Analytics

Overview of Clustering and Other ML Methods Used

County Risk Groups

To address the challenge of providing impactful visualization and rigorous analysis, we used the strategy of categorizing the counties into Risk Groups. Visualizing each counties risk group through time provides too much visual clutter. By creating risk groups, we can represent groups of counties with similar mortality trends by their mean. This also smooths out the inherent noise in estimated mortality rates to better reveal mortality trends. For each state, we categories the counties into low, medium, and high risk groups based on their mortality rates between 2000 and 2017. For the United Sates, we group counties into 6 risk groups ranging from 1:low to 6:high risk.

The risk groups are found by clustering the counties together using the k-means algorithm and then ordering the clusters from low to high by the average mortality rate in 2015-2016. These option was picked after extensive analysis. In Summer 2019, we performed an extensive evaluation of alternative clustering methods such as Divisive Analysis (DIANA) Clustering. R provides clustering functions for both k-means and DIANA. K-means basically tries to group data points into clusters that are the shortest distance from the means of the other points in the cluster. Diana clusters by starting out in one giant cluster and then attempts to partition the data. For the mortality data of interest to MortalityMinder, both approaches produce similar numbers of clusters. We selected k-means because it provided good results and effective visualizations; the means serve as excellent summarizes of cluster. We also did extensive studies of the appropriate number of clusters using cluster quality evaluation functions in R. The results indicated that 3 clusters was a robust choice for each state and 6 clusters for the nations.

Handling States with Few Counties

If a state has six or less counties (i.e. Delaware, Hawaii, and Rhode Island), then it was not clustered at all and becomes an exception case. Exception were handled separately in parts of the app. For example, the trend chart on the State View, shows the mortality rate by county and not the mean mortality rate for cluster (both are over several years). The factor distribution maps also do not exist because there are no clusters for us to map. The box-plots become a single line (there is only one value per social determinant per county, so this is mathematically correct) and the county mortality rate versus factors dot plot below it does not show clusters (the clusters do not exist).

Correlation Analysis

To find determinants of health, we look for factors that differentiate high risk counties from low risk counties within each state or across the entire nation. We used a Kendall Tau test for determining non-parametric rank correlations between the factors and the risk groups of the counties.
Kendall Tau tests whether there is an association between a given and risk groups, and returns correlation values from -1 to 1. Positive correlations are potential destructive determinants of health. Negative correlations are potential protective determinants of health. The higher the absolute value, the greater the association. In MortalityMinder, we want to discover which economic and social factors are related to our clusters with higher mortality risk groups. For states with fewer than 7 counties, we report the Kendall correlation between teh factor and 2015-2017.

After extensive experimentation, we selected Kendall Tau because it calculates non-parametric rank correlations between the factors and risk groups. This yielded robust results across all state and cause of death choices. There is no need to worry about the scale of the factors. Using the correlation with the clusters instead of a the death rate at a single time point makes the results much more robust to noise the mortality rate estimates and imputations.

Analysis for Filtering Out Less Relevant Factors

Originally, there were 168 factors from County Health Rankings, but for the analysis, we reduced the list to a set of approximately 70 factors that were relevant to at least one cause of death at the national level. As part of the process of filtering out factors that were less relevant, we first kept only factors that were rates or other measurements that represented rates on other measurements that did not directly reflect county population size. Then for each state and cause of death, we performed an association study of the factors and risk groups to determine the correlation and significance of each factor. We correct for multiple hypothesis testing using the Benjamini-Hochberg method to help eliminate false discoveries. Factors with p-values less than 0.05 were deemed to be significant. Then finally, we filtered out factors that had too many missing values in most states. Therefore only potential relevant factors to at least one cause of death were deployed in the app. The analysis for filtering out factors is done in an R Notebook that can be accessed by clicking here