Modeling Life Expectancy
Data science Problem Background
Data Science is wildly adapted in health care industry.
Healthcare is a complicated business. Every country has their own model for how to care for its citizens, From robust public single payer systems to private profit driven networks. Many worldwide healthcare providers have restructured to offer multiple healthcare related services to diversify revenue streams, and reduce costs.
Exploring opportunities in foreign markets for healthcare related products can be a costly endeavor. A no-cost initial investigation into a countries' demographics and health trends is an attractive place to start.
The W.H.O. (World Health Organization) is a specialized agency of the United Nations responsible for international public health. Every year they publish data on various health and wellness metrics for every recognized country in the world. This data can be used as an initial exploration tool into the viability of expanding operations into that market.
Understanding The Data
The W.H.O. health report contains 20 variables aggregating data on everything from vaccination rates and infant mortality to government expenditure on healthcare for 15 years for over 250 countries. Understanding the distribution of the variables favorable to low healthcare costs and higher life expectancy can lead to significant insights for market exploration
Body Mass Index
We see is a trimodal distribution, indicating we can generalize the population to three distinct weight categories. Analyzing correlation of this scaled BMI variable reveals a positive correlation to life expectancy, we can surmise we would primarily be interested in the countries represented by the middle and larger mode.
The distribution of alcoholic drinks per week is quite interesting, we see a relatively flat distribution besides for two spikes at 0 and ~5 drinks per week. It seems that there are many countries with a culture of sobriety or enjoying a drink after work.
The dataset contains three variables on vaccination rates for Hepatitis B, Measles, and Diphtheria, they all share the same approximate distribution. The hepatitis B vaccine rate is very telling. We see another tri-modal distribution, the large majority of countries have ~80% of their citizens vaccinated against Hep B, followed by countries approaching 100%, and the third mode representing countries with a very small ~10% of their citizens vaccinated.
When classifying countries by health and financial metrics, it is common to use a developed or undeveloped description, the trimodal behavior of some of these variables indicates 3 categories of development may actually be more descriptive
Most countries believe in the 12 years of education standard. Looking closely we can see 2 other modes almost suppressed by the primary mode. A slight bump at 5-6 years and another at 16. This shows a minority of countries put an emphasis on completing at least a grade school education and slightly more countries with a culture advocating for a 4 year university education.
The majority of countries produce around $6000 per citizen. This value is closely related to the following feature, percent expenditure on healthcare.
Unsurprisingly, the variance inflation index indicates healthcare spending per person is co-linear with GDP per person. In order to develop a stable model, co-linearity must be reduced. We will take the more normally distributed variable, GDP per person to use in our model.
Training A Model Using Data
In order to maximize value over time a healthcare company would prefer to invest in countries with high life expectancy. Predicting how average life expectancy will change with personal choices like alcohol consumption, body mass index, and vaccination status informs better decisions as to what secondary products to market.
Using a combination of stepwise feature selection and reason we can reduce the number of overall features in our multiple linear regression model, increasing it's predictive power and stability.
Descriptor variables like year data is collected and country name are useless in model training and need to be dropped.
There is data redundancy in multiple combinations of features. The feature describing percentage of underweight adolescents is co-linear with percentage of underweight toddlers, therefore we can drop the latter. The same is true for toddler and infant death rates.
Adult mortality is a direct measure of out target, life expectancy therefore can not be used in our model.
The development index is a weighted combination of multiple features and must be dropped due to redundancy and being a direct measure of target.
Stepwise feature selection further reduces the dimensionality of our data leading to the elimination of GDP per person, alcohol consumption, number of measles cases, and country status (developed or undeveloped)
This leaves us with 10 useful features we can use to predict life expectancy.
Feature Engineering for Market Exploration
The W.H.O. data can also be used directly to find acceptable markets for healthcare products. An ideal country would have the following features:
- High Life Expectancy
- Low government expenditure on health
- High vaccination rates
- Low alcohol consumption
Aggregating all relevant variables into a single metric makes discovery of potential markets much simper. In order to maintain variable weight all values will be scaled to a range of 0-1,
Since we need consistency, a higher health metric represents a more desirable market, some variables will be replaced with their opposite. For example, scaling the Alcohol variable will produce a higher value for larger alcohol consumption, since we are looking for lower alcohol consumption we will subtract the scaled alcohol value from 1, and use that value in our metric calculation.
This plot averages our engineered health index for each year data was taken. As we can see, most countries score extremely low on our engineered metric, so our potential markets are going to be limited.
Top 5 Countries by Health Index
An ideal country would also have a stable health index over multiple years. High fluctuations year to year could indicate development instability, assuredly leading to financial unpredictability.
China (red) and Indonesia (green) look the most consistent over time and could be good markets.
According to this model, the primary contributors to high life expectancy are:
- Toddler Mortality Rate
- Body Mass Index
- Country Vaccination Rates
- Infant HIV/AIDs deaths
- Gross Domestic Product
The most surprising result of this model is that a country's average body mass index is positively correlated with life expectancy. For most of recorded history, a persons weight would be related to their access to resources, it is only recently and in prosperous countries that an epidemic of high BMI can reduce average life expectancy. For most of the world, higher weight indicates a healthier population.
Expectedly, the richer a country is, the longer it's citizens will live. This also correlates to education level, more developed nations will educate their population which will lead to high vaccination rates.
More robust linear regression models like Elastic Net would inform better feature selection and fit. Tree based and gradient boosted models like random forest or XGBoost could also result in more accurate predictive capabilities.
Also, based on the tri-modal nature of our variables, clustering before modeling could also improve model performance.
The skills I demoed here can be learned through taking Data Science with Machine Learning bootcamp with NYC Data Science Academy.