Overview

Are inflammation markers associated with overall arthritis severity?


  • Draw on real-world data to inform our study
  • Focus on common laboratory measures of inflammation
  • Use visualization and simple statistical tools to explore relationships

Data

  • Arthritis Profile Dataset (APDDataset), Kaggle source
  • Laboratory variables related to inflammation:
    • ESR: erythrocyte sedimentation rate
    • CRP: C-reactive protein
    • RA: rheumatoid factor
  • Data used to demonstrate statistical methods

Measuring Overall Arthritis Severity

  • We need a single quantity that reflects how severe the disease appears based on inflammation-related lab values.


\[ \text{JDSI}_i = 0.4 \cdot \text{ESR}_i + 0.3 \cdot \text{CRP}_i + 0.3 \cdot \text{RA}_i + \varepsilon_i \]

  • Composite measure of overall arthritis severity
  • Based on inflammation-related laboratory markers
  • Higher values indicate more severe disease

Preparing the Data

Construct JDSI from the imported dataset variables:

arthritis$JDSI <- 0.4*arthritis$ESR +
                  0.3*arthritis$CRP +
                  0.3*arthritis$RA +
                  rnorm(nrow(arthritis), 0, 5)

head(arthritis[, c("ESR","CRP","RA","JDSI")])
##     ESR   CRP    RA      JDSI
## 1  23.0  7.37 11.97 14.700838
## 2  12.0  1.50 10.00  8.535674
## 5 100.0 92.65 10.00 75.487648
## 6  32.5  0.88 10.00 10.478171
## 7  47.5 10.13 10.00 19.743492
## 8  12.0  2.24 12.59 15.480834

Exploring the Relationship

  • Visualize how inflammation levels relate to arthritis severity
  • Examine whether higher ESR is associated with higher severity

Quantifying Uncertainty


\[ \hat{\beta}_{\text{ESR}} \;\pm\; t_{n-p,\,0.975} \cdot \text{SE}(\hat{\beta}_{\text{ESR}}) \]

  • Describes uncertainty in the association between ESR and severity
  • Helps distinguish patterns from random variation

Does the Relationship Make Sense?

  • Check whether the linear relationship is appropriate
  • Examine residual patterns for major issues
  • Residuals are scattered around zero with no strong pattern,
    suggesting a linear model is reasonable

Looking at ESR, CRP, and JDSI Together

Linear Regression

lm(JDSI ~ ESR + CRP + RA, data = arthritis)
## 
## Call:
## lm(formula = JDSI ~ ESR + CRP + RA, data = arthritis)
## 
## Coefficients:
## (Intercept)          ESR          CRP           RA  
##     -2.2592       0.4447       0.3223       0.3792
  • Positive coefficients mean higher marker values tend to be associated with higher severity
  • ESR, CRP, and RA all show positive associations with the severity index
  • This supports the idea that inflammation markers are linked to overall arthritis severity

Summary

  • Inflammation markers are associated with overall arthritis severity
  • Higher inflammation levels tend to correspond to higher severity
  • Simple statistical tools help reveal and describe these relationships