Joint Likelihood Function Research Articles

Control chart for detecting the scale parameter of the zero‐inflated Poisson model

AbstractWhen monitoring risk in public health, count data commonly exhibit an excessive number of zero, and the zero‐inflated Poisson (ZIP) model is often used to fit this type of data. Most previous methods for monitoring of the ZIP model have focused on the changes in the location parameter and the existence of the scale parameter and usually assumed that the scale parameter is zero in the H0 stage. However, in an objective environment, data often have certain fluctuations, meaning that the scale parameter always exists. Therefore, it is more meaningful to monitor the changes in the scale parameter on top of the predefined baseline than to monitor its existence. In this study, we derive a score test statistic based on the generalized Henderson's joint likelihood function, construct a risk‐adjusted exponentially weighted moving average (EWMA) control chart to monitor the variability of the random effects variance component in the ZIP mixed‐effects model. And the convergence property of the score test statistic is proved through derivation, which shows that the new method has theoretical reliability. The simulation results Indicate that when the scale parameter has different predefined baselines and different variation amplitudes, the proposed method is more effective than the existing RA‐ZIP and PR‐ZIP control charts. In addition, the proposed method is applied to real data from a Hong Kong hospital for online influenza surveillance to demonstrate its practicability.

Joint Variational Inference Network for domain generalization

Domain generalization is a machine learning task that involves training a model on a set of domains with the goal of achieving high performance on unseen domains. While most domain generalization methods focus on extracting domain-invariant features, they may ignore domain-specific information beyond object styles which is label-relevant for classification. In this paper, we first propose a two-step data generation process in which the domain label and observed data are sampled from two distributions sequentially, and accordingly develop an end-to-end Joint Variational Inference Network (JVINet) for domain generalization. JVINet is a framework that admits a variational-based discriminative structure, which the domain-specific latent variable is learned and integrated to enhance the feature for classification. When testing on unseen target domains, the potential beneficial domain information is hence utilized to improve generalization ability. The overall objective is to optimize the variational lower bound of the conditional joint likelihood functions for both class and domain labels. We provide theoretical proof that JVINet can achieve an optimal lower bound using a variational-based discriminative approach. To evaluate the effectiveness of our method, we compare it with state-of-the-art methods on both simulated and real-world datasets.

Satellite-Based Localization of IoT Devices Using Joint Doppler and Angle-of-Arrival Estimation

While global navigation satellite system (GNSS) technologies have always been the go-to solution for localization problems, they may not be the best choice for some Internet-of-Things (IoT) applications due to the incurred power consumption and cost. In this paper, we present an alternative satellite-based localization method exploiting the signature of Doppler shifts and angle-of-arrival measurements as seen by a low-Earth-orbit (LEO) satellite. We first derive the joint likelihood function of the measurements, which is represented as a combination of three Gaussian distributions. Then, we show that the maximum likelihood problem reduces to a more-efficient mean squared error minimization in the Gaussian case as inferred from real measurements we collected from low-Earth-orbit satellite using a tracking ground station. Thus, we propose utilizing a stochastic optimizer to search for the global minimum of the mean squared error, which represents the location of the ground IoT device as estimated by the satellite platform. The emulated results show that the IoT device localization, in such a realistic model, can be performed with sufficient accuracy for IoT applications.

Reliability Analysis of Kavya Manoharan Kumaraswamy Distribution under Generalized Progressive Hybrid Data

Generalized progressive hybrid censoring approaches have been developed to reduce test time and cost. This paper investigates the difficulties associated with estimating the unobserved model parameters and the reliability time functions of the Kavya Manoharan Kumaraswamy (KMKu) distribution based on generalized type-II progressive hybrid censoring using classical and Bayesian estimation techniques. The frequentist estimators’ normal approximations are also used to construct the appropriate estimated confidence intervals for the unknown parameter model. Under symmetrical squared error loss, independent gamma conjugate priors are used to produce the Bayesian estimators. The Bayesian estimators and associated highest posterior density intervals cannot be derived analytically since the joint likelihood function is provided in a complicated form. However, they may be evaluated using Monte Carlo Markov chain (MCMC) techniques. Out of all the censoring choices, the best one is selected using four optimality criteria.

Performance of Iterative Coded CDMA Receivers with APP Feedback: A Use of a Weighted Delay Filter

The prohibitive computational complexity of optimal coded multiuser detection necessitates using suboptimal detectors in practical implementations. The filter is very computationally simple and is also demonstrated to provide faster convergence and superior bit error rate (BER) performance. Further investigation of the weighted delay filter concept produces a second filter—derived via the joint likelihood function. It is analytically demonstrated that extrinsic feedback systems will not benefit from weighted delay filtering. A system model is provided that introduces the notion of feedback ‘residue’, which is shown to be the key difference between a-posterior probability (APP) and extrinsic systems when determining the parallel interference cancellation (PIC) output statistics. It is analytically shown that the weighted delay filter derived via a maximum signal-to-noise ratio (SNR) approach is identical to a weighted delay filter derived via the joint likelihood function. It is analytically shown that when extrinsic feedback is used in a coded-code division multiple access (C-CDMA) system, no benefit will be realised by weighted delay filtering, as soft outputs from previous cycles are a merely scaled, noisy version of the most recent data. The notion of a ‘feedback residue’ for systems with APP feedback is introduced, and it is empirically shown that this residue term is a key consideration when determining the PIC output statistics. Using the ‘residual feedback’ model, it is shown that when APP feedback is utilised, data from previous cycles is not simply “a scaled, noisy version” of the current data. For this reason, benefits may be realised by APP feedback use. The simulation results shows that the residue may be trivial at small loads, the residue builds to the substantial value of nearly 0.4 at a reasonably modest load of K/N=15/10, and continues to grow as the load increases.

Reliability Analysis and Applications of Generalized Type-II Progressively Hybrid Maxwell–Boltzmann Censored Data

Today, the reliability or quality practitioner always aims to shorten testing duration and reduce testing costs without neglecting efficient statistical inference. So, a generalized progressively Type-II hybrid censored mechanism has been developed in which the experimenter prepays for usage of the testing facility for T units of time. This paper investigates the issue of estimating the model parameter, reliability, and hazard rate functions of the Maxwell–Boltzmann distribution in the presence of generalized progressive Type-II hybrid censored data by making use of the likelihood and Bayesian inferential methods. Using an inverse gamma prior distribution, the Bayes estimators of the same unknown parameters with respect to the most commonly squared-error loss are derived. Since the joint likelihood function is produced in complex form, following the Monte-Carlo Markov-chain idea, the Bayes’ point estimators as well as the Bayes credible and highest posterior density intervals cannot be derived analytically, but they may be examined numerically. Via the normal approximation of the acquired maximum likelihood and log-maximum-likelihood estimators, the approximate confidence interval bounds of the unknown quantities are derived. Via comprehensive numerical comparisons, with regard to simulated root mean squared-error, mean relative absolute bias, average confidence length, and coverage probability, the actual behavior of the proposed estimation methodologies is examined. To illustrate how the offered methodologies may be used in real circumstances, two different applications, representing the failure time points of aircraft windscreens as well as the daily average wind speed in Cairo during 2009, are explored. Numerical evaluations recommend utilizing a Bayes model via the Metropolis-Hastings technique to produce samples from the posterior distribution to estimate any parameter of the Maxwell–Boltzmann distribution when collecting data from a generalized progressively Type-II hybrid censored mechanism.

Statistical Analysis of Type-II Generalized Progressively Hybrid Alpha-PIE Censored Data and Applications in Electronic Tubes and Vinyl Chloride

A new Type-II generalized progressively hybrid censoring strategy, in which the experiment is ensured to stop at a specified time, is explored when the lifetime model of the test subjects follows a two-parameter alpha-power inverted exponential (Alpha-PIE) distribution. Alpha-PIE’s parameters and reliability indices, such as reliability and hazard rate functions, are estimated via maximum likelihood and Bayes estimation methodologies in the presence of the proposed censored data. The estimated confidence intervals of the unknown quantities are created using the normal approximation of the acquired classical estimators. The Bayesian estimators are also produced using independent gamma density priors under symmetrical (squared-error) loss. The Bayes’ estimators and their associated highest posterior density intervals cannot be calculated theoretically since the joint likelihood function is derived in a complicated form, but they can potentially be assessed using Monte Carlo Markov-chain algorithms. We next go through four optimality criteria for identifying the best progressive design. The effectiveness of the suggested estimation procedures is assessed using Monte Carlo comparisons, and certain recommendations are offered. Ultimately, two different applications, one focused on the failure times of electronic tubes and the other on vinyl chloride, are analyzed to illustrate the effectiveness of the proposed techniques that may be employed in real-world scenarios.

Particle count estimation in dilution series experiments

AbstractEstimation of microorganism concentration in samples (bacterial cells or viral particles) has been a focal point in biomedical experiments for more than a century. Serial dilution of the samples is often used to estimate the target concentrations in immunology, virology, and pharmaceutical industry. A new methodology, called joint likelihood estimation (JLE), is proposed to estimate particles such as the number of microorganisms in a sample from counts obtained by serially diluting the sample. It models count data from the entire single dilution series rather than using only specific dilutions. The theoretical framework is based on the binomial and the Poisson distributions and is consistent with the actual experimental process. The estimator of the target concentration is obtained by MLE with derived joint likelihood functions of the observed counts including right‐censored values. Simulations demonstrated that the new JLE method significantly increases precision and accuracy of the estimate compared to the existing methods. It can be applied to a variety of studies with similar experimental designs, especially when the number of particles in the neat sample is very large.

A statistical model for quantifying age-reading errors and its application to the Antarctic minke whales

A statistical method for quantifying age-reading error, i.e. the extent of bias and inter-reader variability among readers, is introduced. The method assumes the availability of an independent ‘control reader’ who produces reference ages for age-reading structures which are also read by additional readers. This control reader is assumed to provide unbiased or consistently biased age estimates so that the additional readers’ age-reading outcomes can be standardised. Linear structures in bias and variance are incorporated in a conditional probability matrix representing the stochastic nature of age-determination for each reader. A joint likelihood function for the parameters related to age-reading bias, variance and nuisance parameters is defined based on observed age-reading outcomes from both the control and additional readers. The method is applied to data for Antarctic minke whales taken during Japanese commercial (1971/72–1986/87) and scientific (JARPA: 1987/88–2004/05, JARPA II: 2005/06–2010/11) whaling. A total of 250 earplugs selected according to a predetermined protocol were used in the analyses to estimate the inter-reader variation for four Japanese readers. One of the authors acted as the control reader. The Japanese readers and the control reader differed in terms of both the expected age given the true age, and variance in age-estimates. The expected age and random uncertainty in age-estimates differed among the Japanese readers, although the two readers in charge of age-reading for samples taken during Japanese scientific whaling (JARPA and JARPA II) provided quite similar agereading outcomes. These results contribute to analyses using catch-at-age data for this species. It should also be noted that the model and approach in this paper can be applied to populations other than the Antarctic minke whales, if a control reader is available, even retrospectively.

Estimating random effects in a finite Markov chain with absorbing states: Application to cognitive data.

Finite Markov chains with absorbing states are popular tools for analyzing longitudinal data with categorical responses. The one step transition probabilities can be defined in terms of fixed and random effects but it is difficult to estimate these effects due to many unknown parameters. In this article we propose a three-step estimation method. In the first step the fixed effects are estimated by using a marginal likelihood function, in the second step the random effects are estimated after substituting the estimated fixed effects into a joint likelihood function defined as a h-likelihood, and in the third step the covariance matrix for the vector of random effects is estimated using the Hessian matrix for this likelihood function. An application involving an analysis of longitudinal cognitive data is used to illustrate the method.

Computational Analysis for Fréchet Parameters of Life from Generalized Type-II Progressive Hybrid Censored Data with Applications in Physics and Engineering

Generalized progressive hybrid censored procedures are created to reduce test time and expenses. This paper investigates the issue of estimating the model parameters, reliability, and hazard rate functions of the Fréchet (Fr) distribution under generalized Type-II progressive hybrid censoring by making use of the Bayesian estimation and maximum likelihood methods. The appropriate estimated confidence intervals of unknown quantities are likewise built using the frequentist estimators’ normal approximations. The Bayesian estimators are created using independent gamma conjugate priors under the symmetrical squared-error loss. The Bayesian estimators and the associated greatest posterior density intervals cannot be computed analytically since the joint likelihood function is obtained in complex form, but they may be assessed using Monte Carlo Markov chain (MCMC) techniques. Via extensive Monte Carlo simulations, the actual behavior of the proposed estimation methodologies is evaluated. Four optimality criteria are used to choose the best censoring scheme out of all the options. To demonstrate how the suggested approaches may be utilized in real scenarios, two real applications reflecting the thirty successive values of precipitation in Minneapolis–Saint Paul for the month of March as well as the number of vehicle fatalities for thirty-nine counties in South Carolina during 2012 are examined.

Direct Target Localization With Quantized Measurements in Noncoherent Distributed MIMO Radar Systems

In this paper, a direct target localization algorithm with quantized measurements for non-coherent MIMO systems is proposed. In this system, each receiver transmits a low-bit quantized version of the echo rather than the full raw data to the fusion center. We construct a joint likelihood function based on the low-bit data of each receiver, from which the unknown target position can be directly determined. The Cramer-Rao lower bound (CRLB) is derived to analyze the localization performance of our proposed algorithm. To maximize the localization performance, a CRLB-based objective function is designed to obtain the optimum quantization thresholds. The formulated problem is a high-dimensional and non-convex optimization problem that when solved, determines two types of coupled parameters for the quantization thresholds and the complex-valued scaling coefficients of the signal. We propose a batch gradient descent embedded particle swarm optimization algorithm to solve this problem effectively. Numerical results show that the proposed algorithm delivers superior performance in terms of maximizing the overall localization performance, and the 3-bit quantized algorithm is able to provide performance that is very close to the unquantized algorithm. Experimental data recorded by three small radars are also provided to demonstrate the effectiveness of the proposed algorithm.

Reliability Inferences of the Inverted NH Parameters via Generalized Type-II Progressive Hybrid Censoring with Applications

Generalized progressive hybrid censored mechanisms have been proposed to reduce the test duration and to save the cost spent on testing. This paper considers the problem of estimating the unknown model parameters and the reliability time functions of the new inverted Nadarajah–Haghighi (NH) distribution under generalized Type-II progressive hybrid censoring using the maximum likelihood and Bayesian estimation approaches. Utilizing the normal approximation of the frequentist estimators, the corresponding approximate confidence intervals of unknown quantities are also constructed. Using independent gamma conjugate priors under the symmetrical squared error loss, the Bayesian estimators are developed. Since the joint likelihood function is obtained in complex form, the Bayesian estimators and their associated highest posterior density intervals cannot be obtained analytically but can be evaluated via Monte Carlo Markov chain techniques. To select the optimum censoring scheme among different censoring plans, five optimality criteria are used. Finally, to explain how the proposed methodologies can be applied in real situations, two applications representing the failure times of electronic devices and deaths from the coronavirus disease 2019 epidemic in the United States of America are analyzed.

Adaptive Brain Activity Detection in Structured Interference and Partially Homogeneous Locally Correlated Disturbance.

In this paper, we aim to address the problem of subspace detection in the presence of locally-correlated complex Gaussian noise and interference. For applications like brain activity detection using functional magnetic resonance imaging (fMRI) data where the noise is possibly locally correlated, using the sample covariance estimator is not a suitable choice due to significant dependency of its accuracy on the number of observations. In this study, we take advantage of an assumed banded structure in the covariance matrix to model the local dependence in the noise and propose a new covariance estimation approach. In particular, we use the idea of factorizing the joint likelihood function into a few conditional likelihood terms and maximizing each term independently of the others. This process leads to an explicit estimator for banded covariance matrices which requires fewer observations to achieve the same accuracy as the sample covariance. This estimate is then fed into an adaptive matched filter, two-step Rao and two-step Wald tests for detection. Simulation results reveal the superiority of the proposed methods over well known classical detectors. Finally, the proposed methods are applied to functional magnetic resonance imaging (fMRI) data to localize neural activities in the brain. The proposed method can offer better activation maps in terms of accuracy and spatial smoothness. The proposed methods can be seen as alternatives for standard detection approaches which are not perfectly aligned with the properties of fMRI data.

S26 Comparison of Machine and Deep Learning Methods With the Mayo Clinical Risk Score in Predicting 1-Year Mortality in Primary Biliary Cholangitis Patients

Introduction: To compare machine learning (ML) and deep learning (DL) approaches to predict survival outcome in patients at 1- year with Primary Biliary Cholangitis (PBC) and to compare with the Mayo Clinical risk score Methods: The data is taken from a randomized trial in PBC patients conducted between 1974 and 1984 by the Mayo Clinic. The first 312 cases in the dataset were included out of a total of 424 PBC patients referred. The rest that contained subjects with >30% missing data, were excluded. We evaluated the following models: 1) The 5-covariate Mayo model: log(bilirubin), albumin, log(prothrombin time), edema, and age, 2) 17-covariate Cox proportional hazards model by componentwise likelihood based boosting with stepnumber 10 and penalty number 100, 3) 17-covariate Deephit: DeepHit: trains a neural network to learn the estimated joint distribution of survival time and event, while capturing the right-censored nature inherent in survival data. Analysis was done with frac 0.3, relu activation, 0.1 dropout, 100L epochs and a batch size of 32L, 4) 17-covariate Multitask logistic regression model with ranking based feature selection to predict survival using a logistic regression model and the parameters from each model are estimated simultaneously in the maximization of the joint likelihood function, 5) random survival forest with 1000 trees and 6) Support vector machine. For the ML & DL models all 17-covariates were include in the analysis. Analyses were done in RStudio, and missing values were imputed using missRanger package.1 The data is split into 80 percent training and 20 precent validation. All models were 5-fold cross validated. Prediciton statistics was calculated for each model developed. Finally, the ML & DL models were compared with the 5-covariate model of the Mayo Clinic Risk score. Results: Multitask logistic regression model showed the highest AUC (1.00) with a Harrell’s C-statistic of 0.90. Cox boost and random survival forest had equal AUCs (0.87) and C-indices (0.84). But the 5-covariate model of Mayo clinic Risk score had a higher AUC when compared to cox boost, random survival forest, support vector machine or even Deep hit. Conclusion: Machine learning methods offered limited improvement over the Mayo Clinical risk score except for the Multitask logistic regression model in predicting PBC survival outcome at 1-year (Table). Table 1. - Performance of Risk Scores from the 5-Covariate Model in comparison to the machine learning and deep learning models at 1-year S.No. Model specification AUC 95% CI Harrell’s C-statistic 1. 5-covariate model of Mayo clinic Risk score 0.88 0.85-0.91 0.79 2. Cox boost 0.87 0.84-0.90 0.84 3. Deep hit 0.70 0.66-0.74 0.30 4. Multitask logistic regression 1.00 1-1 0.90 5. Random survival forest 0.87 0.84-0.90 0.84 6. Support Vector Machine 0.56 0.52-0.61 0.43

Atmospheric model inversion using infrasound signals from the North Korean underground nuclear explosion and the subsequent collapse event in 2017

SUMMARY This study focuses on the infrasound signals from the September 2017 North Korean underground nuclear explosion (UNE17) and subsequent collapse event (SCE17) that occurred close to the autumnal equinox when the atmospheric temperature structure undergoes rapid change. Multiple arrivals, including contributions from local, diffracted and epicentral infrasound, generated by UNE17, were observed at eight infrasound arrays in the Korean Peninsula and one IMS infrasound station (IS45) in Russia while at the closest five arrays for SCE17 only epicentral infrasound was observed. The UNE17 signals provide the opportunity to explore the utility of each distinct arrival in constraining atmospheric conditions during the change associated with the equinox. The observed characteristics of the multiple epicentral infrasonic phases (celerity, backazimuth, phase velocity and spectra) suggest propagation paths through the tropospheric, stratospheric and thermospheric waveguides, although geometric ray paths based on a global atmospheric model at the time of the explosion predict only thermospheric returns. The absence of predicted stratospheric returns may reflect errors in the atmospheric models due to the lack of predicted stratospheric winds which are weak and changing close to the autumnal equinox or the limited resolution of the fine-scale structure not captured by current atmospheric models. The differences between the model predictions and the observations suggest that the numerical weather forecast models need to be modified to fully explain the observations. In order to explore the model space that can explain the UNE17 data set, an inversion scheme is applied to atmospheric wind model parameters constrained by the multi-array observations. Zonal and meridional wind profiles are parametrized using empirical orthogonal functions (EOFs) estimated from 1-yr of Ground-to-Space atmospheric specifications. A best-fitting atmospheric model is estimated using a Bayesian approach that assesses the uncertainty in the inverse solution using a joint likelihood function combining components of azimuth deviation, traveltime and phase velocity. The updated atmospheric models from six different EOFs inversions have up to 20 m s–1 stronger zonal and meridional wind speeds in the stratosphere compared to the original model, and explain the stratospheric observations in the data set. This investigation illustrates that modest changes to atmospheric wind models at the time of autumnal equinox can improve the prediction of stratospheric returns.

Adaptive measurement-assignment marginal multi-target Bayes filter with logic-based track initiation

The measurement-assignment marginal multi-target Bayes (AMMTB) filter assigns individual observations to either clutter or an object by maximizing the joint likelihood function of the observation partition. A label is also introduced in this filter to provide the target trajectory. However, the AMMTB filter requires that the initial state and error covariance of a newborn target are known in advance. Therefore it fails to track the target appearing from an unknown location. To address this problem, an optimized AMMTB filter is given and an adaptive establishing method of the newborn trajectory is proposed. By applying the adaptive establishing method of the newborn trajectory to the optimized AMMTB filter, an adaptive AMMTB filter with logic-based track initiation is developed. This filter uses the logic-based track initiation technique to establish the newborn track and employs the least squares technique to form the initial mean vector and error covariance of the newborn track. The assignment-based technique is also used in this filter to associate the observations and targets. Simulation results show that the proposed adaptive AMMTB filter can efficiently detect and track the target with an unknown appearing location. It has a lower computational requirement and less cardinality error, OSPA error and OSPA(2) error than the existing adaptive filters.

Domain knowledge-enhanced variable selection for biomedical data analysis

Machine learning has achieved impressive results in biomedical data analysis. To cope with high-dimensional data, variable selection is proposed to identify patterns in the feature space and select informative and predictive variables. However, due to the scarce cases and expensive sampling costs in the biomedical area, the lack of samples has become the main obstacle to the performance improvement of traditional variable selection algorithms in the biomedical data. In this paper, we solve this problem by the feat of domain knowledge, which seems to be a unique method in the biomedicine area due to the abundant and reliable domain knowledge in it. Nevertheless, the empirical study demonstrated that the brute-force implantation of domain knowledge may be counterproductive, especially when unfaithful knowledge exists. To elegantly incorporate domain knowledge into the variable selection framework, this paper starts from the joint likelihood function of the discriminative model and derives the extended form of prior knowledge term based on the existing variable selection framework. Based on this, a novel method is presented. We prove and substantiate with both synthetic and real-world biomedical data that, the proposal could effectively utilize the information from domain knowledge to assist variable selection and simultaneously reject incorrect knowledge.

Jointly modeling of sleep variables that are objectively measured by wrist actigraphy.

Recently developed actigraphy devices have made it possible for continuous and objective monitoring of sleep over multiple nights. Sleep variables captured by wrist actigraphy devices include sleep onset, sleep end, total sleep time, wake time after sleep onset, number of awakenings, etc. Currently available statistical methods to analyze such actigraphy data have limitations. First, averages over multiple nights are used to summarize sleep activities, ignoring variability over multiple nights from the same subject. Second, sleep variables are often analyzed independently. However, sleep variables tend to be correlated with each other. For example, how long a subject sleeps at night can be correlated with how long and how frequent he/she wakes up during that night. It is important to understand these inter-relationships. We therefore propose a joint mixed effect model on total sleep time, number of awakenings, and wake time. We develop an estimating procedure based upon a sequence of generalized linear mixed effects models, which can be implemented using existing software. The use of these models not only avoids computational intensity and instability that may occur by directly applying a numerical algorithm on a complicated joint likelihood function, but also provides additional insights on sleep activities. We demonstrated in simulation studies that the proposed estimating procedure performed well in estimating both fixed and random effects' parameters. We applied the proposed model to data from the Women's Interagency HIV Sleep Study to examine the association of employment status and age with overall sleep quality assessed by several actigraphy measured sleep variables.

Time-to-Event Analysis with Unknown Time Origins via Longitudinal Biomarker Registration

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape function with person-specific disease progression pattern characterized by a random curve registration function, which is further used to model the unknown time origin as a random start time. This random time is used as a link to jointly model the longitudinal and survival data where the unknown time origins are integrated out in the joint likelihood function, which facilitates unbiased and consistent estimation. Since the disease progression pattern naturally predicts time-to-event, we further propose a new functional survival model using the registration function as a predictor of the time-to-event. The asymptotic consistency and semiparametric efficiency of the proposed models are proved. Simulation studies and two real data applications demonstrate the effectiveness of this new approach. Supplementary materials for this article are available online.