Risk Factors for Infection in Caesarian Births
Data from infection from birth by Caesarian section, classified by Risk (two levels),
whether Antibiotics were used (two levels) and whether the Caesarian section was Planned or not.
The outcome is Infection (three levels).
data(Caesar)
A 4-dimensional array resulting from cross-tabulating 4 variables for 251 observations. The variable names and their levels are:
| No | Name | Levels |
| 1 | Infection
|
"Type 1", "Type 2", "None"
|
| 2 | Risk
|
"Yes", "No" (presence of risk factors) |
| 3 | Antibiotics
|
"Yes", "No" (were antibiotics given?) |
| 4 | Planned
|
"Yes", "No" (was the C section planned?) |
Infection is regarded as the response variable here.
There are quite a few 0 cells here, particularly when Risk
is absent and the Caesarian section was unplanned.
Should these be treated as structural or sampling zeros?
Fahrmeir, L. & Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models New York: Springer Verlag, Table 1.1.
caesar for the same data recorded as a frequency data frame
with other variables.
data(Caesar) #display table; note that there are quite a few 0 cells structable(Caesar) require(MASS) # baseline model, Infection as response Caesar.mod0 <- loglm(~Infection + (Risk*Antibiotics*Planned), data=Caesar) # NB: Pearson chisq cannot be computed due to the 0 cells Caesar.mod0 mosaic(Caesar.mod0, main="Baseline model") # Illustrate handling structural zeros zeros <- 0+ (Caesar >0) zeros[1,,1,1] <- 1 structable(zeros) # fit model excluding possible structural zeros Caesar.mod0s <- loglm(~Infection + (Risk*Antibiotics*Planned), data=Caesar, start=zeros) Caesar.mod0s anova(Caesar.mod0, Caesar.mod0s, test="Chisq") mosaic (Caesar.mod0s) # what terms to add? add1(Caesar.mod0, ~.^2, test="Chisq") # add Association of Infection:Antibiotics Caesar.mod1 <- update(Caesar.mod0, ~.+Infection:Antibiotics) anova(Caesar.mod0, Caesar.mod1, test="Chisq") mosaic(Caesar.mod1, gp=shading_Friendly, main="Adding Infection:Antibiotics")
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