedforward model to compensate for internal delay: Data and model

Visually guided reaches are performed in ≈1s. Given unstable feedback control with neural transmission delay, stable visually guided reaching is assumed to require internal feedforward models that generate simulated feedback without delay that combines with actual feedback for stability. We investigated whether stable visually guided reaching requires internal models to handle such delay. Participants performed rapid targeted reaches in a virtual environment with different mappings between speeds of the hand and hand avatar. First, participants reached with visual guidance and constant mapping. Second, feedforward reaches were performed with constant mapping and hand avatar only visible at reach start and end. Reaches were accurate. Third, participants performed reaches with visual guidance and different mappings every trial. We expected performance as in the first condition. Finally, feedforward reaches with variable mapping yielded large errors showing visual guidance in the previous condition was successful despite an ineffective internal model. We simulated reaches using a proportional rate model with disparity Tau controlling the virtual Equilibrium Point in an Equilibrium Point (EP) model. The time dimensioned information and dynamic remained stable with delayed feedback. Finally, we fit movement times using the proportional rate EP model with 0msec, 50msec, and 100msec delay. With the fitted model parameters, we compared the model reach trajectories with the behavioral trajectories. Stable visually guided reaching did not require an internal feedforward model.

Improved semiparametric estimation of the proportional rate model with recurrent event data.

Owing to its robustness properties, marginal interpretations, and ease of implementation, the pseudo-partial likelihood method proposed in the seminal papers of Pepe and Cai and Lin etal. has become the default approach for analyzing recurrent event data with Cox-type proportional rate models. However, the construction of the pseudo-partial score function ignores the dependency among recurrent events and thus can be inefficient. An attempt to investigate the asymptotic efficiency of weighted pseudo-partial likelihood estimation found that the optimal weight function involves the unknown variance-covariance process of the recurrent event process and may not have closed-form expression. Thus, instead of deriving the optimal weights, we propose to combine a system of pre-specified weighted pseudo-partial score equationsvia the generalized method of moments and empirical likelihood estimation. We show that a substantial efficiency gain can be easily achieved without imposing additional model assumptions. More importantly, the proposed estimation procedures can be implemented with existing software. Theoretical and numerical analyses show that the empirical likelihood estimator is more appealing than the generalized method of moments estimator when the sample size is sufficiently large. An analysis of readmission risk in colorectal cancer patients is presented to illustrate the proposedmethodology.

Racial and Ethnic Disparities in Acute Care Utilization Among Patients With Glomerular Disease

The effects of race, ethnicity, socioeconomic status (SES), and disease severity on acute care utilization in patients with glomerular disease are unknown. Prospective cohort study. 1,456 adults and 768 children with biopsy-proven glomerular disease enrolled in the Cure Glomerulonephropathy (CureGN) cohort. Race and ethnicity as a participant-reported social factor. Acute care utilization defined as hospitalizations or emergency department visits. Multivariable recurrent event proportional rate models were used to estimate associations between race and ethnicity and acute care utilization. Black or Hispanic participants had lower SES and more severe glomerular disease than White or Asian participants. Acute care utilization rates were 45.6, 29.5, 25.8, and 19.2 per 100 person-years in Black, Hispanic, White, and Asian adults, respectively, and 55.8, 42.5, 40.8, and 13.0, respectively, for children. Compared with the White race (reference group), Black race was significantly associated with acute care utilization in adults (rate ratio [RR], 1.76 [95% CI, 1.37-2.27]), although this finding was attenuated after multivariable adjustment (RR, 1.31 [95% CI, 1.03-1.68]). Black race was not significantly associated with acute care utilization in children; Asian race was significantly associated with lower acute care utilization in children (RR, 0.32 [95% CI 0.14-0.70]); no significant associations between Hispanic ethnicity and acute care utilization were identified. We used proxies for SES and lacked direct information on income, household unemployment, or disability. Significant differences in acute care utilization rates were observed across racial and ethnic groups in persons with prevalent glomerular disease, although many of these difference were explained by differences in SES and disease severity. Measures to combat socioeconomic disadvantage in Black patients and to more effectively prevent and treat glomerular disease are needed to reduce disparities in acute care utilization, improve patient wellbeing, and reduce health care costs.

COVID-19 and Hospitalization Among Maintenance Dialysis Patients: A Retrospective Cohort Study Using Time-Dependent Modeling

Rationale & ObjectiveThe coronavirus disease 2019 (COVID-19) pandemic has had a profound impact on hospitalizations in general and on dialysis patients in particular. This study modeled the impact of COVID-19 on hospitalizations of dialysis patients in 2020.Study DesignRetrospective cohort study.Setting & ParticipantsMedicare patients on dialysis in calendar year 2020.PredictorsCOVID-19 status was divided into 4 stages: COVID1 (first 10 days after initial diagnosis), COVID2 (extends until the Post-COVID stage), Post-COVID (after 21 days with no COVID-19 diagnosis), and Late-COVID (begins after a hospitalization with a COVID-19 diagnosis); demographic and clinical characteristics; and dialysis facilities.OutcomeThe sequence of hospitalization events.Analytical ApproachA proportional rate model with a nonparametric baseline rate function of calendar time on the study population.ResultsA total of 509,609 patients were included in the study, 63,521 were observed to have a SARS-CoV-2 infection, 34,375 became Post-COVID, and 1,900 became Late-COVID. Compared with No-COVID, all 4 stages had significantly greater adjusted risks of hospitalizations with relative rates of 18.50 (95% CI, 18.19-18.81) for COVID1, 2.03 (95% CI, 1.99-2.08) for COVID2, 1.37 (95% CI, 1.35-1.40) for Post-COVID, and 2.00 (95% CI, 1.89-2.11) for Late-COVID.LimitationsFor Medicare Advantage patients, we only had inpatient claim information. The analysis was based on data from the year 2020, and the effects may have changed due to vaccinations, new treatments, and new variants. The COVID-19 effects may be somewhat overestimated due to missing information on patients with few or no symptoms and possible delay in COVID-19 diagnosis.ConclusionsWe discovered a marked time dependence in the effect of COVID-19 on hospitalization of dialysis patients, beginning with an extremely high risk for a relatively short period, with more moderate but continuing elevated risks later, and never returning to the No-COVID level.

Reliability aspects in a dynamic time-to-failure degradation-based model

Although the ordinary time-to-failure degradation-based model has been extensively used in practice, it also has its limitations. In this paper, we consider a time-to-failure degradation-based model recently proposed by Albabtain et al., where a limiting conditional survival probability entertains further stochastic relationships between the failure time and the degree of degradation. In the particular case where the limited survival probability is available for the proportional failure rate model, the model is developed using two well-known degradation paths, namely the additive degradation path and the multiplicative degradation path, each of which has a component of random variation. Preservation of various stochastic orders and aging properties of the random variation component in the model in the described setting is developed. To illustrate the model in the modified design, some examples of interest in reliability are presented.

Estimating the marginal effect of a continuous exposure on an ordinal outcome using data subject to covariate-driven treatment and visit processes.

In the statistical literature, a number of methods have been proposed to ensure valid inference about marginal effects of variables on a longitudinal outcome in settings with irregular monitoring times. However, the potential biases due to covariate-driven monitoring times and confounding have rarely been considered simultaneously, and never in a setting with an ordinal outcome and a continuous exposure. In this work, we propose and demonstrate a methodology for causal inference in such a setting, relying on a proportional odds model to study the effect of the exposure on the outcome. Irregular observation times are considered via a proportional rate model, and a generalization of inverse probability of treatment weights is used to account for the continuous exposure. We motivate our methodology by the estimation of the marginal (causal) effect of the time spent on video or computer games on suicide attempts in the Add Health study, a longitudinal study in the United States. Although in the Add Health data, observation times are prespecified, our proposed approach is applicable even in more general settings such as when analyzing data from electronic health records where observations are highly irregular. In simulation studies, we let observation times vary across individuals and demonstrate that not accounting for biasing imbalances due to the monitoring and the exposure schemes can bias the estimate for the marginal odds ratio of exposure.

A comparison of semiparametric approaches to evaluate composite endpoints in heart failure trials

In heart failure (HF) trials efficacy is usually assessed by a composite endpoint including cardiovascular death (CVD) and heart failure hospitalizations (HFHs), which has traditionally been evaluated with a time-to-first-event analysis based on a Cox model. As a considerable fraction of events is ignored that way, methods for recurrent events were suggested, among others the semiparametric proportional rates models by Lin, Wei, Yang, and Ying (LWYY model) and Mao and Lin (Mao-Lin model). In our work we apply least false parameter theory to explain the behavior of the composite treatment effect estimates resulting from the Cox model, the LWYY model, and the Mao-Lin model in clinically relevant scenarios parameterized through joint frailty models. These account for both different treatment effects on the two outcomes (CVD, HFHs) and the positive correlation between their risk rates. For the important setting of beneficial outcome-specific treatment effects we show that the correlation results in composite treatment effect estimates, which are decreasing with trial duration. The estimate from the Cox model is affected more by the attenuation than the estimates from the recurrent event models, which both demonstrate very similar behavior. Since the Mao-Lin model turns out to be less sensitive to harmful effects on mortality, we conclude that, among the three investigated approaches, the LWYY model is the most appropriate one for the composite endpoint in HF trials. Our investigations are motivated and compared with empirical results from the PARADIGM-HF trial (ClinicalTrials.gov identifier: NCT01035255), a large multicenter trial including 8399 chronic HF patients.

Semiparametric estimation of the proportional rates model for recurrent events data with missing event category.

Proportional rates models are frequently used for the analysis of recurrent event data with multiple event categories. When some of the event categories are missing, a conventional approach is to either exclude the missing data for a complete-case analysis or employ a parametric model for the missing event type. It is well known that the complete-case analysis is inconsistent when the missingness depends on covariates, and the parametric approach may incur bias when the model is misspecified. In this paper, we aim to provide a more robust approach using a rate proportion method for the imputation of missing event types. We show that the log-odds of the event type can be written as a semiparametric generalized linear model, facilitating a theoretically justified estimation framework. Comprehensive simulation studies were conducted demonstrating the improved performance of the semiparametric method over parametric procedures. Multiple types of Pseudomonas aeruginosa infections of young cystic fibrosis patients were analyzed to demonstrate the feasibility of our proposed approach.

Work Interruption: The Moderate Effect of Workload and Queue Length in the Manufacturing Industry

This paper explores the relationship between process interruption, workload, queue length, and worker productivity. Based on the data from the loading process in a manufacturing enterprise, the Cox proportional hazards rate model was utilized for empirical analysis. By defining two types of stochastic process interruptions (type I and type II), our empirical results found that process interruption harms worker productivity for 30 minutes after the end of the interruption. It was also concluded that the queue length in the loading process strengthens the negative relationship between the two types of interruptions and worker productivity. However, it is a different story for the moderate effect of workload; the negative effect of the type I interruption on worker productivity is stronger under a low workload, while it gets stronger for the type II interruption under a high workload. Our empirical findings firstly validated the strengthened effect of queue length on the relationship between process interruption and worker productivity. Additionally, we also found the different roles of workload on the relationship between different types of interruptions and worker productivity.

Semiparametric estimation of the proportional rates model for recurrent events data with missing event category

Semiparametric estimation of the proportional rates model for recurrent events data with missing event category

Additive-Multiplicative Rates Model for Recurrent Event Data with Intermittently Observed Time-Dependent Covariates.

Regression methods, including the proportional rates model and additive rates model, have been proposed to evaluate the effect of covariates on the risk of recurrent events. These two models have different assumptions on the form of the covariate effects. A more flexible model, the additive-multiplicative rates model, is considered to allow the covariates to have both additive and multiplicative effects on the marginal rate of recurrent event process. However, its use is limited to the cases where the time-dependent covariates are monitored continuously throughout the follow-up time. In practice, time-dependent covariates are often only measured intermittently, which renders the current estimation method for the additive-multiplicative rates model inapplicable. In this paper, we propose a semiparametric estimator for the regression coefficients of the additive-multiplicative rates model to allow intermittently observed time-dependent covariates. We present the simulation results for the comparison between the proposed method and the simple methods, including last covariate carried forward and linear interpolation, and apply the proposed method to an epidemiologic study aiming to evaluate the effect of time-varying streptococcal infections on the risk of pharyngitis among school children. The R package implementing the proposed method is available at www.github.com/TianmengL/rectime.

Recurrent Events Analysis With Data Collected at Informative Clinical Visits in Electronic Health Records

Although increasingly used as a data resource for assembling cohorts, electronic health records (EHRs) pose many analytic challenges. In particular, a patient’s health status influences when and what data are recorded, generating sampling bias in the collected data. In this article, we consider recurrent event analysis using EHR data. Conventional regression methods for event risk analysis usually require the values of covariates to be observed throughout the follow-up period. In EHR databases, time-dependent covariates are intermittently measured during clinical visits, and the timing of these visits is informative in the sense that it depends on the disease course. Simple methods, such as the last-observation-carried-forward approach, can lead to biased estimation. On the other hand, complex joint models require additional assumptions on the covariate process and cannot be easily extended to handle multiple longitudinal predictors. By incorporating sampling weights derived from estimating the observation time process, we develop a novel estimation procedure based on inverse-rate-weighting and kernel-smoothing for the semiparametric proportional rate model of recurrent events. The proposed methods do not require model specifications for the covariate processes and can easily handle multiple time-dependent covariates. Our methods are applied to a kidney transplant study for illustration. Supplementary materials for this article are available online.

Semiparametric modelling and estimation of covariate-adjusted dependence between bivariate recurrent events.

A time-dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one-sample settings. However, the one-sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate-adjusted rate ratio, a measure of covariate-adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo-partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancerrecurrence.