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This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
When planning a clinical trial for a time-to-event endpoint, we require an estimated effect size and need to consider the type of effect. Usually, an effect of proportional hazards is assumed with the hazard ratio as the corresponding…
For a multinomial distribution, suppose that we have prior knowledge of the sum of the probabilities of some categories. This allows us to construct a submodel in a full (i.e., no-restriction) model. Maximum likelihood estimation (MLE)…
Minimizing the number of patients exposed to potentially harmful drugs in early onco logical trials is a major concern during planning. Adaptive designs account for the inherent uncertainty about the true effect size by determining the…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler…
Nonlinear Mixed Effects models (NLME) models are widely used in pharmacometrics and related fields to analyze hierarchical and longitudinal data. However, as the number of parameters and random effects increases, traditional methods for…
Biomedical researchers usually study the effects of certain exposures on disease risks among a well-defined population. To achieve this goal, the gold standard is to design a trial with an appropriate sample from that population. Due to the…
When a novel treatment has successfully passed phase I, different options to design subsequent phase II trials are available. One approach is a single-arm trial, comparing the response rate in the intervention group against a fixed…
We study targeted maximum likelihood estimation (TMLE) of the average treatment effect in a semiparametric regression model whose mean function is indexed by a finite-dimensional parameter, while the additive error distribution is left…
We consider the performance of the difference-in-means estimator in a two-arm randomized experiment under common experimental endpoints such as continuous (regression), incidence, proportion and survival. We examine performance under both…
We study approaches to robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for…
Purpose: We address the challenge of inaccurate parameter estimation in diffusion MRI when the signal-to-noise ratio (SNR) is very low, as in the spinal cord. The accuracy of conventional maximum-likelihood estimation (MLE) depends highly…
Large Language Models (LLMs) are increasingly deployed for clinical reasoning tasks, which inherently require eliciting calibrated probabilistic beliefs based on available evidence. However, real-world clinical data are frequently…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…
We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…
This short note is to point the reader to notice that the proof of high dimensional asymptotic normality of MLE estimator for logistic regression under the regime $p_n=o(n)$ given in paper: "Maximum likelihood estimation in logistic…
This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…