Project 2

Medical Insurance Charges in the United States

1 Executive Summary

The aim of this report is to investigate a dataset from the United States Census Bureau (U.S. CB) that analysed patient medical costs billed from health insurance companies alongside seven variables; age, sex, body mass index (BMI), number of children, smoking status and region.By investigating this dataset this report aimed to identify if any of these variables were associated with greater insurance charges in the U.S.. The data was collected in 2013 and the sample size of the dataset was 1338.

The main stakeholders interested in this dataset would be government, private health insurance companies, employers and individuals. In the United States the government plays a large role in the regulation of private health insurance costs and standards and therefore this information will provide relevant insights into current private health insurance trends (Motaze et al., 2015). Insurance companies are relevant stakeholders as this dataset would allow them to formulate competitive prices and target key demographic groups/areas with relevant incentives (Motaze et al., 2015). Employers would be interested as they provide 49% of all Americans with private health insurance (“Health Insurance Coverage of the Total Population”, 2018). Individuals would be interested as learning more about their health and health behaviors is empowering and can inform future health decisions.

Informed from existing literature (see report for more details) this report chose to specifically investigate: 1.Does age positively correlate with insurance charge? 2.Does BMI positively correlate with insurance charges? 3.What are the differences in insurance costs between patients that smoke and do not smoke?

The main discoveries of this report for each research question were: 1.Using a scatter plot and calculating Pearson’s r age was found to significantly, albeit weakly, positively correlate with insurance charges. 2.A high BMI results was not found to strongly equate to high insurance charges and was analysed using a scatter plot and lowess line. 3.A strong connection between smoking and high insurance costs was found through analysing a double box plot.

This report identified that future research should aim to investigate what medical conditions were related to insurance charges and more discriminating research is needed to eliminate the impact of confounders.

2 Full Report

2.1 Initial Data Analysis (IDA)

2.1.1 Upload data

2.1.2 Data size:

dim(insurance)

## [1] 1338    7

2.1.3 Data variable classification:

str(insurance)

## Classes 'tbl_df', 'tbl' and 'data.frame':    1338 obs. of  7 variables:
##  $ age     : num  19 18 28 33 32 31 46 37 37 60 ...
##  $ sex     : chr  "female" "male" "male" "male" ...
##  $ bmi     : num  27.9 33.8 33 22.7 28.9 ...
##  $ children: num  0 1 3 0 0 0 1 3 2 0 ...
##  $ smoker  : chr  "yes" "no" "no" "no" ...
##  $ region  : chr  "southwest" "southeast" "southeast" "northwest" ...
##  $ charges : num  16885 1726 4449 21984 3867 ...

The variables, age, BMI, children, and charges are classified as num (or numeric) by R signifying that they are quantitaive varibles.

The varibales sex, smoker, and region are classified as chr (or character) and are qualitative varibales. Sex and smoker are binary variables (2 levels - male v female, smoker v non-smoker) and region is nominal (unordered categories).

2.1.4 Packages

install.packages("ggplot2")

## Installing package into 'C:/Users/corde/Documents/R/win-library/3.5'
## (as 'lib' is unspecified)

## package 'ggplot2' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\corde\AppData\Local\Temp\RtmpgRQG89\downloaded_packages

library("ggplot2")

2.1.5 Written Summary

This data set came from Kaggle, an organisation which provides a platform where a community of data scientists and data enthusiasts upload data sets on various disciplines and subject areas (“About Kaggle”, 2018). The original source of the dataset was the United States Census Bureau (USCB) (Lantz, 2013). It is difficult to fully comment on the validity of the dataset as the method used to collect the data was not recorded by the U.S. CB. Furthermore, the Census website stipulates that all of their census results are subject to a degree of nonsampling error (U.S. CB, 2018). However, it is important to note that despite these issues the U.S. CB is a recognised and respected datasource and have numerous quality control procedures in place to minimise error throughout the research process, including data collection, processing, tabulation and analysis (USCB, 2018).

In the dataset, each row represents a different individual.

Each column represents one of the seven variables considered; age, sex, BMI, number of children (children), smoker, place of residence (region) and insurance charges (charges).

2.2 Research Question 1: Does age positively correlate with insurance charge?

scatter_plot <- ggplot(insurance, aes(age, charges))
scatter_plot + geom_point() + labs(x = "Age (years)", y="Charges ($US)") + geom_smooth(method=lm)

cor.test(insurance$age, insurance$charges, method = "pearson", conf.level = 0.95)

## 
##  Pearson's product-moment correlation
## 
## data:  insurance$age and insurance$charges
## t = 11.453, df = 1336, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2494139 0.3470381
## sample estimates:
##       cor 
## 0.2990082

To explore this research question a scatter plot was created and Pearson’s correlation coefficient was calculated to identify potential association. Scatter plots can be used for paired quantitative variables and since age and insurance charges fit this criterion it is therefore an appropriate graphical method to use. Pearson’s correlation coefficient was used as a linear relationship and used for predictions based on existing literature that has consistently found older age to be associated with increased medical costs, particularly in developed countries (Carreras et al., 2013). Upon analysis this report found a weak correlation (r=0.299) with a corresponding p-value of less than 0.05 signifying that this is a null hypothesis and that there was no correlation between the variables and should be rejected. However, the large variability in the graph is caused by the large amounts of outliers. As a result, this correlation does not hold a great degree of real world significance and further research should be undertaken before this correlation is acceptable. Future research should aim to investigate the types of medical conditions associated with the charges as this would provide further insight into age related insurance charges.

2.3 Research Question 2: Does a higher BMI score positively correlate to increased insurance charges?

plot(insurance$bmi, insurance$charges)

plot(insurance$bmi, insurance$charges, xlab = "BMI", ylab = "Charges ($US)", 
    col = "deepskyblue4", pch=19)
lines(lowess(insurance$bmi, insurance$charges))
L = lm(insurance$charges~insurance$bmi)
abline(L)

This research question examines whether higher BMI scores contributes to a higher insurance charge. This question was posed because literature has found that those with weight problems tend to have more medical problems and as a result this leads to increased medical bills (Epstein, 2016), As BMI and insurance charges are quantitative variables a scatter plot was considered an appropriate graphical method to use. A lowless line was applied to the scatter plot due to the noisiness of the data. Lowess is a non-parametric form of fitting a smooth curve to a dataset that allows for the analysis of weaker or non-linear relationships as no assumptions are made about the distribution shape (Stephanie, 2013). Comparing the lowess line to the line of best fit on the graph clearly illustrates that this was the best method to use. In this dataset the lowess line highlights that there is not a strong correlation as despite data clumping there is a high number or outliers. Therefore, from the dataset it can be deduced that a high BMI score does not necessarily equate to an increased insurance cost. This may be caused by different confounding factors contributing to individuals BMI such as location, smoking, age and sex. Further analysis that eliminates these confounders should be undertaken in future research.

2.4 Research Question 3: What are the differences in insurance costs between smoker and non-smoker patients?

p = ggplot(data = insurance, aes(x = factor(smoker), y = charges)) 
p + geom_boxplot()  

This research question investigates the if smoking affects the medical insurance costs of a patient. This questions was formulated because of previous literature showing that on average, smokers will pay up to 50% more for health insurance premiums. Also, smokers often have more chronic health needs and greater health care use compared to non-smokers (Politi, 2016). For this question a double box plot was created as there was one qualitative variable, smoking (binary: yes, no) and one quantitative, insurance charges. The double box plot shows the median insurance chargers for non-smokers is around $25,000 lower than the median of the people who do smoke. Furthermore, when considering the middle 50% of cases non-smokers have a much smaller spread and a lower range of insurance charges (approximately $5000-$11,000) when compared to smokers (approximately $20,000-$41,000). Both datasets have heavy upper tails that signifies the dataset lacks symmetry and is skewed to the right, this is more pronounced in smokers. Thus from this analysis we can deduce that this dataset shows that patients who smoke are more likely to have a higher medical insurance bill than those who do not smoke. Future research should aim to investigate if other factors such as location of where the smoker lives as family life can affect the lifestyle and in turn the insurance cost of a patient.

3 Conclusions

This report specifically found a weak positive correlation between age and insurances charges, no correlation between BMI and insurance charges, and that non-smokers had lower insurance charges than smokers. In conclusion, whilst some relationships could be drawn between particular variables and corresponding insurance charges more research that eliminates confounders and provides a more indepth of analysis into the medical conditions relating to the charges needs to be undertaken before these relationships can be considered significant in statistical and real world terms.

4 References

About Kaggle. (2018). Retrieved April 12, 2018, from https://www.kaggle.com/kaggle.

Carreras, M., Ibern, P., Coderch, J., Sánchez, I., & Inoriza, J. M. (2013). Estimating lifetime healthcare costs with morbidity data. BMC Health Services Research, 13(1), 440. doi:10.1186/1472-6963-13-440.

Epstein, L. (2016, March). Why a higher BMI shouldn’t raise Insurance rates. Retrieved from https://www.investopedia.com/articles/personal-finance/030116/why-higher-bmi-shouldnt-raise-insurance-rates.asp.

“Health Insurance Coverage of the Total Population”. (2018). Retrieved April 12, 2018, from https://www.kff.org/other/state-indicator/total-population/?currentTimeframe=0&sortModel=%7B%22colId%22:%22Location%22,%22sort%22:%22asc%22%7D.

Lantz, B. (2013). Machine learning with R. Birmingham: Packt Publishing.

Motaze, N. V., Chi, C. P., Ongolo-Zogo, P., Ndongo, J. S., & Wiysonge, C. S. (2015). Government regulation of private health insurance. The Cochrane Database of Systematic Reviews, (4), CD011512. Advance online publication. http://doi.org/10.1002/14651858.CD011512.

Politi, M. (2016, September). Another cost of smoking: Sky-high insurance. Retrieved from http://theconversation.com/another-cost-of-smoking-sky-high-insurance-63156.

Stephanie. (2013, October). Lowess smoothing in in statistics: what is it? Retrieved from http://www.statisticshowto.com/lowess-smoothing/.

Stephanie. (2013, October). Lowess smoothing in in statistics: what is it? Retrieved from http://www.statisticshowto.com/lowess-smoothing/.

United States Census Bureau. (2018). Reliability of Data. Retrieved from https://www.census.gov/programs-surveys/economic-census/technical-documentation/methodology/reliability.html.

5 Personal reflection on group work

• The way I contributed was
• What I learnt about group work was …