PICBayes: Bayesian proportional hazards models for partly interval-censored data

Interval-censored failure time data commonly occur in many periodic follow-up studies such as epidemiological experiments, medical studies and clinical trials. By intervalcensored data, we usually mean that one cannot observe the failure time of interest and instead we know that it belongs to a time interval. Correlated failure time data commonly occur when there are multiple events on one individual or when the study subjects are clustered into some small groups. In this situation, study subjects from same subgroup or the failure events from same individuals are usually regarded as dependent, but the subjects in different clusters or failure events from different individuals are assumed to be independent. Besides the correlation between the cluster, sometimes the cluster size may be informative or carry some information about the failure time of interest. Cured subgroup is another interesting topic that has been discussed by many authors. For this situation, unlike the assumptions in traditional survival model that all study subjects would experience the failure event of interest eventually if the follow-up time is long enough, some subjects may never experience or not be susceptible to the event. Such subjects are treated as cured and assumed to belong to a cured subgroup in a study population. The research in this dissertation focuses on regression analysis of correlated intervalcensored data with a cured subgroup via different approaches based on different data structures. In the first part of this dissertation, we discuss clustered interval-censored data with a cured subgroup and informative cluster size. To address this, we present a within-cluster resampling method and in the approach, the multiple imputation procedure is applied for estimation of unknown parameters. To assess the performance of the proposed method, a simulation study is conducted and suggests that it works well in practical situations. Also, the method is applied to a set of real data that motivated this study. In the second part of this dissertation, we consider the clustered interval-censored data with a cured subgroup via a non-mixture cure model. We present a maximum likelihood estimation procedure under the semiparametric transformation nonmixture cure model. To estimate the unknown parameters, an expectation maximization (EM) algorithm based on an augmentation of Poisson variable is developed. To assess the performance of the proposed method, a simulation study is conducted and suggests that it works well in practical situations. An application to a study conducted by the National Aeronautics and Space Administration that motivated this study is also provided. In the third part of this dissertation, we investigate the bivariate interval-censored data with a cured subgroup. A sieve maximum likelihood estimation procedure under the semiparametric transformation non-mixture cure model based on Bernstein polynomials is presented. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that the proposed model works well. Also, a real data application from the study of AIDS Clinical Trial Group 181 is provided.

Interval-censored data arise frequently in medical studies of diseases that require periodic examinations for symptoms of interest, such as disease-free survival (DFS). This paper provides an introduction to the R package ICBayes which implements a set of programs for analyzing case 1 interval-censored data and case 2 interval-censored data under Bayesian semiparametric framework. The main function ICBayes fits commonly-used survival regression models: proportional hazards, proportional odds, and probit. A simulation study is conducted to compare the performance of the package with two R packages that fit Bayesian proportional hazards, proportional odds, and accelerated failure time models. The use of the package is illustrated through analyzing a case 2 interval-censored breast cosmesis data and a case 1 interval-censored animal tumorigenicity data.

Graduation is one of the assessment criteria in the college accreditation process. Students who graduate on time will assist in the assessment of college accreditation. This study aims to determine the distribution that best fits student graduation data and determine the best model to analyze the factors that determine student graduation from IPB University. This study presents some parametric models in survival analysis, specifically, the accelerated failure time (AFT) model and the proportional hazard (PH) model. The objective of this research is to compare the performance of PH model and the AFT models in analyzing the significant factors affecting the student graduation at the IPB University. Based on the study's results, the distribution according to student graduation data is the Burr XII distribution, and the best model using the AIC criteria is the PH Burr XII model. The factors that influence the graduation of IPB University students are gender, faculty, GPA, regional origin, and school status.

This study aims to determine the estimation of interval-censored data with a special distribution, namely the binomial distribution. This research is using quantitative methods, the steps are estimating parameters on the interval-censored binomial distribution using the Maximum Likelihood Estimation method. The second step shows the properties of the estimator on the interval-censored binomial distribution. The last is to determine the parameter estimation of interval-censored data from the binomial distribution in survival analysis and provide an example of research containing interval-censored observations which will then be used as a case study. The results showed that the estimator is a sufficient statistic, meaning that it is unbiased. The case study was conducted using interval-censored data regarding the study of ninety-four breast cancer patients to see which group survived longer (survival value) of the two treatments, namely patients who underwent radiotherapy alone and patients who underwent radiotherapy followed by adjuvant chemotherapy.

A common feature of many failure time data in epidemiological studies or reliability studies is that they are simultaneously censored and truncated. Additionally, survival or reliability data could be truncated. There are also various types of truncation. For example right-truncated data occur in registers. An acquired immune deficiency syndrome (AIDS) register only contains AIDS cases which have already been reported, which generates right-truncated samples of induction times. The chapter defines a marginal non-parametric likelihood for interval-censored and interval-truncated data first introduced in B. W. Turnbull and later studied by A. Alioum and D. Commenges and C. Huber and F. Vonta in connection also to parametric and semi-parametric models. It formulates a complete non-parametric likelihood for interval-censored and interval-truncated data. The chapter discusses consistency in Hellinger distance of the density of survival or reliability under regularity conditions. It considers as the total interval of observation time the interval.

Background: Evaluating the risk of Alzheimer’s disease (AD) in cognitively normal (CN) and patients with mild cognitive impairment (MCI) is extremely important. While MCI-to-AD progression risk has been studied extensively, few studies estimate CN-to-MCI conversion risk. The Cox proportional hazards (PH), a widely used survival analysis model, assumes a linear predictor-risk relationship. Generalizing the PH model to more complex predictor-risk relationships may increase risk estimation accuracy. Objective: The aim of this study was to develop a PH model using an Xgboost regressor, based on demographic, genetic, neuropsychiatric, and neuroimaging predictors to estimate risk of AD in patients with MCI, and the risk of MCI in CN subjects. Methods: We replaced the Cox PH linear model with an Xgboost regressor to capture complex interactions between predictors, and non-linear predictor-risk associations. We endeavored to limit model inputs to noninvasive and more widely available predictors in order to facilitate future applicability in a wider setting. Results: In MCI-to-AD (n = 882), the Xgboost model achieved a concordance index (C-index) of 84.5%. When the model was used for MCI risk prediction in CN (n = 100) individuals, the C-index was 73.3%. In both applications, the C-index was statistically significantly higher in the Xgboost in comparison to the Cox PH model. Conclusion: Using non-linear regressors such as Xgboost improves AD dementia risk assessment in CN and MCI. It is possible to achieve reasonable risk stratification using predictors that are relatively low-cost in terms of time, invasiveness, and availability. Future strategies for improving AD dementia risk estimation are discussed.

This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.

Preface. On the Entropies and Mutual Information of Some Bivariate Continuous Distributions Used in Reliability M. Ahsanullah, M. Habibullah. Initial Conditions Problem in Event History Analysis: An Indirect Inference Procedure M.Y. An. Analysis of Survival Data Under Competing Risks with Missing Cause of Death Information: Application and Implications for Study Design J.W. Andersen, et al. Conditional Proportional Hazards Models B.C. Arnold, Y.H. Kim. A Comparison of Conditional and Unconditional Inference Relating to Log-Gamma Distribution N. Balakrishnan, P.S. Chan. Universal Formulas for Treatment Effects from Noncompliance Data A.A. Balke, J. Pearl. Fundational Issues Concerning the Analysis of Censored Data R.E. Barlow, P. Tsai. Burn-in at the Component and System Level H.W. Block, et al. Identificationof Dependent Competing Risks Models K. Carling, T. Jacobson. Reliability Modelling for Optical Amplified Communication Systems M. Chown, G.A. Whitmore. A Parametric Approach to Measurement Errors in Receiver Operating Characteristic Studies M. Coffin, S. Sukhatme. Models for Degradation Processes and Event Times Based on Gaussian Processes K. Doksum, S.-L. Normand. A Non-Parametric Two-Sample Survival Test Based on a Single Occupancy Fermi-Dirac Model for the Discrete Range Distribution J.T. Efird, F. Pardo. Probability Approximations and Inequalities for Sequential Tests J. Glaz, J.R. Kenyon. Cure Mixture Models in Breast Cancer Survival Studies N.H. Gordon. A General Approach to Derive Chi-Square Type of Goodness-of-Fit Tests for Lifetime Data S. Hawala, J.-L. Wang. Prediction in Survival Analysis: Model or Medic? R. Henderson, M. Jones. Dynamic Reliability Models M. Hollander, E.A. Pena. Generalizations of Current Status Data with Applications N.P. Jewell, M. van der Laan. Trend Analysis of Multiple Counting Processes T. Kamakura. Historical Controls and Model Survival Analysis N. Keiding. A Random Effects Model for Multivariate Life Data A.C. Kimber. Statistical Challenges in Comparing Chemotherapy and Bone Marrow Transplantation as a Treatment for Leukemia J.P. Klein, M.-J. Zhang. Maximum Likelihood Estimation and the Multivariate Bernoulli Distribution: An Application to Reliability P.H. Kvam. Intermediate Clinical Events, Surrogate Markers and Survival M. Lefkopoulou, M. Zelen. A Semiparametric Bootstrap for Proportional Hazards Models T.M. Loughin, K.J. Koehler. Application of Cox Regression with a Change Point in Clinical Studies X. Luo, et al. Burn-in with Age Replacement A.W. Marshall. Fitting Cox's Proportional Hazards Model Using Grouped Survival Data I.W. McKeague, M.-J. Zhang. Statistical Methods for Dependent Competing Risks M.L. Moeschberger, J.P. Klein. Orthogonal Functions of Inverse Gaussian Disbrituions R. Nishii. Statistical Models for Quality of Life Measures Y. Palesch, A.J. Groos. Nonparametric Estimation of Regression Parameters from Censored Data with Two Discrete Covariates M.H. Rahbar. Locally Efficient Median Regressionwith Random Censoring and Surrogate Markers J.M. Robins. Survival Models for Heterogeneity Using the Non-Central Chi-Squared Distribution with Zero Degrees of Freedom C.S. Rocha. Efficiently Weighted Estimating Equations with Application to Proportional Excess Hazards P. Sasieni. Sequential Multi-Hypothesis Testing in Software Reliability J.S. Shieh, Y.L. Tong. Assessing Gamma Frailty Models for Clustered Failure Time Data J.H. Shih,

Several tests for comparing k groups of interval-censored data based on Turnbull's estimator of a survival function are compared by a Monte Carlo simulation study. The tests under consideration include the IWD test proposed by Petroni and Wolfe, the score test derived by Finkelstein, and a logrank type test suggested by Sun. With a large sample size and in a two-sample comparison, simulation results suggest that the IWD test is applicable for early and crossing hazard difference alternatives, whereas Finkelstein's score test, Sun's test and the logrank test are slightly more powerful than the IWD tests under late hazard difference alternatives. The IWD test is designed for the two-sample testing problem. With a large sample size and in a k-sample comparison, Finkelstein's score test is slightly better than the other tests under a proportional hazards model, while Sun's test and the logrank test are slightly better than the score test under early and crossing hazard difference alternatives. However, none of the test statistics is uniformly better than the others for the alternatives considered in this paper with both non-overlapping and overlapping interval-censored data.

Clustered interval-censored failure time data occur when the failure times of interest are clustered into small groups and known only to lie in certain intervals. A number of methods have been proposed for regression analysis of clustered failure time data, but most of them apply only to clustered right-censored data. In this paper, a sieve estimation procedure is proposed for fitting a Cox frailty model to clustered interval-censored failure time data. In particular, a two-step algorithm for parameter estimation is developed and the asymptotic properties of the resulting sieve maximum likelihood estimators are established. The finite sample properties of the proposed estimators are investigated through a simulation study and the method is illustrated by the data arising from a lymphatic filariasis study.

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study.

Survival analysis methods make better use of temporal information, accommodate multiple levels of explanatory variables, and are meant to deal with interval-censored data. In a context of harvest modeling, this approach could improve some known limitations. In this study, we used data from a network of permanent plots in the province of Quebec, Canada, as a real-world case study. We tested the potential of survival analysis to predict plot-level harvest probabilities from plot- and regional-level variables. The approach also included random effects to account for spatial correlations. The results showed the potential of survival analysis to provide annual predictions of harvest occurrence. Both regional and time-varying variables, as well as spatial patterns, had important effects on the probability of a plot to be harvested. Respectively, reductions in the annual allowable cut volumes led to a decrease in the harvest probabilities. Greater harvest probabilities were associated with the broadleaved dynamics class and higher values of basal area. In contrast, they were decreased by stem density and slope classes. The spatial random effect resulted in an improvement of the model fit. Our plot-level model improved some limitations reported in previous studies by taking the effect of a time-varying regional variable into account.

ABSTRACTThis paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided.

Previous studies have established the role of phosphorylated form of insulin-like growth factor type 1 receptor (p-IGF1R) as a good candidate for tumor biomarker. The aims of this study were to investigate p-IGF1R expression status in gastric cancer (GC) specimens and to clarify its clinical significance. A total of 78 GC patients treated with radical resection were enrolled in this study. Immunohistochemistry was used to detect p-IGF1R and phosphatase and tensin homolog deleted on chromosome ten (PTEN) protein expression in paired tumor and adjacent normal tissues. Results showed a higher level of p-IGF1R protein expression in tumor tissues than that in normal tissues, and the rate of p-IGF1R protein high/moderate expression in GC and normal tissues was 52.6% (41/78) and 6.4% (5/78), respectively (p < 0.001). In contrast, PTEN protein expression was downregulated in GC, as compared with normal tissues (negative/low expression 49/78 vs. 8/78, p < 0.001). Moreover, PTEN protein downregulation was consistent with p-IGF1R upregulation. Overexpression of p-IGF1R protein was associated with lymph metastasis, clinical stage, and adverse 3-year progression-free survival (PFS). Survival analysis and Cox proportional hazards model revealed that p-IGF1R overexpression was an independent factor in predicting PFS for GC patients, apart from lymph metastasis. In conclusion, p-IGF1R is highly expressed in GC, which may be a novel biomarker to predict the clinical outcome of GC patients.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.