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Statistical Analysis / Insurance

Medical Insurance Cost Correlation Analysis

A rigorous correlation study for a London investment firm evaluating BMI-linked pricing tiers for employee medical benefits — separating genuine statistical signal from assumption, and pairing the findings with an explicit ethical and legal limitations review.

Type
Correlation Analysis
Domain
Financial Services
Methods
Pearson Correlation, Hypothesis Testing
Status
Completed
CORRELATION STRENGTH
3 VARIABLES TESTED
BMI • r = 0.709 (STRONG)
AGE • r = 0.080 (WEAK)
CHILDREN • r = 0.031 (N.S.)

The Challenge

BMI is the strongest predictor of insurance costs in this dataset, with a strong, highly significant correlation (r = 0.709, p < 0.001) — a finding a London investment firm used to ground its employee medical benefits decision in evidence rather than assumption.

The firm was weighing changes to its employee medical benefits scheme and wanted evidence-based grounds for any BMI-linked pricing tiers, rather than relying on assumption or industry convention. The brief was to quantify, rigorously, which lifestyle and demographic factors actually correlate with insurance costs, and how confident that relationship is.

The analysis used an anonymised insurance dataset covering demographic and lifestyle variables, with the explicit goal of separating genuine statistical signal from noise before any pricing decision was made.

Approach

01
Exploratory Data Analysis
Ran descriptive statistics, scatter plots, and histograms across the anonymised dataset to understand distributions and initial relationships before any formal testing.
02
Statistical Testing
Calculated Pearson correlation coefficients between BMI, age, and number of children against insurance charges, with two-tailed p-value significance testing at α = 0.05.
03
Results Interpretation
Classified each relationship as strong, weak, or non-significant, and distinguished statistical significance from practical, decision-relevant effect size.
04
Limitations & Ethics Review
Explicitly assessed confounding variables (smoking, exercise, medical history), selection and measurement bias, and the equality-legislation implications of any BMI-based pricing before making recommendations.

Results

r = 0.709
BMI vs insurance charges — strong, highly significant correlation (p = 2.06e-153)
r = 0.080
Age vs charges — weak but statistically significant correlation (p = 0.012)
r = 0.031
Number of children vs charges — not statistically significant (p = 0.332)

BMI emerged as by far the strongest predictor of insurance costs among the variables tested, with a strong, highly significant positive correlation. Age showed a real but much weaker relationship, and number of children showed no meaningful link to cost at all — a useful negative finding that rules out a factor the firm might otherwise have assumed was relevant.

Correlation is not causation: a higher BMI correlating with higher charges does not establish that BMI directly causes those costs, and the dataset is cross-sectional, external, and missing likely confounders such as smoking status, exercise habits, and pre-existing conditions. These limitations were surfaced deliberately, alongside the equality-legislation and employee-wellbeing risks of BMI-linked pricing, so the firm could weigh the statistics against the ethical and legal picture together.

Business Impact

The analysis gave the firm a statistically grounded basis for its benefits decision, plus an honest account of what that basis does and doesn't support. Recommendations included transparent, evidence-based BMI pricing tiers if pursued, paired with employee communication that leads with the data rather than the outcome, complementary wellness programmes offering a genuine route to lower costs, and a formal compliance review with legal and HR before implementation, given the discrimination-risk considerations identified during the analysis itself.

Technology Stack

Python Pandas NumPy SciPy Seaborn Matplotlib Pearson Correlation
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