Estimating the ratio of multivariate recurrent event rates with application to a blood transfusion study

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 cancer recurrence.

A semiparametric additive rates model for the weighted composite endpoint of recurrent and terminal events

Recurrent event data with a terminal event commonly arise in longitudinal follow-up studies. We use a weighted composite endpoint of all recurrent and terminal events to assess the overall effects of covariates on the two types of events. A semiparametric additive rates model is proposed to analyze the weighted composite event process and the dependence structure among recurrent and terminal events is left unspecified. An estimating equation approach is developed for inference, and the asymptotic properties of the resulting estimators are established. The finite-sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is illustrated.

Methods for multivariate recurrent event data with measurement error and informative censoring

In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non-parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non-parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson-type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma.

Frailty modelling for multitype recurrent events in clinical trials

Recurrent event outcomes are ubiquitous among clinical trial data which encourages a conventional approach to analysis. Yet a common feature of these data has received less attention, that is, survival times often comprise multiple types of events that may imply a disparity in cost and disease severity. Typically, we neglect this feature of the data by combining event-types or analyzing each type separately, thus ignoring any interdependence among them. This practice may reflect a dearth of readily available methods and software that more appropriately acknowledge the true data structure. We provide a review of the literature on multitype recurrent events and frailty modelling which reflects a renewed interest in the topic over the past decade and the emergence of software for estimation. Thus, a review of available methods seems timely, if not overdue.

Recurrent event frailty models reduced time-varying and other biases in evaluating transfusion protocols for traumatic hemorrhage

OBJECTIVE

Transfusion research seeks to improve survival for severely injured and hemorrhaging patients using optimal plasma and platelet ratios over red blood cells (RBCs). However, most published studies comparing different ratios are plagued with serious bias and ignore time-varying effects. We applied joint recurrent event frailty models to increase validity and clinical utility.

STUDY DESIGN AND SETTING

Using the PRospective Observational Multicenter Major Trauma Transfusion study data, our joint random-effects models estimated the association of (1) clinical covariates with transfusion rate intensities and (2) varying plasma:RBC and platelet:RBC ratios with survival over the 24 hours after hospital admission. Along with survival time, baseline patient vital signs, laboratory values, and longitudinal data on types and volumes of transfusions were included.

RESULTS

Baseline systolic blood pressure, heart rate, pH, and hemoglobin were significantly associated with RBC transfusion rates. Increased transfusion rates (per hour) of plasma (P = 0.05), platelets (P < 0.001), or RBCs were associated with increased 24-hour mortality. Higher ratios of plasma:RBC (P = 0.107) and platelet:RBC (P < 0.001) were associated with reduced mortality in a time-varying pattern (P < 0.001).

CONCLUSIONS

The proposed joint analysis of transfusion rates and ratios offers a more valid statistical approach to evaluate survival effects in the presence of informative censoring by early death.