Statistical Inference Concerning Minimal Mortality of Patients with Congenital Heart Defects after Surgical Repair Open Access
Mao, Wenhao (Spring 2021)
Background: Congenital heart defect (CHD) is a defect in the heart's structure and function due to abnormal heart development before birth. Survival rate after pediatric cardiac surgery has been improved substantially over the last 2-3 decades. Five-year mortality rate reflects the survival experience of the surviving patient sub-population. As the estimated 5-year mortality function had a sharp decline right after the surgery and then rose gradually, the minimal mortality, which is the minimum point of the mortality function and its timing, may characterize the pattern of the 5-year mortality function. However, statistical inference for the timing and minimum mortality is not a standard problem and warrants investigation.
Methods: In this project, we used the Pediatric Cardiac Care Consortium (PCCC) data, a U.S.-based, multicenter registry of pediatric cardiac surgery, as linked to the National Death Index. We tackled two problems. First, we used subsampling method and divide-and-conquer method to construct 95% confidence intervals for timing of the minimum mortality, as we conjectured that the estimator had a cubic root convergence rate. Our goal was to evaluate the feasibility of these confidence intervals. Second, we developed a bias correction procedure for the standard nonparametric minimal mortality estimator, which had a downward bias.
Results: For subsampling method, from simulations with given parameters, the performance of new confidence interval we developed is the best among our methods. When it comes to simulations mimicking the real dataset, it still had a good performance on coverage when the block size is fixed.
The divide-and-conquer method achieved excellent results on simulated data with parameters as obtained by fitting two datasets and performed badly those by fitting single ventricle dataset. It seemed not to be an enough reliable method for inference.
For bias correction for the point estimator of the minimal mortality, our method can reduce bias and mean squared error (MSE). Also, the confidence intervals were close to the nominal level.
Conclusion: Both subsampling and divide-and-conquer methods are state-of-the-art methods for the challenging statistical problem with cube root asymptotics, and they have different assumptions and requirements. Through extensive simulation studies, we found that, unfortunately, neither approach had consistently reliable performance. Further investigation is warranted.
Also, we recommend our bias correction method, which helped us achieve the estimator with smaller bias and MSE.
Table of Contents
1. Introduction 1
2. Materials and Method 3
2.1 Data Sources 3
2.1.1 Pediatric Cardiac Care Consortium data 4
2.1.2 Death Ascertainment 4
2.1.3 Three Datasets 4
2.2 Software and Nominal Level 5
2.3 Statistical Model 5
2.3.1 Data Setting 5
2.3.2 Model 5
2.4 Inference for the timing – subsampling method 7
2.4.1 Asymmetric Confidence Interval 7
2.4.2 Symmetric Confidence Interval 8
2.4.3 Confidence Interval we developed 8
2.4.4 Algorithm 9
2.5 Inference for the timing – divide-and-conquer method 9
2.5.1 Pooled Estimator Based on Mean 9
2.5.2 Pooled Estimator Based on Median 10
2.6 Minimal Mortality 11
2.6.1 Bias of the point estimator 11
2.6.2 Algorithms 12
3. Simulation 14
3.1 simulation models 14
3.2 Evaluation of inference for the timing – subsampling method 14
3.2.1 Artificial Data with Given Parameters 15
3.2.2 Artificial Data with Estimated Parameters after Fitting the Real Dataset – Simple Tetralogy of Fallot Dataset 17
3.2.3 Summary for Subsampling Method 18
3.3 Evaluation of inference for the timing – divide-and-conquer method 19
3.3.1 Artificial Data with Estimated Parameters after Fitting the Real Dataset - Mild Congenital Heart Defect Dataset 19
3.3.2 Artificial Data with Estimated Parameters after Fitting the Real Dataset – Simple Tetralogy of Fallot Dataset 20
3.3.3 Artificial Data with Estimated Parameters after Fitting the Real Dataset – Single Ventricle Dataset 21
3.3.3 Summary for Divide-and-Conquer Method 22
3.4 Estimator and inference for the Minimal Mortality 22
3.4.1 Artificial Data with Given Parameters 23
3.4.2 Artificial Data with Estimated Parameters after Fitting the Real Dataset – Simple Tetralogy of Fallot Dataset 23
3.4.3 Summary 24
4. Application 24
4.1 Subsampling method on Simple Tetralogy of Fallot Dataset 24
4.2 Divide-and-conquer method on Mild Congenital Heart Defect Dataset 25
4.3 Bias correction on Simple Tetralogy of Fallot Dataset 26
5. Discussion and conclusion 26
About this Master's Thesis
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