Publications by Enwu Liu
Plot restricted cubic spline
This note is to study the ‘plotRCS’ package, developed by Dr. Rongrui Huo at Guangxi Medical University Cancer Hospital in Nanning, China. All functions were originally written by Dr. Huo, with minor modifications made by me to suit my specific needs. rcsplot_check <- function(data, outcome = NULL, ...
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Convert a string to a variable name in R function
When writing our own R functions, sometimes we need to convert a string to a variable name to reduce the number of lines of code. The key to doing this is to pass the string with quotes (““) to the function, and then use the eval() and sym()/as.name() functions. Below is the R code to convert”anyI_new” and “all_blocks” to variable n...
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SAS loop errors
If we run the following loop in SAS (loop numbers 2,4,5,6,7,8,9, or any other specific strings), we will get strange SAS error message %macro loop_bmd; %local k j; %let k=1; %let visit="2:4:5:6:7:8:9"; %do %while (%scan(&visit, &k, %str(:)) ne); %let j= %scan(&visit, &k, :); %put &j; %let k = %eval(&k + 1); %end; %mend loop_bmd; %loop_bm...
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Notes for selection model and mixture pattern model
Paper: Sensitivity analysis for clinical trials with missing continuous outcome data using controlled multiple imputation: A practical guide Method 1: equation (1) \[f(R_i|Y_i,X_I,\phi)f(Y_i|X_i,\theta)=f(Y_i,R_i|X_i,\theta,\phi)=f(Y_i|R_i,X_i,\theta)f(R_i|X_i,\phi)\tag{1}\] Prove \[f(R_i|Y_i,X_I,\phi)f(Y_i|X_i,\theta)=f(Y_i,R_i|X_i,\theta,\phi)...
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Linear mixed models for repeated measurements in clinical trials
1. Repeated measurement and clinical tiral Repeated measures are quite common in clinical trials. A repeated measures study involves measuring outcomes at different times; it does not necessarily mean that covariates or predictor variables were also measured repeatedly. For the design of repeated measures studies, general linear mixed models, g...
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Regression analysis for cluster data
Clustered data are quite common in epidemiological studies. For example, in repeated measures, individuals are clustered with themselves. In school surveys, students are clustered within schools and classes. In crossover designs, individuals are clustered with themselves, and in group-based randomized trials, individuals are clustered within t...
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Delta method for predictive models
The Delta method is very useful in predictive modeling, as it enables the calculation of 95% confidence intervals for predicted values in regression models. Interestingly, it can also be applied to determine a 95% confidence interval for probabilities. For instance, in a logistic regression model, the probability is a function of coefficients, ...
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Weighted Least Square Regression
For an ordinary least squares regression we assume that variance of the error term are constant, when this assumption is violated we can use a weighted least square regression method. This note is mainly from STAT 501 of the Pennsylvania State University. Obtain the data set Galton. galton<-read.table("https://online.stat.psu.edu/onlinecourses/s...
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Multiplicative random effect model of meta-analysis
For a random-effect model meta-analysis we usually assume that the random effects are additive. In a multiplicative random-effects model, the variant-specific estimates are assumed to be normally distributed with variance \(\phi^2v_i\) where \(\phi^2\) is an overdispersion parameter. The appropriate value of \(\phi\) can be established by runn...
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Confidence interval for ratios
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. Here is a very good note on Taylor Approximation and the Delta Method. Another one Refer to: 1.Beyene, Joseph, and Rahim Moineddin...
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