Some results for maximum likelihood estimation of adjusted relative risks

Andrade, Bernardo Borba de; Andrade, Joanlise Marco de Leon

doi:10.1080/03610926.2017.1402045

Cited by 8 publications

(11 citation statements)

References 27 publications

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“…Indeed, when estimates are on the boundary of the parameter space, uncertainty evaluation cannot be done by exploiting standard firstorder asymptotic arguments and ad-hoc methods are needed. 26 These difficulties led Zou 12 and Carter et al 25 to consider a quasi-likelihood approach. In particular, the authors propose the use of the Poisson model in place of the Bernoulli one.…”

Section: Modelling Relative Riskmentioning

confidence: 99%

Improved and computationally stable estimation of relative risk regression with one binary exposure

Pozza

Pagui

Salvan

2023

Stat Methods Med Res

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In medical statistics, when the effect of a binary risk factor on a binary response is of interest, relative risk is often the preferred measure due to its direct interpretation. However, statistical inference on this quantity is not as straightforward as for other measures of association, especially when further explanatory variables have to be taken into account. Starting from a review of available methods for inference on relative risk, this paper deals with small and moderate sample size settings for which we show that classical approaches can be problematic. For this reason, we propose the use of improved estimation procedures, aiming at mean or median bias reduction of the maximum likelihood estimator. In particular, these methods are developed for a new alternative specification of a model recently proposed by Richardson et al, where higher computational stability of the estimation methods is achieved. A real-data example and extensive simulation studies show that the proposed methods perform remarkably better than the standard ones.

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Section: Modelling Relative Riskmentioning

confidence: 99%

Improved and computationally stable estimation of relative risk regression with one binary exposure

Pozza

Pagui

Salvan

2023

Stat Methods Med Res

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“…Descriptive statistics were calculated and are presented in Table 1. To test associations between geographic PrEP density and PrEP use, we employed log-binomial regression using an adaptive barrier algorithm to estimate prevalence ratios [56][57][58][59]. We examined bivariate models as well as fully adjusted multivariate models with PrEP provider counts in individual's activity space as the main outcome variable.…”

Section: Statistical Analysesmentioning

confidence: 99%

Geographic Density and Uptake of Pre-exposure Prophylaxis (PrEP) Among Young Gay, Bisexual and Other Sexual Minority Men: A Global Positioning System (GPS) Study

et al. 2021

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The geographic availability of pre-exposure prophylaxis (PrEP) providers is one important factor that significantly affects PrEP uptake. While most previous studies have employed spatial accessibility in static residential neighborhood definitions or self-reported healthcare accessibility, we examined the associations of the objectively measured geographic density of PrEP services with current PrEP use, using global positioning system (GPS) among sexual minority men (SMM) in New York City. 250 HIV-negative SMM participated in a 2-week GPS monitoring (January 2017–January 2018). Geographic PrEP density was measured as total numbers of PrEP providers in (1) individual activity space defined as daily path area of GPS points, (2) residential street network buffers and (3) census tract and ZIP code of residential locations. Geographic PrEP density within GPS-based activity space was positively associated with current PrEP use (prevalence ratio for 50-m activity space = 1.10, 95% confidence interval: [1.02, 1.18]). PrEP provider counts in residential buffer areas and administrative neighborhoods were not associated with PrEP use. Although it is not generalizable beyond New York City, our finding suggests the importance of daily mobility pattern in HIV prevention and PrEP implementation strategies.

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“…There is a lengthy history of proposed MLE and non‐MLE methods for estimating functions of probabilities (like ratios of probabilities, risk ratios, and other forms). Maximum likelihood estimation with a Log Binomial Model (LBM) subject to constraints x ′ i β ≤0,∀ i is a similar problem to the MLE determination with the PPM.…”

Section: Introductionmentioning

confidence: 99%

“…Maximum likelihood estimation with a Log Binomial Model (LBM) subject to constraints x ′ i β ≤0,∀ i is a similar problem to the MLE determination with the PPM. Recent developments in the LBM, have used the function constrOptim in R. This function uses an adaptive barrier algorithm of Lange which manages the linear inequality constraints of the LBM. We use constrOptim in our package lcpm for determining the MLE of the PPM with the linear inequality constraints given above.…”

Section: Introductionmentioning

confidence: 99%

Ordinal outcomes: A cumulative probability model with the log link and an assumption of proportionality

Singh

Fick

2020

Statistics in Medicine

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We present here a study of ordinal outcomes with a cumulative probability model. In particular, we consider the log link with the assumption of proportionality. The logit link is currently the most widely used link with ordinal outcomes in the health research literature. With the logit link, one obtains regression coefficients that are functions of odds. When the log link is used, one obtains regression coefficients that are functions of probabilities. While odds might be preferred with certain studies that are retrospective, many health researchers may prefer to have direct statements about probabilities. There are two classes of models with the log link analogous to those with the logit link. We will call these two classes the Proportional Probability Model (PPM) and the Log Cumulative Probability Model (LCPM). These models introduce a challenge not seen with the logit link models. The log link models have constraints on the parameter space. We must insist that the maximum likelihood estimate (MLE) satisfy these constraints. We present conditions for the uniqueness of the MLE and we present other features of the MLE. Several examples and several closed form expressions for the MLE are presented. While this paper is primarily about the PPM, our R package lcpm contains functions to fit both the PPM and the LCPM.

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Some results for maximum likelihood estimation of adjusted relative risks

Cited by 8 publications

References 27 publications

Improved and computationally stable estimation of relative risk regression with one binary exposure

Improved and computationally stable estimation of relative risk regression with one binary exposure

Geographic Density and Uptake of Pre-exposure Prophylaxis (PrEP) Among Young Gay, Bisexual and Other Sexual Minority Men: A Global Positioning System (GPS) Study

Ordinal outcomes: A cumulative probability model with the log link and an assumption of proportionality

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