Modeling the Effect of Recurrent Events on Time-to-event Processes by Means of Functional Data

Author(s):  
Francesca Ieva ◽  
Marta Spreafico ◽  
Davide Burba
2020 ◽  
Vol 29 (11) ◽  
pp. 3424-3454 ◽  
Author(s):  
Theodor A Balan ◽  
Hein Putter

The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.


Blood ◽  
2019 ◽  
Vol 134 (Supplement_1) ◽  
pp. 1663-1663 ◽  
Author(s):  
Ruben A Mesa ◽  
John Catalano ◽  
Francisco Cervantes ◽  
Timothy Devos ◽  
Jason Gotlib ◽  
...  

Momelotinib (MMB) is a potent, selective, orally-bioavailable, small-molecule inhibitor of JAK1, JAK2 and ACVR1 being developed for the treatment of intermediate and high risk myelofibrosis (MF). Systemic inflammation integral to the pathogenesis of MF leads to increased ACVR1 activity which in turn increases secretion of hepcidin, resulting in perturbed iron homeostasis and an iron-restricted anemia (Physiol Rev. 2013;93:1721-41, Am J Hematol. 2014;89:470-9). MMB's inhibition of ACVR1, unique amongst the JAK inhibitor (JAKi) class, leads to a reduction of hepcidin, restoring iron homeostasis and RBC production and alleviating anemia and transfusion dependency (TD). Chronic, progressive anemia is the key hallmark feature of MF; anemia and TD are strongly predictive of reduced survival (Am J Hematol. 2013;88:312-6). MMB is the only clinical stage JAKi to possess potent ACVR1 inhibitory activity, resulting in improvement of anemia in contrast to ruxolitinib (RUX) which results in worsening. The SIMPLIFY-1 (S1) trial, a double-blind, active-controlled Phase 3 study in which 432 patients received randomized treatment with MMB or RUX for 24 weeks was previously reported (JCO. 2017;35:3844-50). In addition to a significant reduction in splenomegaly and improvement in constitutional symptoms, the study demonstrated that patients in the MMB arm achieved nominal-statistical significance for all anemia endpoints tested, including a higher rate of transfusion independence (p<0.001) and lower rates of TD (p=0.019) at Week 24, compared to patients on RUX, consistent with MMB's pro-erythropoietic effect. Overall, a demonstrably decreased transfusion requirement was noted in patients who received MMB vs RUX. Since transfusion burden is of significant concern to clinicians and patients, to better understand the dynamics of RBC transfusions we further examined the S1 data through statistical models utilizing a variety of novel anemia benefit endpoints including time until transfusion and overall intensity of transfusions across time. The proportions of patients with 0 and 4 transfusions were calculated and time-to-event analyses examining time-to-first and time-to-fifth units transfused also conducted. Since transfusions typically comprise 2 units, the fifth unit transfused represents a de facto third transfusion event. The number of units transfused were also considered to be recurrent events and examined with and without patients' baseline characteristics as covariates. Finally, a mixture model, based on a zero-inflated negative binomial (ZINB) distribution fit to the transfusion data, was employed to compare between the treatment groups the proportions of subjects with zero transfusion burden and the mean transfusion rates. Kaplan-Meier estimates of the proportion of patients who did not require any units transfused during the 24 week randomized treatment period were 73% and 46% for MMB and RUX respectively (p<0.0001; Figure 1), while the proportion of patients requiring 4 or fewer units were 83% and 62% (p<0.0001). When examining units transfused as recurrent events, patients receiving MMB possessed a hazard ratio of approximately one-half that for patients on RUX (HR 0.522; p<0.0001) for models both with and without patients' baseline characteristics as covariates. The ZINB covariate model demonstrated that MMB increased the odds of having zero units transfused in the first 24 weeks by a factor of 9.3 (p<0.0001) vs RUX. Taken together, the novel dynamic and time-to-event analysis methods described are relevant and informative additions to standard measures of transfusion burden in patients with MF. The results of these analyses allow more detailed description of MMB's differentiated anemia benefit as compared to RUX in a double-blind study of JAKi-naïve patients. These results when combined with additional data from the SIMPLIFY studies demonstrate that MMB is able to address the three hallmark features of MF, namely anemia, constitutional symptoms and splenomegaly, differentiating it from other JAK inhibitors. The benefit of MMB in reducing transfusion burden will be further evaluated in MOMENTUM, a future Phase 3 study of MMB in MF patients. In addition to assessment of constitutional symptoms, anemia and splenomegaly, MOMENTUM will provide opportunity to further evaluate associations between anemia benefit and patient reported measures of clinical benefit. Disclosures Mesa: Promedior: Research Funding; Gilead Sciences: Research Funding; Galena Biopharma: Consultancy; AbbVie: Research Funding; Incyte: Other: travel, accommodations, expenses, Research Funding; Genotech: Research Funding; CTI: Research Funding; Novartis: Consultancy, Honoraria, Other: travel, accommodations, expenses; Celgene Corporation: Research Funding; Sierra Oncology: Consultancy; PharmaEssentia: Research Funding; Genentech: Consultancy; NS Pharma: Research Funding; Pfizer: Research Funding; AOP Orphan Pharmaceuticals: Honoraria, Other: travel, accommodations, expenses; LaJolla: Consultancy; Samus: Research Funding; Shire: Honoraria; Baxalta: Consultancy. Catalano:Celgene: Other: Travel support (ASH 2018). Cervantes:Novartis: Honoraria, Speakers Bureau; Celgene: Consultancy, Speakers Bureau. Gotlib:Incyte: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding; Seattle Genetics: Research Funding; Promedior: Research Funding; Gilead: Membership on an entity's Board of Directors or advisory committees, Research Funding; Pharmacyclics: Research Funding; Novartis: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding; Allakos: Honoraria, Membership on an entity's Board of Directors or advisory committees; Blueprint Medicines: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding; Celgene: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding; Deceiphera: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding. Kiladjian:Novartis: Honoraria, Research Funding; Celgene: Consultancy; AOP Orphan: Honoraria, Research Funding. McLornan:Jazz Pharmaceuticals: Honoraria, Speakers Bureau; Novartis: Honoraria. Coart:IDDI: Consultancy, Employment. D'Hollander:IDDI: Consultancy, Employment. Donahue:Sierra Oncology Inc.: Employment. Kowalski:Sierra Oncology Inc.: Employment.


2017 ◽  
Vol 74 (6) ◽  
pp. 885-893 ◽  
Author(s):  
Elsa Goerig ◽  
Theodore Castro-Santos

Culverts can restrict movement of stream-dwelling fish. Motivation to enter and ascend these structures is an essential precursor for successful passage. However, motivation is challenging to quantify. Here, we use attempt rate to assess motivation of 447 brook trout (Salvelinus fontinalis) entering three culverts under a range of hydraulic, environmental, and biological conditions. A passive integrated transponder system allowed for the identification of passage attempts and success of individual fish. Attempt rate was quantified using time-to-event analysis allowing for time-varying covariates and recurrent events. Attempt rate was greatest during the spawning period, at elevated discharge, at dusk, and for longer fish. It decreased during the day and with increasing number of conspecifics downstream of the culvert. Results also show a positive correlation between elevated motivation and successful passage. This study enhances understanding of factors influencing brook trout motivation to ascend culverts and shows that attempt rate is a dynamic phenomenon, variable over time and among individuals. It also presents methods that could be used to investigate other species’ motivation to pass natural or anthropogenic barriers.


2018 ◽  
Vol 51 (2) ◽  
pp. 145-164
Author(s):  
Farhin Rahman ◽  
Munni Begum

Many diseases and clinical outcomes may recur to the same patient. These events are termed as recurrent events. Several statistical models have been proposed in the literature to analyze recurrent events. In this study, we identify the clinical and the genetic risk factors for recurring tumors among prostate cancer patients from The Cancer Genome Atlas (TCGA). Five statistical approaches for modeling recurrent time-to-event are implemented to identify and to determine the effects of the clinical and the genetic risk factors of tumor recurrence. In particular, we consider Andersen-Gill (A-G), Wei-Lin-Weissfeld (WLW), Prentice-Williams-Peterson Total Time (PWP-TT), Prentice-Williams-Peterson Gap Time (PWPGT) and Frailty models. We present and discuss the risk factors influencing the recurrence of tumors and their impacts in prostate cancer patients obtained from five commonly used models in this paper.


2021 ◽  
Author(s):  
Jordache Ramjith ◽  
Andreas Bender ◽  
Kit C. B. Roes ◽  
Marianne A. Jonker

Abstract Background: Recurrent events analysis plays an important role in many applications, including the study of chronic diseases or recurrence of infections. Historically, most models for the analysis of time-to-event data, including recurrent events, have been based on Cox proportional hazards regression. Recently, however, the Piece-wise exponential Additive Mixed Model (PAMM) has gained popularity as a flexible framework for survival analysis. While many papers and tutorials have been presented in the literature on the application of Cox based models, few papers have provided detailed instructions for the application of PAMMs and to our knowledge, none exist for recurrent events analysis. Methods: The PAMM is introduced as a framework for recurrent events analysis. We describe the application of the model to unstratified and stratified shared frailty models for recurrent events. We illustrate how penalized splines can be used to estimate non-linear and time-varying covariate effects without a priori assumptions about their functional shape. The model is motivated for both, analysis on the gap timescale ("clock-reset") and calendar timescale ("clock-forward"). The data augmentation necessary for the application to recurrent events is described and explained in detail. Results: Simulations confirmed that the model provides unbiased estimates of covariate effects and the frailty variance, as well as equivalence to the Cox model when proportional hazards are assumed. Applications to recurrence of staphylococcus aureus and malaria in children illustrates the estimation of seasonality, bivariate non-linear effects, multiple timescales and relaxation of the proportional hazards assumption via time-varying effects. The R package pammtools has been extended to facilitate estimation, visualization and interpretation of PAMMs for recurrent events analysis. Conclusion: PAMMs provide a flexible framework for the analysis of time-to-event and recurrent events data. The estimation of PAMMs is based on Generalized Additive Mixed Models and thus extends the researcher’s toolbox for recurrent events analysis.


2020 ◽  
Vol 91 (4) ◽  
pp. 352-357
Author(s):  
Jessica Tedford ◽  
Valerie Skaggs ◽  
Ann Norris ◽  
Farhad Sahiar ◽  
Charles Mathers

INTRODUCTION: Atrial fibrillation (AF) is one of the most common cardiac arrhythmias in the general population and is considered disqualifying aeromedically. This study is a unique examination of significant outcomes in aviators with previous history of both AF and stroke.METHODS: Pilots examined by the FAA between 2002 and 2012 who had had AF at some point during his or her medical history were reviewed, and those with an initial stroke or transient ischemic attack (TIA) during that time period were included in this study. All records were individually reviewed to determine stroke and AF history, medical certification history, and recurrent events. Variables collected included medical and behavior history, stroke type, gender, BMI, medication use, and any cardiovascular or neurological outcomes of interest. Major recurrent events included stroke, TIA, cerebrovascular accident, death, or other major events. These factors were used to calculate CHA2DS2-VASc scores.RESULTS: Of the 141 pilots selected for the study, 17.7% experienced a recurrent event. At 6 mo, the recurrent event rate was 5.0%; at 1 yr, 5.8%; at 3 yr 6.9%; and at 5 yr the recurrent event rate was 17.3%. No statistical difference between CHA2DS2-VASc scores was found as it pertained to number of recurrent events.DISCUSSION: We found no significant factors predicting risk of recurrent event and lower recurrence rates in pilots than the general population. This suggests CHA2DS2-VASc scores are not appropriate risk stratification tools in an aviation population and more research is necessary to determine risk of recurrent events in aviators with atrial fibrillation.Tedford J, Skaggs V, Norris A, Sahiar F, Mathers C. Recurrent stroke risk in pilots with atrial fibrillation. Aerosp Med Hum Perform. 2020; 91(4):352–357.


2010 ◽  
Vol 4 (1) ◽  
pp. 70-82 ◽  
Author(s):  
Arno Böhler

Nietzsche's model of eternal return triggers a drama of affirmation, the overcoming of a simple miming of our ancestors in favour of an active participation in the counter-actualisation of hidden potentials in recurrent events. Based on a close study of Zarathustra's struggle to free himself from a suffocating nihilism, the paper focuses on the revelatory caesura that ushers in what Deleuze calls the third synthesis of time, a time of ‘doing’ rather than reflection.


2011 ◽  
Vol 4 (2) ◽  
pp. 8-12
Author(s):  
Leo Alexander T Leo Alexander T ◽  
◽  
Pari Dayal L Pari Dayal L ◽  
Valarmathi S Valarmathi S ◽  
Ponnuraja C Ponnuraja C ◽  
...  

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