How To Handle Paired Wilcox Test With Incomplete Follow-up?

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Introduction

In experimental studies, comparing a blood variable at two different points in time on the same participants is a common practice. However, when dealing with non-normal distributed data, traditional parametric tests may not be the best choice. The paired Wilcoxon test, also known as the Wilcoxon signed-rank test, is a non-parametric alternative that can be used to compare paired data. However, when there are incomplete follow-ups, handling the paired Wilcoxon test can be challenging. In this article, we will discuss how to handle paired Wilcoxon test with incomplete follow-up.

Understanding Paired Wilcoxon Test

The paired Wilcoxon test is a non-parametric test used to compare paired data. It is a two-sample test that compares the differences between two related groups. The test is based on the idea that the differences between the two groups are not normally distributed, and therefore, a parametric test may not be the best choice.

Why Use Paired Wilcoxon Test?

The paired Wilcoxon test is a good choice when:

  • The data is not normally distributed.
  • The data is paired, meaning that each observation in one group has a corresponding observation in the other group.
  • The data is ordinal, meaning that the data can be ranked in order.

Handling Incomplete Follow-up

Incomplete follow-up is a common issue in experimental studies. When participants do not complete the follow-up, it can lead to missing data, which can affect the validity of the results. There are several ways to handle incomplete follow-up:

1. Listwise Deletion

Listwise deletion is a simple method where the participant with incomplete follow-up is removed from the analysis. This method is easy to implement, but it can lead to biased results if the missing data is not missing completely at random (MCAR).

2. Pairwise Deletion

Pairwise deletion is a method where the participant with incomplete follow-up is removed from the pair. This method is more robust than listwise deletion, but it can still lead to biased results if the missing data is not MCAR.

3. Multiple Imputation

Multiple imputation is a method where the missing data is imputed multiple times using different models. This method is more robust than listwise and pairwise deletion, but it requires more computational resources.

4. Last Observation Carried Forward (LOCF)

LOCF is a method where the last observation is carried forward to replace the missing data. This method is simple to implement, but it can lead to biased results if the missing data is not MCAR.

5. Regression Imputation

Regression imputation is a method where the missing data is imputed using a regression model. This method is more robust than LOCF, but it requires more computational resources.

Example Code in R

Here is an example code in R using the Wilcoxon function from the coin package:

# Load the necessary libraries
library(coin)
library(ggplot2)

set.seed(123)
n <- 100
x <- rnorm(n)
y <- rnorm(n)
z <- rnorm(n)
df <- data.frame(x, y, z)



test <- wilcoxsign_test(x ~ y, data = df)



print(test)

Conclusion

Handling paired Wilcoxon test with incomplete follow-up can be challenging. However, there are several methods that can be used to handle this issue, including listwise deletion, pairwise deletion, multiple imputation, LOCF, and regression imputation. The choice of method depends on the research question and the characteristics of the data. In this article, we discussed the paired Wilcoxon test and how to handle incomplete follow-up using different methods.

References

  • Hollander, M., & Wolfe, D. A. (1999). Nonparametric statistical methods. Wiley.
  • Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics, 1(1), 80-83.
  • R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing.

Further Reading

  • Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.
  • Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data. Wiley.
  • Schafer, J. L. (1997). Analysis of incomplete multivariate data. Chapman and Hall/CRC.
    Q&A: Handling Paired Wilcoxon Test with Incomplete Follow-up ===========================================================

Introduction

In our previous article, we discussed how to handle paired Wilcoxon test with incomplete follow-up. However, we know that there are many questions that arise when dealing with this issue. In this article, we will answer some of the most frequently asked questions about handling paired Wilcoxon test with incomplete follow-up.

Q: What is the best method to handle incomplete follow-up?

A: The best method to handle incomplete follow-up depends on the research question and the characteristics of the data. Listwise deletion, pairwise deletion, multiple imputation, LOCF, and regression imputation are all valid methods, but they have different strengths and weaknesses. It's essential to consider the assumptions of each method and choose the one that best fits your research question.

Q: What is the difference between listwise deletion and pairwise deletion?

A: Listwise deletion removes the participant with incomplete follow-up from the analysis, while pairwise deletion removes the participant with incomplete follow-up from the pair. Pairwise deletion is more robust than listwise deletion, but it can still lead to biased results if the missing data is not missing completely at random (MCAR).

Q: What is multiple imputation, and how does it work?

A: Multiple imputation is a method where the missing data is imputed multiple times using different models. This method is more robust than listwise and pairwise deletion, but it requires more computational resources. The idea behind multiple imputation is to create multiple versions of the dataset with different imputed values, and then analyze each version separately. The results are then combined to produce a single estimate of the effect size.

Q: What is LOCF, and how does it work?

A: LOCF (Last Observation Carried Forward) is a method where the last observation is carried forward to replace the missing data. This method is simple to implement, but it can lead to biased results if the missing data is not MCAR. LOCF assumes that the missing data is missing at random (MAR), and that the last observation is a good representation of the missing data.

Q: What is regression imputation, and how does it work?

A: Regression imputation is a method where the missing data is imputed using a regression model. This method is more robust than LOCF, but it requires more computational resources. The idea behind regression imputation is to use a regression model to predict the missing data, based on the observed data.

Q: How do I choose the best method for my research question?

A: To choose the best method for your research question, you need to consider the assumptions of each method and the characteristics of your data. You should also consider the research question and the type of data you are working with. It's essential to consult with a statistician or a researcher who has experience with handling incomplete follow-up.

Q: Can I use a combination of methods to handle incomplete follow-up?

A: Yes, you can use a combination of methods to handle incomplete follow-up. For example, you can use multiple imputation to impute the missing data, and then use pairwise deletion to remove the participant with incomplete follow-up from the pair. However, it's essential to consider the assumptions of each method and the characteristics of your data.

Q: How do I report the results of a paired Wilcoxon test with incomplete follow-up?

A: When reporting the results of a paired Wilcoxon test with incomplete follow-up, you should mention the method used to handle the incomplete follow-up. You should also report the results of the test, including the effect size and the p-value. Additionally, you should discuss the limitations of the study and the potential biases that may have arisen due to the incomplete follow-up.

Conclusion

Handling paired Wilcoxon test with incomplete follow-up can be challenging, but there are several methods that can be used to handle this issue. By understanding the assumptions of each method and the characteristics of your data, you can choose the best method for your research question. Remember to report the results of the test, including the effect size and the p-value, and discuss the limitations of the study and the potential biases that may have arisen due to the incomplete follow-up.

References

  • Hollander, M., & Wolfe, D. A. (1999). Nonparametric statistical methods. Wiley.
  • Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics, 1(1), 80-83.
  • R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing.

Further Reading

  • Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.
  • Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data. Wiley.
  • Schafer, J. L. (1997). Analysis of incomplete multivariate data. Chapman and Hall/CRC.