Publications by Enwu Liu
Confidence interval for ratio parameters
There are three methods to construct confidence intervals for ratio parameters, namely: (1) Delta method (2) Fieller’s method and (3) profile-likelihood based interval on generalized linear model (GLM) technique. Refer to: 1.Beyene, Joseph, and Rahim Moineddin. “Methods for confidence interval estimation of a ratio parameter with applicatio...
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Rstudio blank GUI
“when start RStudio, none of the windows inside the main frame come up, and none of the menu options display menu options when clicked. It’s just an blank page.” This problem quite common for R studio software. I also have this problem. I found this solution is working for me. In Windows Explorer, go to C:. Delete the Desktop.ini file F...
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Clumping
Clumping is a procedure in which only the most significant SNP (i.e., the one with the lowest p-value) within each LD block is identified and chosen for further analysis. This process decreases the correlation among the remaining SNPs while preserving those SNPs with the most robust statistical support. Here is the clumping procedure by the pli...
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A note on competing risks in survival data analysis
Competing risks are quite common in epidemiological studies, and various modeling approaches have been developed to assess the impact of covariates on outcome in the presence of these competing risks. These methods include the cause-specific hazard model, the Fine-Gray model (also known as the sub-distribution hazard model), the multi-states m...
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A SAS macro to change all variable names in a dataset.
Sometimes, we need to change the names of variables in a dataset. This is particularly common in Mendelian randomization studies when merging two datasets with many overlapping variable names. To prevent the overwriting of variables with the same names, we must rename one of them. The following SAS macro is highly efficient for performing this ...
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A note on competing risks in survival data analysis
Competing risks are quite common in epidemiological studies, and various modeling approaches have been developed to assess the impact of covariates on outcome in the presence of these competing risks. These methods include the cause-specific hazard model, the Fine-Gray model (also known as the sub-distribution hazard model), the multi-states m...
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Tensor and tensor product
A Tensor is a container which can house data in N dimensions. Tensors are in fact generalizations of matrices to N-dimensional spaces, which is why they’re often used interchangeably with the matrix, (which is specifically a 2-dimensional or Rank2 tensor).\(^1\) Tensor product for the vector:components of the first vector are multiplied by t...
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Simulating survival data with competing risk
Specify the cause-specific hazards \(\alpha_{01}(t)\) and \(\alpha_{02}(t)\).(suppose there were only two competing events) Simulate failure times \(T\) with all-cause hazard \(\alpha_0(t) = \alpha_{01}(t) + \alpha_{02}(t)\). Run a binomial experiment for a simulated failure time \(T\), which decides with probability \(\alpha_{0j}(T)/(\alpha_{01...
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Kolmogorov differential equations
This is a note for the Kolmogorov differential equations from the MIT OpenCourseWare Discrete Stochastic Processes. For the example 6.3.1 a 2-state Markov process where \(q_{01}=\lambda\) and \(q_{10}=\mu\) Use the Kolmogorov forward equations for \(P_{01}(t)\), we get the following equation: \[\dfrac{dP_{01}(t)}{dt} = \lambda -P_{01}(t)(\la...
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MLE and sufficient statistic
The theorem states: Let \(X_1, X_2,...,X_n\) denote a random sample from a distribution that has pdf or pmf \(f(x; \theta), \theta \in \Omega.\) If a sufficient statistic \(Y_1 = u_1(X_1, X_2,...,X_n)\) for \(\theta\) exists and if a maximum likelihood estimator \(\hat{\theta}\) of \(\theta\) also exists uniquely, then \(\hat{\theta}\) is a fun...
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