scholarly journals On the Effect of a Binary Treatment in the Presence of a Control Covariate

2020 ◽  
Vol 72 (1) ◽  
pp. 35-42
Author(s):  
Rajeshwari Majumdar
Keyword(s):  
Linear Regression ◽  
Propensity Score ◽  
Nonparametric Regression ◽  
Conditional Variance ◽  
Conditional Covariance ◽  
Primary 62G08 ◽  
Response Variable ◽  
Second Moments ◽  
Secondary 62J05 ◽  
First Moment

The nonparametric regression of a response variable on a binary treatment and a control covariate equals the nonparametric regression of the response on the control plus the conditional (given the control) linear regression of the resulting residual on the residual of the nonparametric regression of the treatment on the control. While similar decompositions are typically obtained using the technique of orthogonal projection applicable to random variables with finite second moments, this result holds if the response only has a finite first moment and allows the control to be completely arbitrary. Consequently, if the propensity score of the treatment is bounded away from zero and one, the treatment effect, after controlling for the covariate, equals the ratio of the conditional covariance of the response and the treatment to the conditional variance of the treatment. AMS 2020 subject classification: Primary 62G08, Secondary 62J05, 91F10, 62P20, 62P25

scholarly journals Is oxygen therapy beneficial for normoxemic patients with acute heart failure? A propensity score matched study

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yue Yu ◽  
Ren-Qi Yao ◽  
Yu-Feng Zhang ◽  
Su-Yu Wang ◽  
Wang Xi ◽  
...  
Keyword(s):  
Heart Failure ◽  
Linear Regression ◽  
Propensity Score ◽  
Hospital Mortality ◽  
Acute Heart Failure ◽  
Oxygen Therapy ◽  
Ambient Air ◽  
Supplemental Oxygen ◽  
Research Database ◽  
Icu Mortality

Abstract Background The clinical efficiency of routine oxygen therapy is uncertain in patients with acute heart failure (AHF) who do not have hypoxemia. The aim of this study was to investigate the association between oxygen therapy and clinical outcomes in normoxemic patients hospitalized with AHF using real-world data. Methods Normoxemic patients diagnosed with AHF on ICU admission from the electronic ICU (eICU) Collaborative Research Database were included in the current study, in which the study population was divided into the oxygen therapy group and the ambient-air group. Propensity score matching (PSM) was applied to create a balanced covariate distribution between patients receiving supplemental oxygen and those exposed to ambient air. Linear regression and logistic regression models were performed to assess the associations between oxygen therapy and length of stay (LOS), and all-cause in-hospital as well as ICU mortality rates, respectively. A series of sensitivity and subgroup analyses were conducted to further validate the robustness of our findings. Results A total of 2922 normoxemic patients with AHF were finally included in the analysis. Overall, 42.1% (1230/2922) patients were exposed to oxygen therapy, and 57.9% (1692/2922) patients did not receive oxygen therapy (defined as the ambient-air group). After PSM analysis, 1122 pairs of patients were matched: each patient receiving oxygen therapy was matched with a patient without receiving supplemental oxygen. The multivariable logistic model showed that there was no significant interaction between the ambient air and oxygen group for all-cause in-hospital mortality [odds ratio (OR) 1.30; 95% confidence interval (CI) 0.92–1.82; P = 0.138] or ICU mortality (OR 1.39; 95% CI 0.83–2.32; P = 0.206) in the post-PSM cohorts. In addition, linear regression analysis revealed that oxygen therapy was associated with prolonged ICU LOS (OR 1.11; 95% CI 1.06–1.15; P <  0.001) and hospital LOS (OR 1.06; 95% CI 1.01–1.10; P = 0.009) after PSM. Furthermore, the absence of an effect of supplemental oxygen on mortality was consistent in all subgroups. Conclusion Routine use of supplemental oxygen in AHF patients without hypoxemia was not found to reduce all-cause in-hospital mortality or ICU mortality.

Estimation in Dynamic Linear Regression Models with Infinite Variance Errors

1993 ◽  
Vol 9 (4) ◽  
pp. 570-588 ◽  
Author(s):  
Keith Knight
Keyword(s):  
Asymptotic Behavior ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Infinite Variance ◽  
Linear Regression Models ◽  
Asymptotically Normal ◽  
Second Moments ◽  
True Values

This paper considers the asymptotic behavior of M-estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n−½ rate.

On the limit behavior of a multicompartment storage model with an underlying Markov chain

1988 ◽  
Vol 20 (1) ◽  
pp. 208-227
Author(s):  
Eric S. Tollar
Keyword(s):  
Brownian Motion ◽  
Markov Chain ◽  
Limit Behavior ◽  
Moment Conditions ◽  
Storage Model ◽  
Second Moments ◽  
First Moment ◽  
Inputs And Outputs

The present paper considers a multicompartment storage model with one-way flow. The inputs and outputs for each compartment are controlled by a denumerable-state Markov chain. Assuming finite first and second moments, it is shown that the amounts of material in certain compartments converge in distribution while for others they diverge, based on appropriate first-moment conditions on the inputs and outputs. It is also shown that the diverging compartments under suitable normalization converge to functionals of Brownian motion, independent of those compartments which converge without normalization.

scholarly journals Is oxygen therapy beneficial for normoxemic patients with acute heart failure? A propensity score matched study

2020 ◽  
Author(s):  
Yue Yu ◽  
Ren-qi Yao ◽  
Yu-feng Zhang ◽  
Su-yu Wang ◽  
Wang Xi ◽  
...  
Keyword(s):  
Heart Failure ◽  
Linear Regression ◽  
Propensity Score ◽  
Hospital Mortality ◽  
Acute Heart Failure ◽  
Oxygen Therapy ◽  
Ambient Air ◽  
Supplemental Oxygen ◽  
Research Database ◽  
Icu Mortality

Abstract Background The clinical efficiency of routine oxygen therapy is uncertain in patients with acute heart failure (AHF) who do not have hypoxemia. The aim of this study was to investigate the association between oxygen therapy and clinical outcomes in normoxemic patients hospitalized with AHF using real-world data.Methods Normoxemic patients diagnosed with AHF on ICU admission from the electronic ICU (eICU) Collaborative Research Database were included in the current study, in which the study population was divided into the oxygen therapy group and the ambient-air group. Propensity score matching (PSM) was applied to create a balanced covariate distribution between patients receiving supplemental oxygen and those exposed to ambient air. Linear regression and logistic regression models were performed to assess the associations between oxygen therapy and length of stay (LOS), and all-cause in-hospital as well as ICU mortality rates, respectively. A series of sensitivity and subgroup analyses were conducted to further validate the robustness of our findings.Results A total of 2,922 normoxemic patients with AHF were finally included in the analysis. Overall, 42.1% (1,230/2,922) patients were exposed to oxygen therapy, and 57.9% (1,692/2,922) patients did not receive oxygen therapy (defined as the ambient-air group). After PSM analysis, 1,122 pairs of patients were matched: each patient receiving oxygen therapy was matched with a patient without receiving supplemental oxygen. The multivariable logistic model showed that there was no significant interaction between the ambient air and oxygen group for all-cause in-hospital mortality (odds ratio [OR] 1.30; 95% confidence interval [CI] 0.92–1.82; P=0.138) or ICU mortality (OR 1.39; 95% CI 0.83–2.32; P༝0.206) in the post-PSM cohorts. In addition, linear regression analysis revealed that oxygen therapy was associated with prolonged ICU LOS (OR 1.11; 95% CI 1.06–1.15; P༜0.001) and hospital LOS (OR 1.06; 95% CI 1.01–1.10; P༝0.009) after PSM. Furthermore, the absence of an effect of supplemental oxygen on mortality was consistent in all subgroups.Conclusions Routine use of supplemental oxygen in AHF patients without hypoxemia was not found to reduce all-cause in-hospital mortality or ICU mortality.

scholarly journals A Generalized Equilibrium Transform with Application to Error Bounds in the Rényi Theorem with No Support Constraints

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 577 ◽  
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Type Inequality ◽  
Random Variables ◽  
Independent Random Variables ◽  
Exact Order ◽  
Second Moments ◽  
Generalized Equilibrium ◽  
Kantorovich Distance ◽  
The One ◽  
First Moment ◽  
Geometric Sums

We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties. In particular, we prove an optimal moment-type inequality for the Kantorovich distance between a distribution and its equilibrium transform. Using the introduced transform and Stein’s method, we investigate the rate of convergence in the Rényi theorem for the distributions of geometric sums of independent random variables with identical nonzero means and finite second moments without any constraints on their supports. We derive an upper bound for the Kantorovich distance between the normalized geometric random sum and the exponential distribution which has exact order of smallness as the expectation of the geometric number of summands tends to infinity. Moreover, we introduce the so-called asymptotically best constant and present its lower bound yielding the one for the Kantorovich distance under consideration. As a concluding remark, we provide an extension of the obtained estimates of the accuracy of the exponential approximation to non-geometric random sums of independent random variables with non-identical nonzero means.

Regional Flood Relationships by Nonparametric Regression

1995 ◽  
Vol 26 (2) ◽  
pp. 73-90 ◽  
Author(s):  
D. Gringras ◽  
M. Alvo ◽  
K. Adamowski
Keyword(s):  
Linear Regression ◽  
Nonparametric Regression ◽  
Screening Tool ◽  
Relationship Development ◽  
Simulation Studies ◽  
Parametric Regression ◽  
Practical Applications ◽  
Theoretical Assumptions ◽  
Data Deficient ◽  
Mean Square Errors

Since some theoretical assumptions needed in linear regression are not always fulfilled in practical applications, nonparametric regression was investigated as an alternative method in regional flood relationship development. Simulation studies were developed to compare the bias, the variance and the root-mean-square-errors of nonparametric and parametric regressions. It was concluded that when an appropriate parametric model can be determined, parametric regression is preferred over nonparametric regression. However, where an appropriate model cannot be determined, nonparametric regression is preferred. It was found that both linear regression and nonparametric regression gave very similar regional relationships for annual maximum floods from New Brunswick, Canada. It was also found that nonparametric regression can be useful as a screening tool able to detect data deficient relationships.

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