Maximum likelihood estimation of high-dimensional Student-t copulas

2020 ◽  
Vol 159 ◽  
pp. 108678
Author(s):  
Mark Trede
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
High Dimensional

scholarly journals Effect Estimation in Point-Exposure Studies with Binary Outcomes and High-Dimensional Covariate Data – A Comparison of Targeted Maximum Likelihood Estimation and Inverse Probability of Treatment Weighting

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Menglan Pang ◽  
Tibor Schuster ◽  
Kristian B. Filion ◽  
Mireille E. Schnitzer ◽  
Maria Eberg ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
High Dimensional ◽  
Binary Outcomes ◽  
Treatment Model ◽  
Inverse Probability ◽  
Targeted Maximum Likelihood Estimation ◽  
Targeted Maximum Likelihood ◽  
Doubly Robust

AbstractInverse probability of treatment weighting (IPW) and targeted maximum likelihood estimation (TMLE) are relatively new methods proposed for estimating marginal causal effects. TMLE is doubly robust, yielding consistent estimators even under misspecification of either the treatment or the outcome model. While IPW methods are known to be sensitive to near violations of the practical positivity assumption (e. g., in the case of data sparsity), the consequences of this violation in the TMLE framework for binary outcomes have been less widely investigated. As near practical positivity violations are particularly likely in high-dimensional covariate settings, a better understanding of the performance of TMLE is of particular interest for pharmcoepidemiological studies using large databases. Using plasmode and Monte-Carlo simulation studies, we evaluated the performance of TMLE compared to that of IPW estimators based on a point-exposure cohort study of the marginal causal effect of post-myocardial infarction statin use on the 1-year risk of all-cause mortality from the Clinical Practice Research Datalink. A variety of treatment model specifications were considered, inducing different degrees of near practical non-positivity. Our simulation study showed that the performance of the TMLE and IPW estimators were comparable when the dimension of the fitted treatment model was small to moderate; however, they differed when a large number of covariates was considered. When a rich outcome model was included in the TMLE, estimators were unbiased. In some cases, we found irregular bias and large standard errors with both methods even with a correctly specified high-dimensional treatment model. The IPW estimator showed a slightly better root MSE with high-dimensional treatment model specifications in our simulation setting. In conclusion, for estimation of the marginal expectation of the outcome under a fixed treatment, TMLE and IPW estimators employing the same treatment model specification may perform differently due to differential sensitivity to practical positivity violations; however, TMLE, being doubly robust, shows improved performance with richer specifications of the outcome model. Although TMLE is appealing for its double robustness property, such violations in a high-dimensional covariate setting are problematic for both methods.

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