Bivariate pseudo-observations for recurrent event analysis with terminal events

Abstract Background When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up. This phenomenon is known as left censoring, and simply ignoring these prior episodes can lead to biased and inefficient estimates. We aimed to propose a statistical method that performs well in this setting. Methods Our proposal was based on the use of models with specific baseline hazards. In this, the number of prior episodes were imputed when unknown and stratified according to whether the subject had been at risk of presenting the event before t = 0. A frailty term was also used. Two formulations were used for this “Specific Hazard Frailty Model Imputed” based on the “counting process” and “gap time.” Performance was then examined in different scenarios through a comprehensive simulation study. Results The proposed method performed well even when the percentage of subjects at risk before follow-up was very high. Biases were often below 10% and coverages were around 95%, being somewhat conservative. The gap time approach performed better with constant baseline hazards, whereas the counting process performed better with non-constant baseline hazards. Conclusions The use of common baseline methods is not advised when knowledge of prior episodes experienced by a participant is lacking. The approach in this study performed acceptably in most scenarios in which it was evaluated and should be considered an alternative in this context. It has been made freely available to interested researchers as R package miRecSurv.

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Builiding Methods for a Proactive Prescription Drug Surveillance System

Online Journal of Public Health Informatics ◽

10.5210/ojphi.v9i1.7591 ◽

2017 ◽

Vol 9 (1) ◽

Author(s):

Fan Xiong

Keyword(s):

Prescription Drug ◽

Surveillance System ◽

Recurrent Event ◽

Epidemiological Methods ◽

High Dose ◽

Prescription Opioids ◽

Event Analysis ◽

Cross Sectional ◽

Opioid Prescription ◽

Dependent Observations

ObjectiveThis study aims to show the application of longitudinal statisticaland epidemiological methods for building a proactive prescriptiondrug surveillance system for public health.IntroductionPrescription Drug Monitoring Programs (PDMPs) are operating in49 states and several U.S. territories. Current methods for surveillanceof prescription drug related behaviors, include the mean daily dosageof morphine milligram equivalent (MME) per patient, annualpercentage of days with overlapping prescriptions per patient, andannual multiple provider episodes for multiple controlled substanceprescription drugs per patient that are described elsewhere.1,2Thiswork builds on these efforts by extending longitudinal methodsto prescription drug behavior surveillance in order to predict risksassociated with prescription drug use.MethodsSchedule II prescription opioids from January 1, 2014 to February29, 2016 from the Kansas Tracking and Reporting of ControlledSubstances (KTRACS) was used for this analysis. Prescription opioidswere linked to the 2016 version of the morphine milligram equivalentconversion table from the National Center for Injury Preventionand Control.3Population estimates were based on the 2015 CountyVintage single-year of age bridged-race estimates from the NationalCenter for Health Statistics and used to calculate age-adjusted rates. Adaily high dose opioid prescription was defined as having greater thanor equal to 90 morphine milligram equivalent. Since this is a unit-daymeasure with patients experiencing multiple daily high dose opioiddays, the Prentice, William, and Peterson (PWP) recurrent eventmodel was used to estimate the number of high-dose opioid days forKansas patients by gender and age groups.4,5Start time was the firstprescription date with a high-dose opioid and stop time was the nexthigh-dose opioid date during a study period from January 1, 2014to Feb 29, 2016. The PWP model is a statistical model that allowsfor the estimation of covariates on an event history (i.e. total timewith prescription opioids, specifically high-dose opioids). Analysiswas completed with a stratified Cox-proportional hazard model,sandwich covariance for dependent observations, and statisticalsignificance was assessed with a Wald Chi-square. PROC PHREGin SAS/STAT(R) 14.1 was used since it has a new FAST option forfitting large proportional counting process hazard model.ResultsThe age-adjusted rate of daily high-dose opioid patients was3.2 patients per 100 Kansas population-year (95% CI: 3.1 – 3.2).Kansas patients aged 85 and older had the highest age-specific rateof 11.7 (95% CI: 11.5 –11.9). Preliminary recurrent event analysisshows on average nearly a quarter of approximately 50 millionSchedule II opioid patient days were high-dose opioid patient daysamong 785,514 Kansan patients with any prescribed opioid history.In an initial result stratified by the number of high-dose opioid daysand adjusting only for age, males on average had approximately 7%higher hazard of recurrent Schedule II high-dose opioid prescriptiondays than females (β: 0.07, S.E: 0.002, p<0.0001). Kansas patientsaged 45 to 54 compared to Kansas patients 85 and older on averagehad approximately 14% higher hazard of recurrent Schedule II high-dose opioid prescription days (β: 0.14, S.E: 0.007, p<0.0001).ConclusionsThis work demonstrates the application of survival analysistechniques to estimate the population at risk for high-dose opioids,which varies by the length of the total opioid prescription history. Earlyresults from the recurrent event analysis showed that Kansas maleand patients aged 45 to 54 years had the longest history of high-doseopioids. Annual cross-sectional population estimates may incorrectlyestimate the estimated risk of high-dose prescription opioids sinceit assumes all patients have the same prescription history. PDMPsare longitudinal databases. Survival analysis methods like recurrentevent models can leverage the longitudinal structure to more preciselyestimate risk statistics. Future work includes incorporation of healthoutcomes data and further prescription covariates to assess the timingand intensity of opioid potency escalation.

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