Here's how you can address missing data in statistical analysis.

The mathematics and consequences of the various methods are clear and well-documented. Perhaps my favorite article on this is "An Introduction to Modern Missing Data Analysis" by Baraldi and Enders 2009 which details most of the approaches in this discussion and more with the drawbacks of each. Essentially it comes down to Multiple imputation (MI) methods being the best or the use of Generalized Estimating Equations (GEE) or the use of GEE and MI in conjunction. Do note that in the treatment of missing data, begin with the basics: what is the mechanism? MCAR, MAR, MNAR? This will help inform your choice(s). And note that a complete statistical analysis will include thorough discussion and justification for the chosen method.

To simply remove a line of response from the data set because it has missing data might seem the most obvious and logical way to proceed in a statistical analysis but when the missing data shows patterns, it is not Missing Completely at Random (MCAR) anymore but rather it is either associated with flaws in data collection/input methods or maybe just the response being due to some order associated with the data collection. Hence it is necessary to check if MCAR exists for such cases or not.

Pairwise deletion is useful since we use the other variables in the list which contain data. Meaning, the variables which are relevant to the study are used in pairs from each data list / response despite having missing values in one of the variables of the response. So, the data which exists are paired to be used in statistical analysis, leading to different sample sizes for different studies. So, it is not necessary to delete a whole response if some of the data is missing in it as it can be used to facilitate other needs of the analysis by utilizing the remaining data in the response which is relevant to the study.

The "drawbacks" listed in the left panel <-- are important, but not the most important. The most important problem is that unconditional mean (also median, mode, and any other single measure) completely ignores the information included in other dimensions/predictors/variables (name it as you want). Lots of data does NOT exist "alone", but are mutually related. E.g. in a dataset storing data of a lipidogram, don't even try to impute independently LDL, HDL, non-HDL, TG, Total, you're guaranteed to obtain nonsenses. In less related data one also cannot rule out internal relationships. Not to mention, when you INTENTIONALLY are going to analyse some data variable interactions, and yet you impute data through an unconditional mean.

Usually when there is missing data in the variables of a data set, it is replaced with the mean of that particular variable column. So, the mean simply becomes the response of that particular variable under that line of data. Sometimes this is unreliable when the missing data is not MCAR leading to the existence of some kind of pattern in the data responses. This is usually solved by replacing missing data with median or mode of all the other responses of the same variable, but it still carries the danger of bias and unreliability.

Multiple imputation also creates a framework for sensitivity analyses under MNAR (missing not at random), like tipping point analysis for the delta-change: you select some key parameter(s) you believe it affects the whole imputation process, and shift it or multiply by the "delta" parameter obtained from some plausible range (or a grid), perform the imputation over this affected dataset, do the analysis of analysis, pool the results, and observe the outcome: confidence intervals, p-values, effect sizes. If it's stable over the parameter space, fine. If it's not stable, you likely have a serious MNAR pattern and need to be very careful in interpreting and communicating the results. Also MI relaxes the MCAR assumption for the GEE imputation.

- ?? Identify missing data patterns to understand the nature and extent of missingness in your dataset. - ?? Use KNN imputation to fill in missing values by finding the most similar instances based on non-missing variables, preserving data relationships. - ??? Determine the appropriate number of neighbors (k) to balance accuracy and computational efficiency, typically using cross-validation. - ?? Standardize or normalize data before applying KNN to ensure that distance calculations accurately reflect similarities. - ?? Validate the imputation results by comparing imputed values with known values in a subset of the data, ensuring the method's effectiveness.

KNN identifies the 'k' nearest neighbors in the dataset for each data point with missing values. These neighbors are the most similar observations based on the available features (non-missing values). The missing value is then imputed using a statistical method like averaging or weighted averaging the corresponding values from the k nearest neighbors. If the pattern of missing values is related to the underlying structure of the data (e.g., missing values tend to occur for specific combinations of other features), KNN can exploit these relationships for accurate imputations. Careful selection is required for the choice of the 'k' parameter (number of neighbors) and the distance metric used to determine similarity.

The point about "domain expertise" is worth emphasising. For decades, for example, the economic contribution and significance of information technology was understated by economic analysts in Australia and New Zealand because they were looking at the wrong datasets and failing to re organise that their imputations were ignoring 2/3 of IT industry employment ( software and services and consulting). They failed to ask the domain experts!

In addition to Adrian’s wise recommendations, also take into account the proportion of missing data. The key really is having a firm grasp on the data collection process coupled with domain knowledge. Pay attention to study design to limit risk of missing data and potential biases.

One thing that I have found helpful when facing missing data is the R package mice which stands for multiple imputation using chain equation.

Items 1-6 describe some missing data "repair" methodologies. It is far more important to understand the entire data collection and editing processes. If you don't ask, they won't tell you. Your perception might be that the only missing data is that with which one has been provided. This may not be the case. Think deeply about whether certain data categories may be predisposed to becoming missing data and the likely analysis impact. Sometimes one needs some additional targeted better data collection to resolve missing data issues. Other times one may discover that much of the missing data was manufactured via prior data processing rules. Again, if you don't ask, they won't tell you. When it comes to data take nothing at its face value.