Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation
Issue:
Volume 10, Issue 5, October 2022
Pages:
176-204
Received:
6 September 2022
Accepted:
4 October 2022
Published:
17 October 2022
DOI:
10.11648/j.ajam.20221005.11
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Abstract: Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even though they are random variables, typically derived from a logistic regression analysis applied to the same cohort with treatment use as the outcome. Bootstrapping the entire process of weight-derivation, Cox regression analysis and estimation produces valid confidence intervals that account for the variability in the weights, but this method may be time- and resource-intensive for large cohorts. Here the delta method is used to derive large sample interval estimates of treatment effects and event risks that account for variability in the weights analytically. External time-dependent covariates, left truncation, and cohort sampling study designs are accommodated. Simulation studies show that this method provides confidence interval coverage probabilities at or above nominal level for small and moderate sample sizes. Stabilization of the weights by multiplying them by the overall treatment rate noticeably improves confidence interval coverage probabilities. Software to perform the calculations is freely available.
Abstract: Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even th...
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On the Caginalp for a Conserved Phase-Field with Two Temperatures
Narcisse Batangouna,
Cyr Séraphin Ngamouyih Moussata,
Urbain Cyriaque Mavoungou
Issue:
Volume 10, Issue 5, October 2022
Pages:
205-211
Received:
15 December 2021
Accepted:
7 March 2022
Published:
24 October 2022
DOI:
10.11648/j.ajam.20221005.12
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Abstract: The general theme of this article is the theorical study of phase field systems, more precisely that of Caginalp. This work is motivated by their immense applications in many physical fields, industriels… The Caginalp problem gives the authors a formulation based on the fact that the phases separated by an unknown regular interface, which evolves in a regular way. The authors’ aim in this paper is to study on Caginalp for a conserved Phase-field with two temperatures. The authors have worked on the existence and uniqueness of the Caginalp phase field in a conservative version. Moreover, the authors have also used Dirichlet type boundary conditions with a regular potential; existence and uniqueness are analyzed by means of absorbing bounded sets. The authors build the solution of the conservative problem on the estimates which lead authors to treat the problem well to arrive at the result. These equations are known as the conserved phase-field based on type II heat conduction and two temperatures. The authors consider a regular potential, more precisely a polynomial with edge conditions of Dirichlet type. More precisely, the authors prove the existence and uniqueness of solutions.
Abstract: The general theme of this article is the theorical study of phase field systems, more precisely that of Caginalp. This work is motivated by their immense applications in many physical fields, industriels… The Caginalp problem gives the authors a formulation based on the fact that the phases separated by an unknown regular interface, which evolves i...
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Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System
Mayaka Augustine Ayanga,
Mathew Ngugi Kinyanjui,
Jeconia Okelo Abonyo,
Johana Kibet Sigey
Issue:
Volume 10, Issue 5, October 2022
Pages:
212-222
Received:
30 August 2022
Accepted:
12 October 2022
Published:
24 October 2022
DOI:
10.11648/j.ajam.20221005.13
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Abstract: In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite difference method based on the forward-time central-space scheme. The resulting difference equations are simulated in MATLAB software to obtain the profiles of the flow variables. The skin-friction coefficient and the rates of heat and mass transfer are also computed. The simulation results are presented graphically and in tabular forms, and also discussed. The main findings are that an increase in the joule heating parameter results in a uniform increase in the velocity and temperature profiles near the plate but remain constantly distributed away from the plate. This observation implies that the flow is influenced substantially by the strength of joule heating near the plate and in the bulk of the fluid. The results obtained in this study regarding thermal and mass diffusion effects can be applied in the industry, for instance, in the separation of isotopes contained in a mixture of very light molecular-weight gases (for instance, hydrogen and helium) and medium molecular-weight gases (for instance, nitrogen and air).
Abstract: In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite differenc...
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