## 7.20 Influential observations

Check for influential observations by examining standardized DFBetas (see Section 5.21). Fit the model, plot the DFBetas, and, if there are observations with values that are large, conduct a sensitivity analysis to see if their removal impacts your overall conclusions (see Section 5.24). A cutoff of 0.2 is reasonable .

# Compute DFBETAS
DFBETAS <- resid(cox.ex7.6, type = "dfbetas")
# Examine the first few rows
head(DFBETAS)
##        [,1]      [,2]      [,3]       [,4]      [,5]      [,6]
## 1 0.0040352 -0.005820 -0.004481 -0.0001244 -0.017555  0.009765
## 2 0.2085628 -0.012956 -0.104859 -0.0335294 -0.091015  0.084854
## 3 0.0048140  0.013115 -0.018220  0.0001619  0.001473 -0.003342
## 4 0.0023748  0.014455  0.002487  0.0001607 -0.014082 -0.002793
## 5 0.0012622  0.001298  0.003561  0.0030316  0.003920  0.004394
## 6 0.0006693  0.009121  0.003413 -0.0273620  0.002322 -0.006725
# Plot
par(mfrow=c(2,3))
plot(DFBETAS[, 1], ylab="RF_PPTERMYes")
abline(h = c(-0.2, 0.2), lty = 2, col = "red")
plot(DFBETAS[, 2], ylab="MAGER")
abline(h = c(-0.2, 0.2), lty = 2, col = "red")
plot(DFBETAS[, 3], ylab="MRACEHISPNH Black")
abline(h = c(-0.2, 0.2), lty = 2, col = "red")
plot(DFBETAS[, 4], ylab="MRACEHISPNH Other")
abline(h = c(-0.2, 0.2), lty = 2, col = "red")
plot(DFBETAS[, 5], ylab="MRACEHISPHispani")
abline(h = c(-0.2, 0.2), lty = 2, col = "red")
plot(DFBETAS[, 6], ylab="DMARUnmarried")
abline(h = c(-0.2, 0.2), lty = 2, col = "red") Figure 7.24: DFBetas from a Cox regression

There appear to be a number of influential observations (Figure 7.24). For MRACEHISP = “Other” (lower left panel), there is a group of observations with standardized DFBeta > 0.2. Upon closer examination, we find that these individuals are the entire group of preterm births among non-Hispanic Other mothers. This group is small enough, and the prevalence of preterm birth is small enough, that there are only a few events in this group. Thus, removing any one of them highly impacts the regression coefficient (they each have a large DFBeta value).

# "MRACEHISPNH Other" is the 4th term in the model
SUB <- DFBETAS[, 4] > 0.2

# Race x Preterm among those with large DFBetas
table(natality.complete$MRACEHISP[ SUB], natality.complete$preterm01[ SUB])
##
##             1
##   NH White  0
##   NH Black  0
##   NH Other 13
##   Hispanic  0
# Race x Preterm among those without large DFBetas
table(natality.complete$MRACEHISP[!SUB], natality.complete$preterm01[!SUB])
##
##              0   1
##   NH White 865  96
##   NH Black 233  58
##   NH Other 128   0
##   Hispanic 299  51

### References

Harrell, Frank E, Jr. 2015. Regression Modeling Strategies. 2nd ed. Switzerland: Springer International Publishing.