In statistics, missing data refers to the absence of observations or values in a dataset. There are different types of missingness that can occur, and understanding these types is important when deciding how to handle missing data.

1. Missing Completely at Random (MCAR)

   • The probability of a value being missing is the same for all observations in the dataset, regardless of the observed values. 

   • The missingness is completely random and unrelated to any other variable in the dataset.

2. Missing at Random (MAR)

   • The probability of a value being missing depends on other variables in the dataset, but not on the missing value itself. 

   • The missingness is related to observed variables in the dataset.

3. Missing Not at Random (MNAR)

   • The probability of a value being missing depends on the missing value itself or on some unobserved variable in the dataset. 

   • The missingness is related to the value that is missing or to some other variable that was not measured or recorded.

Understanding the type of missingness is important because it determines the most appropriate method for handling missing data. MCAR missingness can be handled using any imputation method, while MAR missingness can be handled using imputation methods that incorporate observed variables. MNAR missingness is more challenging to handle, and it often requires more sophisticated imputation methods or the use of sensitivity analysis to examine the impact of the missingness on the results.

1. Fill the nulls of EMTALA Y/N(Patient Status Details) as "No" Where the  “Request Status” equal to “Accepted”

2. Fill LOS Outlier as "Not Outlier" Where the  “Request Status” equal to “Accepted” & LOS is not null

Rows where "Request Status" is "Accepted"

By analyzing the missingness patterns using techniques such as matrix, heat maps, and tree diagrams. It seems that the missing values in both datasets belong to the type of Missing at Random (MAR). This means that the probability of a value being missing depends on the observed values in the dataset, but not on the missing values themselves.

KNN imputation is a method where the missing values in a dataset are imputed based on the values of the k-nearest neighbors of the observation with the missing value. This method can be used for both numeric and categorical data. 

MICE (Multiple Imputation by Chained Equations) is a method where missing values are imputed iteratively modeling each variable with missing values conditional on the other variables and imputing missing values based on that model. This method is also applicable to both numeric and categorical data. 

1. KNN imputed categories and KNN imputed numerics separately on original data: 

1. • Applied KNN imputation separately for the categorical and numeric variables in the dataset. 

   • This approach can work well if the missingness patterns for these two types of variables are different. However, if the missingness patterns are similar, it may be more efficient to apply KNN imputation on the entire dataset, regardless of variable type. 

1. KNN imputed the whole original data:

   • Applied KNN imputation on the entire dataset, including both categorical and numeric variables. 

   • This approach can be effective if the missingness patterns are similar across all variables. 

3. MICE imputed on data of request status is accepted: 

   • Applied MICE imputation only on the subset of the data where the request status was accepted. 

   • This approach can work well if the missingness patterns are different for accepted requests compared to rejected requests. 

4. KNN imputed categories and MICE imputed numerics on data of request status is accepted: 

   • Applied KNN imputation for the categorical variables and MICE imputation for the numeric variables, but only on the subset of the data where the request status was accepted. 

   • This approach can be effective if the missingness patterns for these two types of variables are different, and if the missingness patterns for accepted requests are different from those for rejected requests. 

Overall, the choice of imputation method and strategy will depend on the specific characteristics of the data and the research question trying to answer. It is important to carefully evaluate the performance of different imputation methods and strategies, and to consider the assumptions underlying each method.

The kernel density plots suggests that the imputation of the filtered data performs better.

• A kernel density plot with four different curves, representing the density of the variable "LOS" after different imputation techniques have been applied. 

• A kernel density plot with four different curves, representing the density of the variable "Age" after different imputation techniques have been applied. 

Based on the kernel density plots, both KNN and MICE imputation techniques on the filtered data appear to have similar performance.

• A kernel density plot with three different curves, representing the density of the variable "LOS" after different imputation techniques have been applied. 

• A kernel density plot with three different curves, representing the density of the variable "Age" after different imputation techniques have been applied.