arXiv subjects

Anthony Sisti

Publications and source records attributed to Anthony Sisti.

4 recordsLinked to original sources

arXiv2025

A Bayesian Framework for Latent Compliance Modeling in Cluster Randomized Trials with One-Sided Noncompliance

In pragmatic cluster randomized controlled trials (PCRCTs), healthcare providers are randomized while both providers and patients may deviate from the assigned intervention. In many PCRCTs, cluster-level implementation is measured using multiple continuous metrics, while individual compliance is recorded as a binary indicator. Standard complier average causal effect (CACE) estimands focus on individual-level compliance and do not account for heterogeneity in implementation across clusters. When intervention uptake is shaped by both provider- and patient-level processes, it is of scientific interest to characterize how effects vary across these sources of compliance. We propose a Bayesian framework for PCRCTs with one-sided binary noncompliance at the individual level and one-sided partial compliance at the cluster level. The method uses a latent mixture model to summarize heterogeneity in cluster-level implementation based on baseline characteristics and observed implementation measures, and links these latent implementation types to individual compliance and outcomes through a joint model. Because compliance is only observed in treated clusters, the model imputes unobserved compliance behavior for clusters and individuals assigned to control. The framework enables estimation of finite- and super-population intent-to-treat (ITT) and CACE estimands, both marginally and within latent implementation types. We apply the method to the METRIcAL trial, a pragmatic cluster randomized study evaluating a personalized music intervention for nursing home residents with dementia. The analysis illustrates how accounting for implementation heterogeneity and individual compliance can provide insights beyond standard ITT analyses.}{Causal inference; Principal stratification; Complier average causal effect; Cluster randomized trials; Noncompliance; Bayesian methods; Latent variable models; Interference.

stat.AP↗

arXiv2024

A Bayesian Method for Adverse Effects Estimation in Observational Studies with Truncation by Death

Death among subjects is common in observational studies evaluating the causal effects of interventions among geriatric or severely ill patients. High mortality rates complicate the comparison of the prevalence of adverse events (AEs) between interventions. This problem is often referred to as outcome "truncation" by death. A possible solution is to estimate the survivor average causal effect (SACE), an estimand that evaluates the effects of interventions among those who would have survived under both treatment assignments. However, because the SACE does not include subjects who would have died under one or both arms, it does not consider the relationship between AEs and death. We propose a Bayesian method which imputes the unobserved mortality and AE outcomes for each participant under the intervention they did not receive. Using the imputed outcomes we define a composite ordinal outcome for each patient, combining the occurrence of death and the AE in an increasing scale of severity. This allows for the comparison of the effects of the interventions on death and the AE simultaneously among the entire sample. We implement the procedure to analyze the incidence of heart failure among geriatric patients being treated for Type II diabetes with sulfonylureas or dipeptidyl peptidase-4 inhibitors.

stat.ME↗

arXiv2020

Lyapunov exponent and variance in the CLT for products of random matrices related to random Fibonacci sequences

We consider three matrix models of order 2 with one random entry $ε$ and the other three entries being deterministic. In the first model, we let $ε\sim\textrm{Bernoulli}\left(\frac{1}{2}\right)$. For this model we develop a new technique to obtain estimates for the top Lyapunov exponent in terms of a multi-level recursion involving Fibonacci-like sequences. This in turn gives a new characterization for the Lyapunov exponent in terms of these sequences. In the second model, we give similar estimates when $ε\sim\textrm{Bernoulli}\left(p\right)$ and $p\in [0,1]$ is a parameter. Both of these models are related to random Fibonacci sequences. In the last model, we compute the Lyapunov exponent exactly when the random entry is replaced with $ξε$ where $ε$ is a standard Cauchy random variable and $ξ$ is a real parameter. We then use Monte Carlo simulations to approximate the variance in the CLT for both parameter models.

math.PR↗

arXiv2018

A derivation of the Black-Scholes option pricing model using a central limit theorem argument

The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most well-known formulas in mathematical finance. For their discovery, Merton and Scholes have been awarded the 1997 Nobel prize in Economics. The standard method of deriving the Black-Scholes European call option pricing formula involves stochastic differential equations. This approach is out of reach for most students learning the model for the first time. We provide an alternate derivation using the Lindeberg-Feller central limit theorem under suitable assumptions. Our approach is elementary and can be understood by undergraduates taking a standard undergraduate course in probability.

q-fin.GN↗