Parameters Of Mixture Model Research Articles

Inertial stochastic PALM and applications in machine learning

Inertial algorithms for minimizing nonsmooth and nonconvex functions as the inertial proximal alternating linearized minimization algorithm (iPALM) have demonstrated their superiority with respect to computation time over their non inertial variants. In many problems in imaging and machine learning, the objective functions have a special form involving huge data which encourage the application of stochastic algorithms. While algorithms based on stochastic gradient descent are still used in the majority of applications, recently also stochastic algorithms for minimizing nonsmooth and nonconvex functions were proposed. In this paper, we derive an inertial variant of a stochastic PALM algorithm with variance-reduced gradient estimator, called iSPALM, and prove linear convergence of the algorithm under certain assumptions. Our inertial approach can be seen as generalization of momentum methods widely used to speed up and stabilize optimization algorithms, in particular in machine learning, to nonsmooth problems. Numerical experiments for learning the weights of a so-called proximal neural network and the parameters of Student-t mixture models show that our new algorithm outperforms both stochastic PALM and its deterministic counterparts.

Some estimation methods for mixture of extreme value distributions with simulation and application in medicine

In recent years, statisticians have grown increasingly engaged in research of mixture models, particularly in the previous decade, without adequate consideration of challenge of estimating the parameters of mixture models from a frequentist perspective. Except for maximum likelihood estimation, this study addresses this vacuum by discussing the two other classical methods of estimation for mixture model. We commence by briefly describing the three frequentist approaches, namely maximum likelihood, ordinary, and weighted least squares, and then comparing them through extensive numerical simulations. The model’s applicability is illustrated by its application to simulated and real-world data, which yields promising results in terms of enhanced estimation.

An Improved Mixture Density Network Via Wasserstein Distance Based Adversarial Learning for Probabilistic Wind Speed Predictions

This paper develops a novel improved mixture density network via Wasserstein distance-based adversarial learning (WA-IMDN) for achieving more accurate probabilistic wind speed predictions (PWSP). The proposed method utilizes the historical supervisory control and data acquisition (SCADA) system data collected from multiple wind turbines (WTs) in different wind farms to predict the wind speed probability density function (PDF) of a targeted WT at the next timestamp. To better capture the fluctuation pattern of historical wind speed sequences and estimate parameters of the probability mixture model for approximating the wind speed PDF, an improved mixture density network (IMDN) is proposed. To address drawbacks of the traditional maximum likelihood estimation (MLE) on training the mixture density network, a Wasserstein distance (WD)-based adversarial learning is developed and the reparameterization trick is employed for the gradient delivery. The effectiveness of the proposed WA-IMDN is validated based on SCADA data (One dataset is publicly accessible) by benchmarking against a set of the commonly considered and recently reported PWSP methods, such as the mixture density network (MDN), maximum likelihood estimation (MLE) based mixture density attention network (MLE-IMDN), recent DMDNN and Improved Deep Mixture Density Network (IDMDN). Results demonstrate the superior performance of the proposed WA-IMDN on the PWSP. To demonstrate the repeatability of the presented research, we release our code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/IkeYang/WA-IMDN-</uri> .

Image Compression Based on Hybrid Domain Attention and Postprocessing Enhancement.

Deep learning-based image compression methods have made significant achievements recently, of which the two key components are the entropy model for latent representations and the encoder-decoder network. Both the inaccurate estimation of the entropy estimation model and the existence of information redundancy in latent representations lead to a reduction in the compression efficiency. To address these issues, the study suggests an image compression method based on a hybrid domain attention mechanism and postprocessing improvement. This study embeds hybrid domain attention modules as nonlinear transformers in both the main encoder-decoder network and the hyperprior network, aiming at constructing more compact latent features and hyperpriors and then model the latent features as parametric Gaussian-scale mixture models to obtain more precise entropy estimation. In addition, we propose a solution to the errors introduced by quantization in image compression by adding an inverse quantization module. On the decoding side, we also provide a postprocessing enhancement module to further increase image compression performance. The experimental results show that the peak signal-to-noise rate (PSNR) and multiscale structural similarity (MS-SSIM) of the proposed method are higher than those of traditional compression methods and advanced neural network-based methods.

Stochastic Variational Optimization of a Hierarchical Dirichlet Process Latent Beta-Liouville Topic Model

In topic models, collections are organized as documents where they arise as mixtures over latent clusters called topics. A topic is a distribution over the vocabulary. In large-scale applications, parametric or finite topic mixture models such as LDA (latent Dirichlet allocation) and its variants are very restrictive in performance due to their reduced hypothesis space. In this article, we address the problem related to model selection and sharing ability of topics across multiple documents in standard parametric topic models. We propose as an alternative a BNP (Bayesian nonparametric) topic model where the HDP (hierarchical Dirichlet process) prior models documents topic mixtures through their multinomials on infinite simplex. We, therefore, propose asymmetric BL (Beta-Liouville) as a diffuse base measure at the corpus level DP (Dirichlet process) over a measurable space. This step illustrates the highly heterogeneous structure in the set of all topics that describes the corpus probability measure. For consistency in posterior inference and predictive distributions, we efficiently characterize random probability measures whose limits are the global and local DPs to approximate the HDP from the stick-breaking formulation with the GEM (Griffiths-Engen-McCloskey) random variables. Due to the diffuse measure with the BL prior as conjugate to the count data distribution, we obtain an improved version of the standard HDP that is usually based on symmetric Dirichlet (Dir). In addition, to improve coordinate ascent framework while taking advantage of its deterministic nature, our model implements an online optimization method based on stochastic, at document level, variational inference to accommodate fast topic learning when processing large collections of text documents with natural gradient. The high value in the predictive likelihood per document obtained when compared to the performance of its competitors is also consistent with the robustness of our fully asymmetric BL-based HDP. While insuring the predictive accuracy of the model using the probability of the held-out documents, we also added a combination of metrics such as the topic coherence and topic diversity to improve the quality and interpretability of the topics discovered. We also compared the performance of our model using these metrics against the standard symmetric LDA. We show that online HDP-LBLA (Latent BL Allocation)’s performance is the asymptote for parametric topic models. The accuracy in the results (improved predictive distributions of the held out) is a product of the model’s ability to efficiently characterize dependency between documents (topic correlation) as now they can easily share topics, resulting in a much robust and realistic compression algorithm for information modeling.

A Mixture of Gamma-Gamma, Loglogistic-Gamma Distributions for the Analysis of Heterogenous Survival Data

Survival analysis deals with failure time data. The presence of censoring makes the application of the classical parametric and nonparametric methods of survival analysis inadequate and as such need’s modifications. Parametric mixture models are applied where a single classical model may not suffice. The parametric mixture needs to be made more robust to address the heterogeneity of survival data. This paper proposed a mixture of two distributions for the analysis of survival data, the models consist of Gamma-Gamma, and Loglogistic-Gamma distributions. Data was simulated to investigate the performance of the models, and used to estimate the maximum likelihood parameters of the models by employing Expectation Maximization (EM). Parameters of the models were estimated and were all close the postulated values. Simulations were repeated to test the consistency and stability of the models through mean square error (MSE) and root mean square error (RMSE), and were all found to be stable and consistent. Real data was applied to determine the best fit among the mixture models and classical distributions using information criteria. Mixture models were found to model the data and the mixture of two different distributions gives the best fit.

Heterogeneity in Survival with Immune Checkpoint Inhibitors and Its Implications for Survival Extrapolations: A Case Study in Advanced Melanoma.

BackgroundSurvival heterogeneity and limited trial follow-up present challenges for estimating lifetime benefits of oncology therapies. This study used CheckMate 067 (NCT01844505) extended follow-up data to assess the predictive accuracy of standard parametric and flexible models in estimating the long-term overall survival benefit of nivolumab plus ipilimumab (an immune checkpoint inhibitor combination) in advanced melanoma.MethodsSix sets of survival models (standard parametric, piecewise, cubic spline, mixture cure, parametric mixture, and landmark response models) were independently fitted to overall survival data for treatments in CheckMate 067 (nivolumab plus ipilimumab, nivolumab, and ipilimumab) using successive data cuts (28, 40, 52, and 60 mo). Standard parametric models allow survival extrapolation in the absence of a complex hazard. Piecewise and cubic spline models allow additional flexibility in fitting the hazard function. Mixture cure, parametric mixture, and landmark response models provide flexibility by explicitly incorporating survival heterogeneity. Sixty-month follow-up data, external ipilimumab data, and clinical expert opinion were used to evaluate model estimation accuracy. Lifetime survival projections were compared using a 5% discount rate.ResultsStandard parametric, piecewise, and cubic spline models underestimated overall survival at 60 mo for the 28-mo data cut. Compared with other models, mixture cure, parametric mixture, and landmark response models provided more accurate long-term overall survival estimates versus external data, higher mean survival benefit over 20 y for the 28-mo data cut, and more consistent 20-y mean overall survival estimates across data cuts.ConclusionThis case study demonstrates that survival models explicitly incorporating survival heterogeneity showed greater accuracy for early data cuts than standard parametric models did, consistent with similar immune checkpoint inhibitor survival validation studies in advanced melanoma. Research is required to assess generalizability to other tumors and disease stages.HighlightsGiven that short clinical trial follow-up periods and survival heterogeneity introduce uncertainty in the health technology assessment of oncology therapies, this study evaluated the suitability of conventional parametric survival modeling approaches as compared with more flexible models in the context of immune checkpoint inhibitors that have the potential to provide lasting survival benefits.This study used extended follow-up data from the phase III CheckMate 067 trial (NCT01844505) to assess the predictive accuracy of standard parametric models in comparison with more flexible methods for estimating the long-term survival benefit of the immune checkpoint inhibitor combination of nivolumab plus ipilimumab in advanced melanoma.Mixture cure, parametric mixture, and landmark response models provided more accurate estimates of long-term overall survival versus external data than other models tested.In this case study with immune checkpoint inhibitor therapies in advanced melanoma, extrapolation models that explicitly incorporate differences in cancer survival between observed or latent subgroups showed greater accuracy with both early and later data cuts than other approaches did.

Learning Diagonal Gaussian Mixture Models and Incomplete Tensor Decompositions

This paper studies how to learn parameters in diagonal Gaussian mixture models. The problem can be formulated as computing incomplete symmetric tensor decompositions. We use generating polynomials to compute incomplete symmetric tensor decompositions and approximations. Then the tensor approximation method is used to learn diagonal Gaussian mixture models. We also do the stability analysis. When the first and third order moments are sufficiently accurate, we show that the obtained parameters for the Gaussian mixture models are also highly accurate. Numerical experiments are also provided.

MCMC Sampling Estimation of Poisson-Dirichlet Process Mixture Models

In this article, we aim to estimate the parameters of Poisson-Dirichlet mixture model with multigroup data structure by empirical Bayes. The number of mixture components with Bayesian nonparametric process priors is not fixed in advance and it can grow with the increase of data. Empirical Bayes is the useful method to estimate the mixture components without information on them in advance. We give the procedure to construct smooth estimates of base distribution G 0 and estimates of the two parameters α , θ . The performances of estimations for parameters under multigroup data are better than those of the single-group data with the same total size of individuals in the perspectives of bias, standard deviations, and mean squared errors by numerical simulation. Also, we applied Poisson-Dirichlet mixture models to well-known real datasets.

Bayesian Analysis of Cancer Data Using a 4-Component Exponential Mixture Model.

Cancer is among the major public health problems as well as a burden for Pakistan. About 148,000 new patients are diagnosed with cancer each year, and almost 100,000 patients die due to this fatal disease. Lung, breast, liver, cervical, blood/bone marrow, and oral cancers are the most common cancers in Pakistan. Perhaps smoking, physical inactivity, infections, exposure to toxins, and unhealthy diet are the main factors responsible for the spread of cancer. We preferred a novel four-component mixture model under Bayesian estimation to estimate the average number of incidences and death of both genders in different age groups. For this purpose, we considered 28 different kinds of cancers diagnosed in recent years. Data of registered patients all over Pakistan in the year 2012 were taken from GLOBOCAN. All the patients were divided into 4 age groups and also split based on genders to be applied to the proposed mixture model. Bayesian analysis is performed on the data using a four-component exponential mixture model. Estimators for mixture model parameters are derived under Bayesian procedures using three different priors and two loss functions. Simulation study and graphical representation for the estimates are also presented. It is noted from analysis of real data that the Bayes estimates under LINEX loss assuming Jeffreys' prior is more efficient for the no. of incidences in male and female. As far as no. of deaths are concerned again, LINEX loss assuming Jeffreys' prior gives better results for the male population, but for the female population, the best loss function is SELF assuming Jeffreys' prior.

Block-Wise Variable Selection for Clustering Via Latent States of Mixture Models

Mixture modeling is a major paradigm for clustering in statistics. In this article, we develop a new block-wise variable selection method for clustering by exploiting the latent states of the hidden Markov model on variable blocks or the Gaussian mixture model. The variable blocks are formed by depth-first-search on a dendrogram created based on the mutual information between any pair of variables. It is demonstrated that the latent states of the variable blocks together with the mixture model parameters can represent the original data effectively and much more compactly. We thus cluster the data using the latent states and select variables according to the relationship between the states and the clusters. As true class labels are unknown in the unsupervised setting, we first generate more refined clusters, namely, semi-clusters, for variable selection and then determine the final clusters based on the dimension reduced data. Experiments on simulated and real data show that the new method is highly competitive in terms of clustering accuracy compared with several widely used methods. Supplementary materials for this article are available online.

Modeling in Forestry Using Mixture Models Fitted to Grouped and Ungrouped Data

The creation and maintenance of complex forest structures has become an important forestry objective. Complex forest structures, often expressed in multimodal shapes of tree size/diameter (DBH) distributions, are challenging to model. Mixture probability density functions of two- or three-component gamma, log-normal, and Weibull mixture models offer a solution and can additionally provide insights into forest dynamics. Model parameters can be efficiently estimated with the maximum likelihood (ML) approach using iterative methods such as the Newton-Raphson (NR) algorithm. However, the NR algorithm is sensitive to the choice of initial values and does not always converge. As an alternative, we explored the use of the iterative expectation-maximization (EM) algorithm for estimating parameters of the aforementioned mixture models because it always converges to ML estimators. Since forestry data frequently occur both in grouped (classified) and ungrouped (raw) forms, the EM algorithm was applied to explore the goodness-of-fit of the gamma, log-normal, and Weibull mixture distributions in three sample plots that exhibited irregular, multimodal, highly skewed, and heavy-tailed DBH distributions where some size classes were empty. The EM-based goodness-of-fit was further compared against a nonparametric kernel-based density estimation (NK) model and the recently popularized gamma-shaped mixture (GSM) models using the ungrouped data. In this example application, the EM algorithm provided well-fitting two- or three-component mixture models for all three model families. The number of components of the best-fitting models differed among the three sample plots (but not among model families) and the mixture models of the log-normal and gamma families provided a better fit than the Weibull distribution for grouped and ungrouped data. For ungrouped data, both log-normal and gamma mixture distributions outperformed the GSM model and, with the exception of the multimodal diameter distribution, also the NK model. The EM algorithm appears to be a promising tool for modeling complex forest structures.

Comparison on micromechanical properties of interfacial transition zone in concrete with iron ore tailings or crushed gravel as aggregate

Using recycling iron ore tailings (IOTs) from industrial solid waste as concrete aggregates agrees with the sustainable development of the construction industry and carbon neutrality commitment. As the interfacial transition zone (ITZ) between IOTs and cement paste is significant to concrete performance but rarely studied, the present work is focused on the micromechanical property of ITZ in concrete with IOTs. Comparative studies were conducted on ITZ of IOTs concrete and crushed gravel (natural aggregate, NA) concrete by statistical grid nanoindentation technique, scanning electron microscope (SEM), atomic force microscope (AFM), energy dispersive spectroscopy (EDS), and micro indentation. Maximum likelihood estimation (MLE) method with the expectation-maximization (EM) algorithm was adopted as a deconvolution technique to find the optimized parameters of the two-dimensional Gaussian mixture model (GMM) for the nanoindentation data. With the errors from −8.6% to +1.7% of the two-dimensional GMM for phases identification, results show that ITZ of IOT samples have much higher volume fractions of LD-C-S-H phase, HD-C-S-H phase, CH phase and even the UHD-C-S-H phase compared to NA samples. The hydrated phase assemblage of IOT samples was further proved by micro indentation to formed a denser microstructure in ITZ with enhanced bonding properties of reduced modulus M = 8.13 GPa and hardness H = 0.44, compared to M = 6.63 GPa and H = 0.37 of NA samples. According to the results, because of the local low water-binder ratio, ITZ of IOTs concrete showed a denser microstructure and higher micromechanical properties than NA concrete. This study presented a theoretical ground for recycling IOTs as aggregate in concrete.

Order-of-addition mixture experiments

In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. Existing literature on mixture designs ignores the order of addition of the mixture components. This paper considers the Order-of-Addition (OofA) mixture experiment, where the response depends on both the mixture proportions of components and their order of addition. Empirical study demonstrates that if mixture-order interactions exist, then the optimal mixture proportions identified by traditional models may be misleading. Full Mixture OofA designs are created which ensure orthogonality between mixture model terms and addition order effects. These designs allow for the estimation of (1) typical mixture model parameters and (2) order-of-addition effects. Moreover, models which include both main effects and key mixture-order interactions are introduced.

Gaussian Mixture Model Parameter Optimization in Range Points Migration-Based Three-Dimensional Radar Imaging

Millimeter-wave (MMW) imaging radar is one of the major environmental sensors in recent self-driving or driver assistance systems and provides environmentally robust sensing even in optically challenging conditions. As a promising three-dimensional (3-D) radar imaging technique, this study focuses on the range points migration (RPM) method, which has advantages in terms of accuracy and low complexity. In the original RPM algorithm, the parameters are manually or empirically determined by considering the sensor configuration and target shape or distance. To address this limitation, we introduced a novel parameter optimization scheme based on the Gaussian mixture model (GMM) and the expectation maximization (EM) algorithm. In addition, we used the k-space decomposition-based parameter determination scheme to determine target shape-dependent parameter selection. The results, assuming the human body imaging scenario, showed that our proposed method retains a highly accurate target image without requiring empirical parameter selection.

Probabilistic model updating via variational Bayesian inference and adaptive Gaussian process modeling

The estimation of the posterior probability distribution of unknown parameters remains a challenging issue for model updating with uncertainties. Most current studies are based on stochastic simulation techniques. This paper proposes a novel variational Bayesian inference approach to estimate posterior probability distributions by using the vibration responses of civil engineering structures. An adaptive Gaussian process modeling technique is used to represent the “expensive-to-evaluate” likelihood function, and the unknown posterior probability distribution is represented using a Gaussian mixture model. The evidence lower bound (ELBO) and its gradients can be computed analytically using the built Gaussian process and mixture models. The unknown parameters in the Gaussian mixture model can be identified by maximizing the value of ELBO. The stochastic gradient descent method is applied to perform the optimization. Numerical studies on an eight-story shear-type building and a simply supported beam are conducted to verify the accuracy and efficiency of using the proposed approach for probabilistic model updating and damage identification. Experimental studies on a laboratory steel frame structure are also conducted to validate the proposed approach. Results demonstrate that the posterior probability distributions of the unknown structural parameters can be successfully identified, and reliable probabilistic model updating and damage identification can be achieved.

Infinite Gaussian Mixture Modeling with an Improved Estimation of the Number of Clusters

Infinite Gaussian mixture modeling (IGMM) is a modeling method that determines all the parameters of a Gaussian mixture model (GMM), including its order. It has been well documented that it is a consistent estimator for probability density functions in the sense that, given enough training data from sufficiently regular probability density functions, it will converge to the shape of the original density curve. It is also known, however, that IGMM provides an inconsistent estimation of the number of clusters. The current paper shows that the nature of this inconsistency is an overestimation, and we pinpoint that this problem is an inherent part of the training algorithm. It stems mostly from a "self-reinforcing feedback'' which is a certain relation between the likelihood function of one of the model hyperparameters (alpha) and the probability of sampling the number of components, that sustain their mutual growth during the Gibbs iterations. We show that this problem can be resolved by using informative priors for alpha and propose a modified training procedure that uses the inverse chi-square for this purpose. The modified algorithm successfully recovers the ``known" order in all the experiments with synthetic data sets. It also demonstrates good results when compared to other methods used to evaluate model order, using real-world databases. Furthermore, the improved performance is attained without undermining the fidelity of estimating the original PDFs and with a significant reduction in computational cost.

Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

This paper presents an in-depth analysis of tennis match scene classification using an adaptive Gaussian mixture model parameter estimation simulation algorithm. We divided the main components of semantic analysis into type of motion, distance of motion, speed of motion, and landing area of the tennis ball. Firstly, for the problem that both people and tennis balls in the video frames of tennis matches from the surveillance viewpoint are very small, we propose an adaptive Gaussian mixture model parameter estimation algorithm, which has good accuracy and speed on small targets. Secondly, in this paper, we design a sports player tracking algorithm based on role division and continuously lock the target player to be tracked and output the player region. At the same time, based on the displacement information of the key points of the player’s body and the system running time, the distance and speed of the player’s movement are obtained. Then, for the problem that tennis balls are small and difficult to capture in high-speed motion, this paper designs a prior knowledge-based algorithm for predicting tennis ball motion and landing area to derive the landing area of tennis balls. Finally, this paper implements a prototype system for semantic analysis of real-time video of tennis matches and tests and analyzes the performance indexes of the system, and the results show that the system has good performance in real-time, accuracy, and stability.

Modeling and Analysis of Short Distance Sub-Terahertz Communication Channel via Mixture of Gamma Distribution

With the recent developments on opening the terahertz (THz) spectrum for experimental purposes by the Federal Communications Commission, transceivers operating in the range of 0.1THz-10THz, which are known as THz bands, will enable ultra-high throughput wireless communications. However, actual implementation of the high-speed and high reliability THz band communication systems should start with providing extensive knowledge in regards to the propagation channel characteristics. Considering the huge bandwidth and the rapid changes in the characteristics of THz wireless channels, ray tracing and one-shot statistical modeling are not adequate to define an accurate channel model. In this work, we propose Gamma mixture based channel modeling for the THz band via the expectation-maximization (EM) algorithm. First, maximum likelihood estimation (MLE) is applied to characterize the Gamma mixture model parameters, and then EM algorithm is used to compute MLEs of the unknown parameters of the measurement data. The accuracy of the proposed model is investigated by using the Weighted relative mean difference (WMRD) error metrics, Kullback-Leibler (KL)-divergence, and Kolmogorov-Smirnov (KS) test to show the difference between the proposed model and the actual probability density functions (PDFs) that are obtained via the designed test environment. To efficiently evaluate the performance of the proposed method in more realistic scenarios, all the analysis is done by examining measurement data from a measurement campaign in the 240 GHz to 300 GHz frequency range, using a well-isolated anechoic chamber. According to WMRD error metrics, KL-divergence, and KS test results, PDFs generated by the mixture of Gamma distributions fit to the actual histogram of the measurement data. It is shown that instead of taking pseudo-average characteristics of sub-bands in the wide band, using the mixture models allows for determining channel parameters more precisely.

What Did Time Tell Us? A Comparison and Retrospective Validation of Different Survival Extrapolation Methods for Immuno-Oncologic Therapy in Advanced or Metastatic Renal Cell Carcinoma.

The immuno-oncologic (IO) mechanism of action may lead to an overall survival (OS) hazard that changes over time, producing shapes that standard parametric extrapolation methods may struggle to reflect. Furthermore, selection of the most appropriate extrapolation method for health technology assessment is often based on trial data with limited follow-up. To examine this problem, we fitted a range of extrapolation methods to patient-level survival data from CheckMate 025 (NCT01668784, CM-025), a phase III trial comparing nivolumab with everolimus for previously treated advanced renal cell carcinoma (aRCC), to assess their predictive accuracy over time. Six extrapolation methods were examined: standard parametric models, natural cubic splines, piecewise models combining Kaplan-Meier data with an exponential or non-exponential distribution, response-based landmark models, and parametric mixture models. We produced three database locks (DBLs) at minimum follow-ups of 15, 27, and 39 months to align with previously published CM-025 data. A three-step evaluation process was adopted: (1) selection of the distribution family for each method in each of the three DBLs, (2) internal validation comparing extrapolation-based landmark and mean survival with the latest CM-025 dataset (minimum follow-up, 64 months), and (3) external validation of survival projections using clinical expert opinion and long-term follow-up data from other nivolumab studies in aRCC (CheckMate 003 and CheckMate 010). All extrapolation methods, with the exception of mixture models, underestimated landmark and mean OS for nivolumab compared with CM-025 long-term follow-up data. OS estimates for everolimus tended to be more accurate, with four of the six methods providing landmark OS estimates within the 95% confidence interval of observed OS as per the latest dataset. The predictive accuracy of survival extrapolation methods fitted to nivolumab also showed greater variation than for everolimus. The proportional hazards assumption held for all DBLs, and a dependent log-logistic model provided reliable estimates of longer-term survival for both nivolumab and everolimus across the DBLs. Although mixture models and response-based landmark models provided reasonable estimates of OS based on the 39-month DBL, this was not the case for the two earlier DBLs. The piecewise exponential models consistently underestimated OS for both nivolumab and everolimus at clinically meaningful pre-specified landmark time points. This aRCC case study identified marked differences in the predictive accuracy of survival extrapolation methods for nivolumab but less so for everolimus. The dependent log-logistic model did not suffer from overfitting to early DBLs to the same extent as more complex methods. Methods that provide more degrees of freedom may accurately represent survival for IO therapy, particularly if data are more mature or external data are available to inform the long-term extrapolations.