A note on A. Albert and J. A. Anderson's conditions for the existence of maximum likelihood estimates in logistic regression models

Biometrika ◽  
1986 ◽  
Vol 73 (3) ◽  
pp. 755-758 ◽  
Author(s):  
THOMAS J. SANTNER ◽  
DIANE E. DUFFY
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Regression Models ◽  
Maximum Likelihood Estimates ◽  
Logistic Regression Models

On the existence of posterior mean for Bayesian logistic regression

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Huong T. T. Pham ◽  
Hoa Pham
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Sufficient Conditions ◽  
Maximum Likelihood Estimates ◽  
Logistic Regression Models ◽  
Posterior Mean ◽  
Different Types ◽  
Data Points ◽  
Necessary And Sufficient ◽  
Bayesian Logistic Regression

Abstract Existence conditions for posterior mean of Bayesian logistic regression depend on both chosen prior distributions and a likelihood function. In logistic regression, different patterns of data points can lead to finite maximum likelihood estimates (MLE) or infinite MLE of the regression coefficients. Albert and Anderson [On the existence of maximum likelihood estimates in logistic regression models, Biometrika 71 1984, 1, 1–10] gave definitions of different types of data points, which are complete separation, quasicomplete separation and overlap. Conditions for the existence of the MLE for logistic regression models were proposed under different types of data points. Based on these conditions, we propose the necessary and sufficient conditions for the existence of posterior mean under different choices of prior distributions. In this paper, a general wide class of priors, which are informative priors and non-informative priors having proper distributions and improper distributions, are considered for the existence of posterior mean. In addition, necessary and sufficient conditions for the existence of posterior mean for an individual coefficient is also proposed.

Dealing with Separation in Logistic Regression Models

2016 ◽  
Vol 24 (3) ◽  
pp. 339-355 ◽  
Author(s):  
Carlisle Rainey
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Prior Distribution ◽  
Regression Models ◽  
Prior Information ◽  
Jeffreys Prior ◽  
Logistic Regression Models ◽  
Explanatory Variables ◽  
Point Estimates ◽  
Quantities Of Interest

When facing small numbers of observations or rare events, political scientists often encounter separation, in which explanatory variables perfectly predict binary events or nonevents. In this situation, maximum likelihood provides implausible estimates and the researcher might want incorporate some form of prior information into the model. The most sophisticated research uses Jeffreys’ invariant prior to stabilize the estimates. While Jeffreys’ prior has the advantage of being automatic, I show that it often provides too much prior information, producing smaller point estimates and narrower confidence intervals than even highly skeptical priors. To help researchers assess the amount of information injected by the prior distribution, I introduce the concept of a partial prior distribution and develop the tools required to compute the partial prior distribution of quantities of interest, estimate the subsequent model, and summarize the results.

The impact of SPY angiography on intraoperative decision making and outcomes for post-mastectomy reconstruction

2019 ◽  
pp. 1-5
Keyword(s):  
Decision Making ◽  
Logistic Regression ◽  
Skin Necrosis ◽  
Regression Models ◽  
Multivariable Analysis ◽  
P Value ◽  
Flap Necrosis ◽  
Single Institution ◽  
Logistic Regression Models ◽  
The Impact

Objective: While the use of intraoperative laser angiography (SPY) is increasing in mastectomy patients, its impact in the operating room to change the type of reconstruction performed has not been well described. The purpose of this study is to investigate whether SPY angiography influences post-mastectomy reconstruction decisions and outcomes. Methods and materials: A retrospective analysis of mastectomy patients with reconstruction at a single institution was performed from 2015-2017.All patients underwent intraoperative SPY after mastectomy but prior to reconstruction. SPY results were defined as ‘good’, ‘questionable’, ‘bad’, or ‘had skin excised’. Complications within 60 days of surgery were compared between those whose SPY results did not change the type of reconstruction done versus those who did. Preoperative and intraoperative variables were entered into multivariable logistic regression models if significant at the univariate level. A p-value <0.05 was considered significant. Results: 267 mastectomies were identified, 42 underwent a change in the type of planned reconstruction due to intraoperative SPY results. Of the 42 breasts that underwent a change in reconstruction, 6 had a ‘good’ SPY result, 10 ‘questionable’, 25 ‘bad’, and 2 ‘had areas excised’ (p<0.01). After multivariable analysis, predictors of skin necrosis included patients with ‘questionable’ SPY results (p<0.01, OR: 8.1, 95%CI: 2.06 – 32.2) and smokers (p<0.01, OR:5.7, 95%CI: 1.5 – 21.2). Predictors of any complication included a change in reconstruction (p<0.05, OR:4.5, 95%CI: 1.4-14.9) and ‘questionable’ SPY result (p<0.01, OR: 4.4, 95%CI: 1.6-14.9). Conclusion: SPY angiography results strongly influence intraoperative surgical decisions regarding the type of reconstruction performed. Patients most at risk for flap necrosis and complication post-mastectomy are those with questionable SPY results.

scholarly journals Effect of prostatic apex shape (Lee types) and urethral sphincter length in preoperative MRI on very early continence rates after radical prostatectomy

2021 ◽  
Author(s):  
Mike Wenzel ◽  
Felix Preisser ◽  
Matthias Mueller ◽  
Lena H. Theissen ◽  
Maria N. Welte ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Radical Prostatectomy ◽  
Regression Models ◽  
Urethral Sphincter ◽  
Anatomical Characteristics ◽  
Logistic Regression Models ◽  
Pad Test ◽  
Type D ◽  
Multivariable Logistic Regression ◽  
Type C

Abstract Purpose To test the effect of anatomic variants of the prostatic apex overlapping the membranous urethra (Lee type classification), as well as median urethral sphincter length (USL) in preoperative multiparametric magnetic resonance imaging (mpMRI) on the very early continence in open (ORP) and robotic-assisted radical prostatectomy (RARP) patients. Methods In 128 consecutive patients (01/2018–12/2019), USL and the prostatic apex classified according to Lee types A–D in mpMRI prior to ORP or RARP were retrospectively analyzed. Uni- and multivariable logistic regression models were used to identify anatomic characteristics for very early continence rates, defined as urine loss of ≤ 1 g in the PAD-test. Results Of 128 patients with mpMRI prior to surgery, 76 (59.4%) underwent RARP vs. 52 (40.6%) ORP. In total, median USL was 15, 15 and 10 mm in the sagittal, coronal and axial dimensions. After stratification according to very early continence in the PAD-test (≤ 1 g vs. > 1 g), continent patients had significantly more frequently Lee type D (71.4 vs. 54.4%) and C (14.3 vs. 7.6%, p = 0.03). In multivariable logistic regression models, the sagittal median USL (odds ratio [OR] 1.03) and Lee type C (OR: 7.0) and D (OR: 4.9) were independent predictors for achieving very early continence in the PAD-test. Conclusion Patients’ individual anatomical characteristics in mpMRI prior to radical prostatectomy can be used to predict very early continence. Lee type C and D suggest being the most favorable anatomical characteristics. Moreover, longer sagittal median USL in mpMRI seems to improve very early continence rates.

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