Visualizing restricted cubic splines in glm.nb

Question

I am trying to visualize the relationship between a continuous variable ("marker") and a count variable ("count") using a negative binomial regression with a restricted cubic spline term.

Now I wanted to visualize the relationship and used the following code:

fit <- MASS::glm.nb(count ~ rcs(marker, 3), data = df.splines)

x_seq <- seq(min(df.splines$marker, na.rm = TRUE), 
             max(df.splines$marker, na.rm = TRUE), length.out = 800)

# Create a new dataframe for prediction
new_data <- data.frame(
  marker= x_seq
)
log_preds <- predict(fit, newdata = new_data, type = "link", 
                     se.fit = TRUE)

new_data$IRR <- exp(log_preds$fit)
new_data$IRR_lower <- exp(log_preds$fit - 1.96 * log_preds$se.fit)
new_data$IRR_upper <- exp(log_preds$fit + 1.96 * log_preds$se.fit)

ggplot(new_data, aes(x = marker)) +
  geom_line(aes(y = IRR), color = "blue") +
  geom_rug(aes(x = marker), data = df.splines) +
  geom_ribbon(aes(ymin = IRR_lower, ymax = IRR_upper), alpha = 0.2) +
  labs(x = "marker", y = "Incidence Rate Ratio (IRR)") +
  theme_bw()
summary(fit)

It seems as if the range is between 1-2 for the marker variable is associated with a significantly higher incidence ratio of "Count". However, when looking at the summary none of the term show statistical significance, even remotely.

Call:
glm.nb(formula = count ~ rcs(marker, 
    3), data = df.splines, init.theta = 0.5572638248, link = log)

Coefficients:
                                                      Estimate Std. Error z value Pr(>|z|)
(Intercept)                                             0.6568     0.4058   1.619    0.106
rcs(marker, 3)marker                                    0.2144     0.3538   0.606    0.545
rcs(marker, 3)marker'                                  -0.4016     0.4272  -0.940    0.347

(Dispersion parameter for Negative Binomial(0.5573) family taken to be 1)

    Null deviance: 49.048  on 47  degrees of freedom
Residual deviance: 48.002  on 45  degrees of freedom
AIC: 183.82

Number of Fisher Scoring iterations: 1

              Theta:  0.557 
          Std. Err.:  0.193 

 2 x log-likelihood:  -175.824 

Is my statistical approach in creating the plot correct? What does the discordance between the plot and the summary regarding statistical significance mean?

Answer 1

Is my statistical approach in creating the plot correct?

Yes, you've correctly computed the confidence band for the conditional mean.

What does the discordance between the plot and the summary regarding statistical significance mean?

Keep in mind that the estimated coefficients and the associated tests don't say much about a statistical test of hypothesis at a particular value of $x$. Rather, when using splines, you need to evaluate the coefficients together through either a joint test of some hypothesis (e.g. that there is no linearity, evaluated possibly through a likelihood ratio test), or that the predicted value is different from some value under a null hypothesis (as you do here graphically).