Reassessing the Effectiveness of Right Heart Catheterization (RHC) in the Initial Care of Critically Ill Patients using Targeted Maximum Likelihood Estimation

Citation: Akosile M, Zhu H, Zhang S, Johnson NP, Lai D, et al. (2018) Reassessing the Effectiveness of Right Heart Catheterization (RHC) in the Initial Care of Critically Ill Patients using Targeted Maximum Likelihood Estimation. Int J Clin Biostat Biom 4:018. doi.org/10.23937/2469-5831/1510018 Accepted: July 26, 2018: Published: July 28, 2018 Copyright: © 2018 Akosile M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Introduction
Despite its long-standing clinical use since 1970 [1], right heart catheterization (RHC) for critically ill patients remains controversial.Initial observational series [2] and subsequent randomized controlled trials [3] failed to demonstrate benefit.While RHC remains a fundamental diagnostic tool in the outpatient setting for a variety of cardiopulmonary diseases (notably pulmonary hypertension, severe heart failure or prior heart transplantation, and shunt quantification), some observers have written "obituaries" for the pulmonary artery catheter used to perform RHC in critical care settings [4].Although RHC for cardiogenic shock remains a distinct entity with possible advantage [5], its broader role in critically ill patients has been appropriately limited due to the results of clinical trials.
One of the first studies to question the value of RHC in critically ill patients used an observational design [2].Not only did it show no benefit, but it suggested increased mortality.Because this signal of harm was not seen in a subsequent meta-analysis of over 5,000 patients from 13 randomized trials [3], a reasonable hypothesis suggests that unadjusted bias existed within the observational cohort where RHC was selected for clinical indications [2].

TMLE
TMLE is a two-step semiparametric method.Denote A as the treatment assignment such that A = 1 means the patient received RHC and A = 0 means the patient did not receive RHC.Let W denote patient baseline covariates, and denote ( ) , S t A W as the survival probability of a patient at time t given treatment assignment A and baseline covariates W. Define the target parameter as , where Ψ maps a distribution P to a real number in R, P 0 is the true data-generating distribution, Q 0 is a portion of P 0 relevant to Ψ.
In the first step, obtain an initial estimation of P 0 or Q 0 by using machine learning (super learner).Denote the initial estimator as 0 n Q .Given an initial estimator, we can build a fluctuation working model and define a proper loss function of which the derivative with respect to ∈ equals the influence curve of the target parameter.In the second step, update the initial estimate in a step targeted toward making an optimal bias-variance tradeoff for the parameter of interest ( )( ) , instead of the whole distribution P 0 .We can In medical research, the marginal treatment effect at the population level is often of particular interest.It is the average causal effect of the treatment on the outcome by comparing the population if everyone was treated to the population if everyone were untreated.In practice, potential confounding covariates will invalidate such causal effects.Propensity score methods (PSM) [6,7] are widely used to address measured confounding, and Connors, et al. [2] used PSM to analyze their observational series.However, PSM suffers from problems that can make the study results misleading, biased, or challenging to interpret.First, the effect and validity of PSM for removing confounding bias heavily depends on the correct specification of the parameter propensity score model.But restricted parametric statistical models with a finite number of unknown parameters used for calculating the propensity score may not capture the true, complicated, underlying probability distribution of the real world.Second, maximum likelihood estimation (MLE) relies on an overall fit of the entire probability distribution, but the parameter of interest (such as the marginal difference of the treatment effects) is usually related to just a relevant subset.As a result, the estimation is not efficient.Third, as an estimating-equation-based methods, PSM is not robust to sparsity.Specifically, extreme propensity scores can result in unstable estimates with high variance.The estimates may be even outside the constraints of the statistical model.TMLE [8] has been proposed to overcome these problems by offering the following advantages.First, TMLE is an instrumental tool used in semiparametric or nonparametric models avoiding the assumption of a misspecified parametric statistical model.Moreover, TMLE has excellent flexibility in incorporating a variety of machine learning methods to estimate the outcome and exposure mechanisms, which can minimize bias in comparison with misspecified regressions.Using machine learning algorithms can be particularly advantageous in avoiding model misspecification when there is a large number of covariates and potentially complex relationships among them.With semiparametric and machine learning techniques, TMLE can capture the true probability distribution.Second, TMLE targets learning with a specific focus on the parameter of interest instead of the whole distribution.As a result, it is more efficient than traditional MLE.Third, TMLE is doubly robust, which means that TMLE leads to unbiased estimates even under misspecification of one of the outcome models or the treatment model.Fourth, TMLE employs a substitution estimator that is more robust to outliers and sparsity than the estimating-equation-based estimators.Fifth, results from TMLE can be interpreted as causal effects under standard causal assumptions.However, due to its novelty and theoretical difficulty, TMLE has seldom been used in critical care studies.Therefore, we re-analyzed the original observational study of RHC in critically ill patients but using TMLE instead of their original PSM as a novel application to study its ability to match the results of randomized con-were -0.06 (95% CI, (-0.087, -0.033)) and -0.06 (95% CI, (-0.089, -0.031)), respectively.All the results (Table 2) showed that patients who did not undergo RHC had a significantly higher survival probability than patients who underwent RHC.

Conclusion
Connors, et al. [2] used PSM to analyze the dataset in the SUPPORT study.However, there are many problems with PSM that make the study results misleading, biased, and challenging to interpret.This paper used an innovative alternative to PSM, TMLE, to confirm that patients with RHC had a significantly decreased 30-day and 60-day survival in comparison to patients without RHC during initial care.This paper will advance the understanding of TMLE for analysis of observational studies, and promote the application of TMLE in the critical care studies.
update the initial estimator by estimating ∈ through an interated or a one-step process (usually a logistic regression) and denote the updated version as n P * and n Q * .The TMLE is the substitution estimator obtained by plugging n P * or n Q * into the target parameter mapping ( ) ( )( ) * * denotes the observed influence curve under distribution n P * .Under regular conditions, we have