EM Algorithm for Estimating the Parameters of Weibull Competing Risk Model
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ABSTRACT:
SUBMITTER: Kayid M
PROVIDER: S-EPMC8553452 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.
| S-EPMC9041931 | biostudies-literature
Project description:Here, we consider time-to-event data where individuals can experience two or more types of events that are not distinguishable from one another without further confirmation, perhaps by laboratory test. The event type of primary interest can occur only once. The other types of events can recur. If the type of a portion of the events is identified, this forms a validation set. However, even if a random sample of events are tested, confirmations can be missing nonmonotonically, creating uncertainty about whether an individual is still at risk for the event of interest. For example, in a study to estimate efficacy of an influenza vaccine, an individual may experience a sequence of symptomatic respiratory illnesses caused by various pathogens over the season. Often only a limited number of these episodes are confirmed in the laboratory to be influenza-related or not. We propose two novel methods to estimate covariate effects in this survival setting, and subsequently vaccine efficacy. The first is a pathway expectation-maximization (EM) algorithm that takes into account all pathways of event types in an individual compatible with that individual's test outcomes. The pathway EM iteratively estimates baseline hazards that are used to weight possible event types. The second method is a non-iterative pathway piecewise validation method that does not estimate the baseline hazards. These methods are compared with a previous simpler method. Simulation studies suggest mean squared error is lower in the efficacy estimates when the baseline hazards are estimated, especially at higher hazard rates. We use the pathway EM-algorithm to reevaluate the efficacy of a trivalent live-attenuated influenza vaccine during the 2003-2004 influenza season in Temple-Belton, Texas, and compare our results with a previously published analysis.
| S-EPMC4209209 | biostudies-literature
Project description:BackgroundRisk of encapsulating peritoneal sclerosis (EPS) is strongly associated with the duration of peritoneal dialysis (PD), such that patients who have been on PD for some time may consider elective transfer to haemodialysis to mitigate the risk of EPS. There is a need to determine this risk to better inform clinical decision making, but previous studies have not allowed for the competing risk of death.MethodsThis study included new adult PD patients in Australia and New Zealand (ANZ; 1990-2010) or Scotland (2000-08) followed until 2012. Age, time on PD, primary renal disease, gender, data set and diabetic status were evaluated as predictors at the start of PD, then at 3 and 5 years after starting PD using flexible parametric competing risks models.ResultsIn 17 396 patients (16 162 ANZ, 1234 Scotland), EPS was observed in 99 (0.57%) patients, less frequently in ANZ patients (n = 65; 0.4%) than in Scottish patients (n = 34; 2.8%). The estimated risk of EPS was much lower when the competing risk of death was taken into account (1 Kaplan-Meier = 0.0126, cumulative incidence function = 0.0054). Strong predictors of EPS included age, primary renal disease and time on PD. The risk of EPS was reasonably discriminated at the start of PD (C-statistic = 0.74-0.79) and this improved at 3 and 5 years after starting PD (C-statistic = 0.81-0.92).ConclusionsEPS risk estimates are lower when calculated using competing risk of death analyses. A patient's estimated risk of EPS is country-specific and can be predicted using age, primary renal disease and duration of PD.
| S-EPMC6735880 | biostudies-literature
Project description:In this paper, empirical data are used to estimate the parameters of a sociohydrological flood risk model. The proposed model, which describes the interactions between floods, settlement density, awareness, preparedness, and flood loss, is based on the literature. Data for the case study of Dresden, Germany, over a period of 200 years, are used to estimate the model parameters through Bayesian inference. The credibility bounds of their estimates are small, even though the data are rather uncertain. A sensitivity analysis is performed to examine the value of the different data sources in estimating the model parameters. In general, the estimated parameters are less biased when using data at the end of the modeled period. Data about flood awareness are the most important to correctly estimate the parameters of this model and to correctly model the system dynamics. Using more data for other variables cannot compensate for the absence of awareness data. More generally, the absence of data mostly affects the estimation of the parameters that are directly related to the variable for which data are missing. This paper demonstrates that combining sociohydrological modeling and empirical data gives additional insights into the sociohydrological system, such as quantifying the forgetfulness of the society, which would otherwise not be easily achieved by sociohydrological models without data or by standard statistical analysis of empirical data.
| S-EPMC6472491 | biostudies-literature
Project description:In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured covariates. Instrumental variable methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. On the basis of a semiparametric additive hazard model for the subdistribution hazard, we propose an instrumental variable estimator to yield consistent estimation of efficacy in the presence of unmeasured confoundings for competing risk settings. We derived the asymptotic properties for the proposed estimator. The estimator is shown to be well performed under finite sample size according to simulation results. We applied our method to a real transplant data example and showed that the unmeasured confoundings lead to significant bias in the estimation of the effect (about 50% attenuated). Copyright © 2017 John Wiley & Sons, Ltd.
| S-EPMC5479873 | biostudies-literature
Project description:PurposeAccurate risk assessment is necessary for decision-making around breast cancer prevention. We aimed to develop a breast cancer prediction model for postmenopausal women that would take into account their individualized competing risk of non-breast cancer death.MethodsWe included 73,066 women who completed the 2004 Nurses' Health Study (NHS) questionnaire (all ≥57 years) and followed participants until May 2014. We considered 17 breast cancer risk factors (health behaviors, demographics, family history, reproductive factors) and 7 risk factors for non-breast cancer death (comorbidities, functional dependency) and mammography use. We used competing risk regression to identify factors independently associated with breast cancer. We validated the final model by examining calibration (expected-to-observed ratio of breast cancer incidence, E/O) and discrimination (c-statistic) using 74,887 subjects from the Women's Health Initiative Extension Study (WHI-ES; all were ≥55 years and followed for 5 years).ResultsWithin 5 years, 1.8 % of NHS participants were diagnosed with breast cancer (vs. 2.0 % in WHI-ES, p = 0.02), and 6.6 % experienced non-breast cancer death (vs. 5.2 % in WHI-ES, p < 0.001). Using a model selection procedure which incorporated the Akaike Information Criterion, c-statistic, statistical significance, and clinical judgement, our final model included 9 breast cancer risk factors, 5 comorbidities, functional dependency, and mammography use. The model's c-statistic was 0.61 (95 % CI [0.60-0.63]) in NHS and 0.57 (0.55-0.58) in WHI-ES. On average, our model under predicted breast cancer in WHI-ES (E/O 0.92 [0.88-0.97]).ConclusionsWe developed a novel prediction model that factors in postmenopausal women's individualized competing risks of non-breast cancer death when estimating breast cancer risk.
| S-EPMC5093031 | biostudies-literature
Project description:The four-parameter logistic (4PL) model has recently attracted much interest in educational testing and psychological measurement. This paper develops a new Gibbs-slice sampling algorithm for estimating the 4PL model parameters in a fully Bayesian framework. Here, the Gibbs algorithm is employed to improve the sampling efficiency by using the conjugate prior distributions in updating asymptote parameters. A slice sampling algorithm is used to update the 2PL model parameters, which overcomes the dependence of the Metropolis–Hastings algorithm on the proposal distribution (tuning parameters). In fact, the Gibbs-slice sampling algorithm not only improves the accuracy of parameter estimation, but also enhances sampling efficiency. Simulation studies are conducted to show the good performance of the proposed Gibbs-slice sampling algorithm and to investigate the impact of different choices of prior distribution on the accuracy of parameter estimation. Based on Markov chain Monte Carlo samples from the posterior distributions, the deviance information criterion and the logarithm of the pseudomarginal likelihood are considered to assess the model fittings. Moreover, a detailed analysis of PISA data is carried out to illustrate the proposed methodology.
| S-EPMC7530206 | biostudies-literature
Project description:BackgroundAtomic Solvation Parameters (ASP) model has been proven to be a very successful method of calculating the binding free energy of protein complexes. This suggests that incorporating it into docking algorithms should improve the accuracy of prediction. In this paper we propose an FFT-based algorithm to calculate ASP scores of protein complexes and develop an ASP-based protein-protein docking method (ASPDock).ResultsThe ASPDock is first tested on the 21 complexes whose binding free energies have been determined experimentally. The results show that the calculated ASP scores have stronger correlation (r ≈ 0.69) with the binding free energies than the pure shape complementarity scores (r ≈ 0.48). The ASPDock is further tested on a large dataset, the benchmark 3.0, which contain 124 complexes and also shows better performance than pure shape complementarity method in docking prediction. Comparisons with other state-of-the-art docking algorithms showed that ASP score indeed gives higher success rate than the pure shape complementarity score of FTDock but lower success rate than Zdock3.0. We also developed a softly restricting method to add the information of predicted binding sites into our docking algorithm. The ASP-based docking method performed well in CAPRI rounds 18 and 19.ConclusionsASP may be more accurate and physical than the pure shape complementarity in describing the feature of protein docking.
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Project description:In this paper, we consider two well-known parametric long-term survival models, namely, the Bernoulli cure rate model and the promotion time (or Poisson) cure rate model. Assuming the long-term survival probability to depend on a set of risk factors, the main contribution is in the development of the stochastic expectation maximization (SEM) algorithm to determine the maximum likelihood estimates of the model parameters. We carry out a detailed simulation study to demonstrate the performance of the proposed SEM algorithm. For this purpose, we assume the lifetimes due to each competing cause to follow a two-parameter generalized exponential distribution. We also compare the results obtained from the SEM algorithm with those obtained from the well-known expectation maximization (EM) algorithm. Furthermore, we investigate a simplified estimation procedure for both SEM and EM algorithms that allow the objective function to be maximized to split into simpler functions with lower dimensions with respect to model parameters. Moreover, we present examples where the EM algorithm fails to converge but the SEM algorithm still works. For illustrative purposes, we analyze a breast cancer survival data. Finally, we use a graphical method to assess the goodness-of-fit of the model with generalized exponential lifetimes.
| S-EPMC9041914 | biostudies-literature
Project description:Accurate HPV genotyping is crucial in facilitating epidemiology studies, vaccine trials, and HPV-related cancer research. Contemporary HPV genotyping assays only detect < 25% of all known HPV genotypes and are not accurate for low-risk or mixed HPV genotypes. Current genomic HPV genotyping algorithms use a simple read-alignment and filtering strategy that has difficulty handling repeats and homology sequences. Therefore, we have developed an optimized expectation-maximization algorithm, designated HPV-EM, to address the ambiguities caused by repetitive sequencing reads. HPV-EM achieved 97-100% accuracy when benchmarked using cell line data and TCGA cervical cancer data. We also validated HPV-EM using DNA tiling data on an institutional cervical cancer cohort (96.5% accuracy). Using HPV-EM, we demonstrated HPV genotypic differences in recurrence and patient outcomes in cervical and head and neck cancers.
| S-EPMC7459114 | biostudies-literature