Why are the results from the linear spline regression showing physiologically implausible coefficients?

Machine Learning and Modeling
1

Why are the results from the linear spline regression showing physiologically implausible coefficients?

For example, consider the following formula:


model_nstatin <- lm(ldl ~ bs(pa, knots = c(600, 2400, 4200), degree = 1) + 
              bs(age, knots = c(45, 55, 65), degree = 1) + sex + 
              education + smoking + bs(mds, knots = c(4, 7), degree = 1), 
            data = chol_nstatin)

This model yields an intercept of 3.42 and spline coefficients for physical activity (measured in MET min/week) as follows:

  • -0.047 for values less than 600
  • -0.091 for values between 600 and 2400
  • -0.112 for values between 2400 and 4200
  • -0.102 for values greater than or equal to 4200

These coefficients are for LDL cholesterol measured in mmol/L. However, the predictions and the plot provided below are mathematically and physiologically reasonable. Why do the spline coefficients appear incorrect physiologically?

Here's the code used for prediction and plotting:


nstatin <- data.frame(
  pa = seq(min(chol_nstatin$pa), max(chol_nstatin$pa), length.out = 117283),
  age = mean(chol_nstatin$age),
  sex = factor("Male", levels = levels(chol_nstatin$sex)),
  education = factor("Vocational", levels = levels(chol_nstatin$education)),
  smoking = factor("Ex-smoker", levels = levels(chol_nstatin$smoking)),
  mds = mean(chol_nstatin$mds)
)

predictions_nstatin <- predict(model_nstatin, newdata = nstatin, interval = "confidence")

nstatin$ldl_pred <- predictions_nstatin[, "fit"]
nstatin$lower <- predictions_nstatin[, "lwr"]
nstatin$upper <- predictions_nstatin[, "upr"]

knots <- c(600, 2400, 4200)
x_limit <- 6000
x_interval <- 600

ggplot(nstatin, aes(x = pa, y = ldl_pred)) +
  geom_line(linewidth = 1.2, color = "red") +
  geom_ribbon(aes(x = pa, ymin = lower, ymax = upper), fill = "lightblue", alpha = 0.2) +
  geom_vline(xintercept = knots, linetype = "dashed", color = "blue") +
  scale_x_continuous(
    limits = c(0, x_limit),
    breaks = seq(0, x_limit, by = x_interval),
    labels = seq(0, x_limit, by = x_interval)
  ) +
  labs(title = "Linear Spline Fit with Confidence Intervals", 
       x = "Physical activity (MET min/week)", y = "LDL cholesterol (mmol/L)") +
  theme_minimal()