Conditional Regression Analysis for Recurrence Time Data

Few methods are currently available for group sequential analysis of recurrent events data subject to a terminal event in the clinical trial setting. This research helps fill this gap by developing a completely nonparametric group sequential monitoring procedure for use with the two-sample Tayob and Murray statistic. Advantages of the Tayob and Murray statistic include high power to detect treatment differences when there is correlation between recurrent event times or between recurrent and terminal events in an individual. This statistic does not suffer bias from dependent censoring, regardless of the correlation between event times in an individual. This manuscript briefly reviews the Tayob and Murray statistic, develops and describes how to use methods for its group sequential analysis, and through simulation, compares its operating characteristics with those of Cook and Lawless, which is currently in use as the only available nonparametric method for group sequential analysis of recurrent event data. The merits of our proposed approach are most clearly demonstrated when gap times between recurrent events are correlated; when gap times between events are independent, the Cook and Lawless method is difficult to beat. Simulations demonstrate that as correlation between recurrent event times grows, the reduction in power using the Cook and Lawless approach is substantial when compared to our method. Finally, we use our method to analyze recurrent acute exacerbation outcomes from the azithromycin in chronic obstructive pulmonary disease trial.

Panel count data is common in cancer screening. In the context of colorectal cancer screening, our work focuses on the prediction of the probability of advanced adenoma conditional on patient-level risk factors and/or event history. We implement the joint frailty model proposed by Huang et al. which involves a non-stationary Poisson process for recurrent adenoma events and informative screening time using semi-parametric Cox models correlated by a latent frailty variable, where coefficients and baseline intensity functions are estimated by estimating equations. Subject-specific frailty value is estimated by the borrow-strength method. In addition, marginal models for the adenoma and screening events are also applicable when average covariate effects on the population level are of interest. Predictions based on the marginal model and predictions based on the frailty models for patients with or without a screening history are compared. When a patient's screening history is available and sufficient adenoma events are observed, the predictions based on the frailty model with estimated subject-specific frailty are superior. However, in the cases of early censoring when adenoma events are not observed for most patients and screening history is not available, the prediction based on the marginal model has better performance. Furthermore, for patients' future screening, the individualized screening intervals derived from the dynamic predictions of advanced adenoma risks will detect adenoma events earlier with shorter lag time between the adenoma state transition and the screening compared to the current practice of regular screening intervals.

ABSTRACTThe assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

Patients with pancreatic cancer (PC) have poor prognosis and a high incidence of recurrence. Since further treatment is applicable for specific recurrent events, it is important to predict recurrence patterns after surgery. This study aimed to identify and predict early and late recurrence patterns of PC using a histology-based machine learning model. Patients who underwent upfront curative surgery for PC between 2001 and 2014 were included. The timing of recurrence and prognosis of each first recurrence site were examined. A histology-based supervised machine learning method, which combined convolutional neural networks and random forest, was used to predict the recurrence and respective sites of metastasis. Accuracy was evaluated using area under the receiver operating characteristic curve (AUC). In total, 524 patients were included. Recurrence in the liver accounted for 47.8% of all recurrence events in the first year after surgery. Meanwhile, recurrence in the lung occurred later and could become apparent more than 5 years post-surgery, with indications for further surgery. In terms of substantial distant organ metastases, liver and lung metastases were identified as representative early and late recurrence events. The predictive AUCs of the machine learning model for training and test data were 1.000 and 0.861, respectively, and for predicting nonrecurrence were 1.000 for both. We identified the liver and lung as early and late recurrence sites, which could be distinguished with high probability using a machine learning model. Prediction of recurrence sites using this model may be useful for further treatment of patients with PC.

Recurrent event data are frequently encountered in long-term follow-up studies. In many applications, the gap times between two successive recurrent events are natural outcomes of interest. Investigation on patterns of associations among recurrent gap times within subjects is an important inferential issue. In this paper, we introduce flexible functions of previous gap times to create a class of summary measures of serial associations for a sequence of recurrent gap times through Kendall's tau. Such a general class of serial association measures provides a useful tool to quantify the predictive abilities of event history with different aspects. Non-parametric estimators of the proposed measures of serial associations are developed by generalizing the existing estimator of Kendall's tau for two serial gap times, in which inverse probability of censoring weights is used to overcome the induced dependent censoring. Various tests are further constructed for testing the constancy of serial associations over different events. Our method is applied to Denmark schizophrenia data and the results show that association structures are different for distinct ages of onset of schizophrenia.

Introduction: Recurrent event data are common in many longitudinal studies. Often, a terminating event such as death can be correlated with the recurrent event process. A shared frailty model applied to account for the association between recurrent and terminal events. In some situations, a fraction of subjects experience neither recurrent events nor death; these subjects are cured.
 Methods: In this paper, we discussed the Bayesian approach of a joint frailty model for recurrent and terminal events in the presence of cure fraction. We compared estimates of parameters in the Frequentist and Bayesian approaches via simulation studies in various sample sizes; we applied the joint frailty model in the presence of cure fraction with Frequentist and Bayesian approaches for breast cancer.
 Results: In small sample size Bayesian approach compared to Frequentist approach had a smaller standard error and mean square error, and the coverage probabilities close to nominal level of 95%. Also, in Bayesian approach, the sampling means of the estimated standard errors were close to the empirical standard error.
 Conclusion: The simulation results suggested that when sample size was small, the use of Bayesian joint frailty model in the presence of cure fraction led to more efficiency in parameter estimation and statistical inference.

Recurrent events data refers to the observation of individuals, which contains the recurrent event time of interest. In this paper, we focus on the statistical analysis of recurrent event, and present a composite model based on the proportional intensity function and additive hazard function, and then prove the consistency and asymptotic properties of the estimation under certain regularity conditions.

For most continuous time models formulated in finance, there is no closed form for the likelihood function and estimation of the parameters on the basis of discrete data will be based on an approximation rather than an exact discretization. For example, the Euler method introduces discretization bias because it ignores the internal dynamics that can be excessively erratic. We view the approximation as a difference equation and note that the solution of the continuous time model does not satisfy this difference equation. The effectiveness of the approximation will depend on the rate at which the underlying process is sampled. We investigate how much it matters: can we get significantly different estimates of the same structural parameter when we use say hourly data as compared with using monthly data under given discretization? If yes, then that discretization when applied to a data set in hand, as is done in practice, cannot be said to give robust results. We compare numerically the application of methods by Yu and Phillips (2001), Shoji and Ozaki (1998) and Ait-Sahalia (2002) in the maximum likelihood estimation of the unrestricted interest rate model proposed by Chan et al. (1992). We find that reducing the sampling rate yield large biases in the estimation of the parameters. The AitSahalia method is shown to offer a good approximation and has the advantage of reducing some of the temporal aggregation bias.

This paper considers the analysis of a repeat event outcome in clinical trials of chronic diseases in the context of dependent censoring (e.g. mortality). It has particular application in the context of recurrent heart failure hospitalisations in trials of heart failure. Semi‐parametric joint frailty models (JFMs) simultaneously analyse recurrent heart failure hospitalisations and time to cardiovascular death, estimating distinct hazard ratios whilst individual‐specific latent variables induce associations between the two processes. A simulation study was carried out to assess the suitability of the JFM versus marginal analyses of recurrent events and cardiovascular death using standard methods. Hazard ratios were consistently overestimated when marginal models were used, whilst the JFM produced good, well‐estimated results. An application to the Candesartan in Heart failure: Assessment of Reduction in Mortality and morbidity programme was considered. The JFM gave unbiased estimates of treatment effects in the presence of dependent censoring. We advocate the use of the JFM for future trials that consider recurrent events as the primary outcome. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

111 Background: Local prostate radiotherapy (LPRT) is associated with improved overall survival in patients with low metastatic burden (MB) and is now standard of care. However, the role of LPRT in reducing symptomatic local events (SLE) in metastatic prostate cancer (MPC) remains unclear and requires long-term follow-up. The purpose of this study was two-fold: i) identify the risk factors associated with SLE, and ii) evaluate the association between LPRT and SLE in MPC. Methods: We conducted a retrospective, population-based cohort study of patients diagnosed with initial MPC between 2005 and 2016. Patients were identified through the Alberta Cancer Registry and patient, tumour, and treatment characteristics were collected by chart review. Data were linked to physician billing claims between 2004 and 2017 for diagnostic or therapeutic procedures potentially related to genitourinary (GU) and gastrointestinal (GI) SLE including percutaneous nephrostomy (PCN) and ureteric stent insertion (USI), cystoscopy, TURP, TURBT, colonoscopy and proctosigmoidoscopy. Both Andersen-Gill recurrent event and multivariable Cox regression time to first event analyses were conducted to evaluate the effect of LPRT on the occurrence of these procedures. Patients who underwent radical prostatectomy were excluded. LPRT was defined as 40 Gy or higher total dose to the prostate within one year of diagnosis. Patients with a SLE occurring after diagnosis but prior to LPRT were allocated to the control group. MB was defined as per STAMPEDE. Covariates for both models included MB, age at diagnosis, PSA at diagnosis, clinical T- and N-stage, and Gleason score (GS). Results: Of a total cohort of 1363 patients, 745 (54.7%) had high MB and 450 (33%) had low MB. Fifty-four (4%) received LPRT, of which 14.8% had high MB. Of those receiving LPRT, median PSA was 9.4, 79.6% had GS of 8-10, and 59.3% had T3-T4 disease. One or more SLE were observed in 43.5% and 37% of the control and LPRT groups, respectively. Among those with SLE, the median SLE frequency was 2 (interquartile range [IQR], 2-5) and 1 (IQR, 1-2.3) for the control and LPRT groups, respectively. On recurrent event analysis, LPRT was associated with lower risk of composite GU SLE (HR 0.34, 95% CI 0.17-0.67; p = 0.002), PCN and USI (HR 0.20, 95% CI 0.05-0.84; p = 0.027) and cystoscopy (HR 0.38, 95% CI 0.15-0.96; p = 0.041). Risk factors for GU SLE were T4 disease, GS of 8-10 and unknown GS. Risk factors for PCN and USI were T3, TX and N1 disease, GS of 8-10 and unknown GS. On time to first event analysis, there were no statistically significant differences for all outcomes between the control and LPRT groups. MB was not a risk factor for SLE in both analyses. Conclusions: LPRT was associated with lower risk for recurrent GU SLE, PCN and USI, and cystoscopy. The associated benefit in SLE reduction with LPRT warrants further study to determine if this effect is modified by MB and whether there may be a role for LPRT in patients with high MB.

We adopt a lognormal distribution for earthquake interval times, and we use a locally determined rather than a generic coefficient of variation, to estimate the probability of occurrence of characteristic earthquakes. We extend previous methods in two ways. First, we account for the aseismic period since the last event (the “seismic drought”) in updating the parameter estimates. Second, in calculating the earthquake probability we allow for uncertainties in the mean recurrence time and its variance by averaging over their likelihood. Both extensions can strongly influence the calculated earthquake probabilities, especially for long droughts in regions with few documented earthquakes. As time passes, the recurrence time and variance estimates increase if no additional events occur, leading eventually to an affirmative answer to the question in the title. The earthquake risk estimate begins to drop when the drought exceeds the estimated recurrence time. For the Parkfield area of California, the probability of a magnitude 6 event in the next 5 years is about 34 per cent, much lower than previous estimates. Furthermore, the estimated 5-year probability will decrease with every uneventful year after 1988. For the Coachella Valley segment of the San Andreas Fault, the uncertainties are large, and we estimate the probability of a large event in the next 30 years to be 9 per cent, again much smaller than previous estimates. On the Mojave (Pallett Creek) segment the catalog includes 10 events, and the present drought is just approaching the recurrence interval, so the estimated risk is revised very little by our methods.

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.

In today’s modern wide-field galaxy surveys, there is the necessity for parametric surface brightness decomposition codes characterised by accuracy, small degree of user intervention, and high degree of parallelisation. We try to address this necessity by introducing MORPHOFIT, a highly parallelisable python package for the estimate of galaxy structural parameters. The package makes use of wide-spread and reliable codes, namely, SEXTRACTOR and GALFIT. It has been optimised and tested in both low-density and crowded environments, where blending and diffuse light makes the structural parameters estimate particularly challenging. MORPHOFIT allows the user to fit multiple surface brightness components to each individual galaxy, among those currently implemented in the code. Using simulated images of single Sérsic and bulge plus disk galaxy light profiles with different bulge-to-total luminosity (B/T) ratios, we show that MORPHOFIT is able to recover the input structural parameters of the simulated galaxies with good accuracy. We also compare its estimates against existing literature studies, finding consistency within the errors. We use the package in a companion paper to measure the structural parameters of cluster galaxies in order to study the wavelength dependence of the Kormendy relation of early-type galaxies. The package is available on github1 and on the Pypi server2.

A new time-domain method is suggested in this paper for simultaneous identification of the structural parameters and the time history of the input excitation using output-only measurements. The proposed method is based on an iterative identification procedure consisting of the least-squares identification technique and a modification process between each iterative step. The modification process is introduced to convert the spatial information of the external excitation into mathematical conditions. First, the unknown force vector is conjectured through the equation of motion using the initial guess of the structural parameters and the measured structural responses. The estimated input force vector is then modified to force it comply with the spatial distribution of the external excitations. The modified input force vector is further used to provide new estimation of structural parameters. Repeat the aforementioned procedure until the structural parameters satisfy the preset convergence criterion. Numerical examples as shear building and truss bridge model are employed to evaluate the feasibility of the proposed method. In the numerical examples, typical scenario of complete and noise-free as well as incomplete and noise-contaminated output measurements are considered. The results demonstrate that the proposed method can accurately identify both the structural parameters and the input time history for the cases that the structural responses are not polluted or slightly contaminated by measurement noise.

The structural parameters, like the inclination, i and the position angle of the line of nodes (PA_lon) of the disk of the Large Magellanic Cloud (LMC) are estimated using the JH photometric data of red clump stars from the Infrared Survey Facility - Magellanic Cloud Point Source Catalog (IRSF-MCPSC). The observed LMC region is divided into several sub-regions and stars in each region are cross identified with the optically identified red clump stars to obtain the near infrared magnitudes. The peak values of H magnitude and (J-H) colour of the observed red clump distribution are obtained by fitting a profile to the distributions and also by taking the average value of magnitude and colour of the red clump stars in the bin with largest number. Then the dereddened peak H0 magnitude of the red clump stars in each sub-region is obtained. The RA, Dec and relative distance from the center of each sub-region are converted into x, y & z Cartesian coordinates. A weighted least square plane fitting method is applied to this x,y,z data to estimate the structural parameters of the LMC disk. A reddening map based on (J-H) colour of the RC stars is presented. When the peaks of the red clump distribution were identified by averaging, an inclination of 25.7 +/- 1.6 and PA_lon = 141.5 +/- 4.5 were obtained. We estimate a distance modulus of 18.47 +/- 0.1 mag to the LMC. Extra-planar features which are in front as well as behind the fitted plane are identified which match with the optically identified extra-planar features. The bar of the LMC is found to be part of the disk within 500 pc. The estimates of the structural parameters are found to be independent of the photometric bands used for the analysis. We find that the inner disk, within 3.0, is less inclined and has larger value of PA_lon when compared to the outer disk.