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Survival Analysis 5

Presenter: Theodor Adrian Balan

When: Friday, July 15, 2016      Time: 9:00 AM - 10:30 AM

Room: Salon A Carson Hall (Level 2)

Session Synopsis:

Dynamic frailty models for recurrent events data

Recurrent events data are increasingly common in clinical studies. Within the framework of survival analysis, several models have been proposed to analyze such data (Cook & Lawless 2007). In particular, the frailty model has been commonly employed to account for population heterogeneity due to individual-specific unmeasured factors. The frailty is a random effect generally assumed to be constant in time. Considering the longitudinal character of the data, this is a real limitation. In other words, it is implicitly assumed that the unmeasured factors that the frailty accounts for do not change in time, nor do their effects change in time. This assumption may not always be justifiable. We adapt the model of Putter and van Houwelingen (2015) to accommodate recurrent events data. They proposed replacing the frailty by a dynamic frailty process which can vary over. A time-dependent frailty can be seen as accounting for unmeasured time-dependent covariates or unmeasured covariates with time-dependent effects. In many cases, this might be more plausible than a time-constant frailty model. Furthermore, the proposed method allows for a flexible autocorrelation structure, in addition to accommodating a large family of distributions for the random effects, including the gamma and the positive stable distributions. We discuss the implications of this model for parameters of interest, such as the baseline intensity of the recurrent events process and the covariate effects. The interpretation, advantages and limitations of the dynamic frailty process approach are discussed in the light of a simulation study. Finally, the proposed methods are illustrated on a data set comprising recurrent infections on patients of chronic granulomatous disease. Cook, R. J. & Lawless, J. F. The statistical analysis of recurrent events. Springer Science & Business Media (2015) Putter, H. & van Houwelingen, H. C. (2015). Dynamic frailty models based on compound birth-death processes. Biostatistics (2015) 16 (3): 550-564

Survival Analysis 5

Presenter: Yun-Hee Choi

When: Friday, July 15, 2016      Time: 9:00 AM - 10:30 AM

Room: Salon A Carson Hall (Level 2)

Session Synopsis:

Frailty Model for the Joint Modeling of Screening Visit and Disease Processes in Lynch Syndrome Families

Individuals with Lynch Syndrome have a very high risk of developing colorectal cancer (CRC) and other cancers. Mutation carriers have been recommended to receive screening with colonoscopy every 1-2 years with the aim of detecting and removing adenoma polyps and thus decreasing CRC risk1. The evaluation of CRC screening is complicated by many statistical challenges: the visit intervals vary across individuals depending on several factors (e.g. gender, age, polyps detection, and proband’s age); the visit process can affect CRC risk, which in turn can also change the visit process; residual familial dependence can affect both the visit and disease processes. To address these challenges, we propose a joint frailty model2,3 for recurrent screening visits and CRC event, which incorporates familial dependence and non-random familial ascertainment. The proposed model accounts for two sources of dependence arising both at the individual or family levels. Individual shared frailties are introduced to specify the correlation between the visit and disease processes while family-specific frailties account for residual familial correlation. We apply this new joint frailty model to a series of Lynch syndrome families from Newfoundland1 to estimate covariate effects on the two processes and their association parameters. We also evaluate the effect of screening process on CRC risks. The performance of the proposed joint model will be evaluated by simulation. References: 1. S. Stuckless, J.S. Green, M. Morgenstern et al. (2012) Impact of colonoscopic screening in male and female Lynch syndrome carriers with an MSH2 mutation. Clinical Genetics, 82: 439-445. 2. V. Rondeau, S. Mathoulin-pelissier, H. Jacqmin-gadda, et al. (2007) Joint frailty models for recurring events and death using maximum penalized likelihood estimation: application on cancer events. Biostatistics, 8: 708-721. 3. V. Rondeau, L. Filleul, and P. Joly (2006) Nested frailty models using maximum penalized likelihood estimation. Statistics in Medicine, 25: 4036-4052.

Survival Analysis 5

Presenter: Mia Grand

When: Friday, July 15, 2016      Time: 9:00 AM - 10:30 AM

Room: Salon A Carson Hall (Level 2)

Session Synopsis:

A joint model for an interval censored multi-state outcome and a longitudinal outcome with clusters

Uveitis is a disease that manifests as an inflammation of the eye that affects the visual acuity of the patients. Accurate assessment of the risk of inflammation and poor visual acuity are highly relevant for these patients as uveitis is the leading cause of legal blindness in the working population in the western world. The data consist of 258 patients that frequented the Rotterdam Eye Hospital in the period from 1979 to 2015. At each visit information was collected on the inflammation status, visual acuity and covariates, such as treatment. The data have a number of interesting features. First of all, the inflammation is reversible, and both the recovery and inflammation time are interval censored, since the status of the inflammation is only accessed at the visits to the hospital. Secondly, the visual acuity is affected by the status of the inflammation and it is non-linear in time. Furthermore, each subject contributed with two eyes which cannot be assumed to be independent. Our aim is to jointly model the inflammation and visual acuity processes. The inflammation is modelled with a two state multi-state process, one for each eye, indicating whether it is active or silent. Treatment is included in the model as a time-dependent covariate. It is assumed that treatment directly affects the inflammation, and only indirectly, through the inflammation and recovery rates, affects the visual acuity. We introduce correlated log-normal frailties to the inflammation and recovery rates, which are assumed to be shared by the two eyes, to account for the unobserved heterogeneity. The model is fitted with an EM-algorithm.

Survival Analysis 5

Presenter: Gregory Nuel

When: Friday, July 15, 2016      Time: 9:00 AM - 10:30 AM

Room: Salon A Carson Hall (Level 2)

Session Synopsis:

Estimating Piecewise Constant Hazard Rates in Survival Analysis through Adaptive Ridge

In survival analysis, an attractive model for the estimation of hazard rates is the piecewise constant hazard (PCH) model [1]. In this model, we assume the hazard rates to be constant on arbitrary chosen time intervals (ex: one interval for every 10 years of age like in [2]). Due to its simplicity of use and presentation, this model is widespread in the context of time to event data from cancer, cardiovascular diseases, neuro-degenerative diseases, etc. Obviously, the choice of the time intervals is critical for the PCH model, but surprisingly, literature provides very little help on the matter. Here we present a new method whose purpose is to estimate automatically the number and localisation of time intervals for PCH models using a penalized likelihood method. More precisely, we consider the likelihood of a PCH model where each observed age has its own hazard and penalize it by a penalty term times the number of differences between consecutive hazards. The whole procedure is handled very efficiently by combining a linear Newton-Raphson maximization algorithm with an iteratively reweighted Ridge penalty (Adaptive Ridge procedure [3]). The output includes the full regularization path from the overfitted model (small penalty) to the exponential one (large penalty) and model selection is performed either using asymptotic criteria like BIC or finite distance heuristics like the dimension jump or slope heuristics [4]. Being basically linear in term of number of observations, the new method is fast enough to handle large datasets, and proves itself very efficient both on simulated and real datasets. [1] Aalen, O. O., Borgan, Ø. & Gjessing, H. K. (2008). Survival and Event History Analysis. Statistics for Biology and Health. Springer. [2] Antoniou, A., Pharoa, P., Smith, P. & Easton, D. (2004). The BODICEA model of genetic susceptibility to breast and ovarian cancer. British Journal of Cancer 91, 1580-1590. [3] Frommlet, F. & Nuel, G. (2015). An adaptive Ridge procedure for L0 regularization. To appear. [4] Baudry, J.-P., Maugis, C. & Michel, B. (2012). Slope heuristics: overview and implementation. Statistics and Computing 22(2), 455-470.

Survival Analysis 5

Presenter: Jason Shao

When: Friday, July 15, 2016      Time: 9:00 AM - 10:30 AM

Room: Salon A Carson Hall (Level 2)

Session Synopsis:

Joint Frailty Mixed Models: Accounting for Heterogeneity in Sieve Analysis of Vaccine Efficacy

In randomized trials of preventative vaccines, we are often interested in whether efficacy differs based on some characteristic of the disease endpoint, such as the serotype of an infecting pathogen. It has been shown that evaluation of vaccine efficacy is sensitive to assumptions about the protective mechanism of the vaccine. Currently, statistical methods designed to test for differential efficacy across disease types (“sieve analysis”), assume that the effect of the vaccine is to reduce the risk of each disease type by the same factor for all treated participants (a homogeneous “leaky vaccine” model). Significant biases can occur in estimation and testing of vaccine efficacies when this assumption does not hold. We propose a class of mixed models, incorporating subject-level random effects (“frailties”) to account for unobserved heterogeneity in participant response to vaccination. We make the simplifying assumption that, for each disease type, the vaccine provides complete immunity for some proportion of subjects, and partial protection to the rest. This model encompasses the leaky vaccine model while also allowing for a wider variety of protective mechanisms. Estimating parameter values and testing for a sieve effect are straightforward procedures using readily available numeric optimization methods. Using simulation studies, we show that all parameters in the model can be reliably estimated using maximum likelihood. Our approach performs comparably to existing methods in cases where the leaky vaccine assumption is appropriate, and favorably when the assumptions do not hold. In some cases, however, very large sample sizes are needed in order to distinguish between different plausible sets of parameters in the joint frailty model. We discuss the implications of such for the design and interpretation of efficacy studies. Despite some of the limitations and assumptions of frailty mixed models, we have demonstrated an approach to sieve analysis that improves upon current methodology by accounting for unobserved subject heterogeneity.

Survival Analysis 5

Presenter: Federico Rotolo

When: Friday, July 15, 2016      Time: 9:00 AM - 10:30 AM

Room: Salon A Carson Hall (Level 2)

Session Synopsis:

Evaluation of failure time surrogate endpoints in individual patient data meta-analyses of randomized clinical trials. A Poisson approach

In clinical trials, surrogate endpoints are often used instead of well-established clinical endpoints for practical convenience: they are usually cheaper, more rapid, or less invasive to measure. The meta-analytic approach to evaluation of surrogate endpoints [1] focuses on two on individual level surrogacy, as measured by R2indiv, and on trial level surrogacy, captured by R2trial. This approach was extended to the survival data case [2], with a first step using copulas to measure individual level surrogacy in terms of Kendall’s ? or Spearman’s ?, and a second step using a measurement-error-model regression to compute R2trial. Despite being the reference method for survival data today, this approach can suffer from convergence problems in typical applications, and inference for R2trial requires a high number of trials. We propose using a bivariate survival model with (i) an individual random effect shared between the two endpoints to assess individual level surrogacy (Kendall’s ?) and (ii) correlated treatment-by-trial interactions to assess R2trial. We consider an auxiliary Poisson mixed model [3,4] to jointly estimate the parameters of the model. We study the operating characteristics of the model by using a simulation study and we illustrate its application on an individual patient data meta-analysis including 4,069 patients from 20 randomized advanced gastric cancer trials [5]. In this meta-analysis, we used different models with increasingly complex structures of random effects. With individual frailties only, individual-level surrogacy was ? =0.44 (95% confidence interval: 0.43–0.45). With random treatment-trial interactions only, trial-level surrogacy was R2=0.54 (0.42–0.72). With both random effects and interactions, ?=0.45 (0.44–0.46) and R2=0.28 (0.09–1.0). In conclusion, the use of auxiliary Poisson mixed models represents a competitive approach to the evaluation of failure time surrogate endpoints in individual patient data meta-analyses of randomized clinical trials. [1] Buyse, Molenberghs, Burzykowski, Renard, Geys. Biostatistics 2000; 1:49–67 [2] Burzykowski, Molenberghs, Buyse, Geys, Renard. J R Stat Soc C-Appl 2001, 50:405–22 [3] Whitehead. J R Stat Soc C-Appl 1980, pages 268–75 [4] Ma, Krewski, Burnett. Biometrika 2003, 90:157–69 [5] Paoletti, Oba, Bang et al. J Nat Cancer Inst 2013, 105:1667–70