Interpreting Logistic Coefficients

Create the Confounded Data Set and Save.

# eval=FALSE so the data is not over-written on re-running the script

df <- read.csv("~/teach/550/www/lab.csv")
df$LabTest <- as.integer(as.character(df$LabTest))
df <- df[!is.na(df$LabTest), ]
labTest <- df[!duplicated(df$ID), "LabTest"]
wts <- sqrt(labTest)/sum(sqrt(labTest))
lab2 <- sample(labTest, 200, prob = labTest, replace = TRUE)
lab1 <- sample(labTest, 200, replace = TRUE)
l1 <- 2 - lab1/8
l2 <- 5 - lab2/8
p1 <- 1/(1 + exp(-l1))
p2 <- 1/(1 + exp(-l2))
ys <- runif(400) < c(p1, p2)
gp <- rep(1:2, rep(200, 2))
df <- data.frame(dvt = yes.no(ys), Trt = factor(gp, labels = c("Long", "Short")), 
    Test = c(lab1, lab2))
save(df, file = "DVT.covar.rda")
## Warning: coercing argument of type 'double' to logical
##       Yes            95% CI    
## Long    7/200( 3.5%)  1.4%-7.1%
## Short  14/200( 7.0%) 3.9%-11.5%
## Estimated difference (Short-Long): 3.5%
## 95% Limits for Difference: -0.858% to 7.86%
##     Fisher's exact (2-sided):  P=0.177 
##     Uncorrected Chi-square:  P=0.117

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##  Difference  S.E.(Diff)     t-value     P-value Pooled s.d.        d.f. 
##      -6.630       1.920      -3.460       0.001      19.200     398.000 
##  C.I. Width CI. (lower) CI. (upper) 
##       3.770     -10.400      -2.870
## 
## Call:
## glm(formula = dvt ~ Trt + Test, family = binomial)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.4135  -0.1099  -0.0259  -0.0133   2.8233  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   4.7376     1.2865    3.68  0.00023 ***
## TrtShort      2.0424     0.6705    3.05  0.00232 ** 
## Test         -0.1679     0.0314   -5.35    9e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 164.649  on 399  degrees of freedom
## Residual deviance:  69.667  on 397  degrees of freedom
## AIC: 75.67
## 
## Number of Fisher Scoring iterations: 8

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##              Estimate Std. Error   Pr(>|z|)   2.5 %     97.5 %
## (Intercept) 114.15767   1.286516 2.3097e-04 9.17108 1420.98577
## TrtShort      7.70882   0.670477 2.3180e-03 2.07146   28.68790
## Test          0.84542   0.031409 8.9894e-08 0.79495    0.89911