# R code for spline transformation as part of the logistic regression

I am working on logistic regression and was hoping to spline transform my continuous predictor (percentage). I have several questions as follows and would be very grateful for any guidance.

1. Below is my attempt to incorporate the spline transformation into my predictor. I want to know whether I am doing this correctly?
library(splines)
knots <- quantile(final\$percentage, p = c(0.25, 0.5, 0.75))
model <- glm (disease ~ bs(percentage, knots = knots), data = final, family=binomial)
1. If so, how can I interpret the below output from the above code? For example, how can I obtain the odds ratio based on these coefficients?
glm.fit: fitted probabilities numerically 0 or 1 occurred
Call:
glm(formula = disease ~ bs(percentage, knots = knots), family = binomial,
data = final)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.9502  -1.2835   0.5687   0.9548   1.3618

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                        0.4845     1.1982   0.404    0.686
bs(percentage, knots = knots)1     2.7183     3.3578   0.810    0.418
bs(percentage, knots = knots)2    -1.7655     2.3966  -0.737    0.461
bs(percentage, knots = knots)3     2.1134     3.1838   0.664    0.507
bs(percentage, knots = knots)4    -6.1535    10.9851  -0.560    0.575
bs(percentage, knots = knots)5    -8.1928    56.9180  -0.144    0.886
bs(percentage, knots = knots)6 10636.9163  8119.2865   1.310    0.190

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 61.513  on 46  degrees of freedom
Residual deviance: 51.817  on 40  degrees of freedom
AIC: 65.817

Number of Fisher Scoring iterations: 14

Here is my dataset:

structure(list(percentage = c(5.5, 72.1, 7.9, 80.6, 56.3, 11.5,
15.3, 12.3, 30.9, 27.5, 0.3, 5.3, 19.6, 19.8, 0.3, 40.5, 16.8,
38, 13.8, 29.9, 15.8, 15.3, 22.8, 17.2, 41.2, 17.2, 31.6, 41.2,
19.6, 38, 41.2, 29.9, 15.3, 29.9, 38, 30.9, 31.6, 15.3, 15.3,
38, 31.6, 41.3, 21.4, 0.4, 41.2, 7.6, 29.9),
SmokingNA = structure(c(2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L), .Label = c("non-smoking",
"smoking"), class = "factor"), disease = structure(c(1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L), .Label = c("none", "disease"), class = "factor")), row.names = c(NA,
-47L), class = "data.frame")

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