plotting on logarithmic scale (with asymptotes) and Zero in ggplot2

Question

I am plotting dose-response curves which have asymptotic tails. I would really like to include the vehicle (control) dosage in the plot showing 0

0 is generally calculated as a dosage of .0000000001 - a common practice in these plots.

I really like how the image below displays this, image was taken from a pdf on how to plot using the program: GraphPad: PRISM

Side note: I've found how to do this using basic graphics, but not using ggplot2..

A similar, but different SE question was posed regarding matlab: here

My R Code is as follows:

library(ggplot2)
library(scales)

ggplot(df, aes(x=dose,y=probability, group=model))+

  geom_ribbon(aes(ymin=Lower,ymax=Upper,x=dose,
                  fill=model, col=model,alpha=2))+

  #Axis log transformation:
  annotation_logticks(scaled = TRUE,sides="b") +
  scale_x_log10(breaks = 10^(-1:10),
                labels = trans_format("log10", math_format(10^.x)))+
  #Axes labels:
  labs(x="dosage (log scale)", y="response",size=1)

data:

df<-structure(list(dose = c(1.0000001, 1.04737100217022, 1.09698590648847,1.14895111335032, 1.20337795869652, 1.26038305255123, 1.32008852886009,1.38262230716338, 1.44811836666478, 1.51671703328309, 61.5098612858473,64.4236386159454, 67.4754441930906, 70.6718165392165, 74.0196039119089,77.525978976861, 81.1984541753771, 85.0448978198478, 89.073550951683,93.2930449978201, 97.7124202636365, 102.341145301888, 107.189137199173,112.266782823381, 117.584961077656, 123.155066208544, 128.98903221828,135.099358433491, 141.499136285126, 148.202077356965, 155.222542762819,162.575573915347, 6294.98902185499, 6593.18830115198, 6905.51354792318,7232.63392192496, 7575.25028161186, 7934.09668573241, 8309.9419660568,8703.59137460616, 9115.88830891252, 9547.71611900591, 10000),probability = c(0.000541224108467882, 0.000604351222894496,0.000674836364822755, 0.000753535950764922, 0.000841405774529429,0.000939512464066553, 0.00104904624066603, 0.00117133512397466,0.00130786074096225, 0.00146027591282991, 0.909137675722837,0.917853710549939, 0.925801889950727, 0.933037137930218,0.939612877653328, 0.945580543661554, 0.950989225589167,0.955885424480555, 0.960312903543462, 0.964312616478569,0.967922698169444, 0.971178504317829, 0.974112688435394,0.976755306362936, 0.979133940122965, 0.981273834388139,0.983198040151417, 0.984927561312444, 0.986481500855764,0.987877204102597, 0.989130397184622, 0.990255319432183,0.99999839386077, 0.999998561719608, 0.999998712035413, 0.999998846641614,0.999998967180029, 0.999999075120889, 0.99999917178077, 0.999999258338655,0.999999335850309, 0.999999405261159, 0.999999467417826),Lower = c(-0.000843143037924429, -0.000920390477371509, -0.00100418185380549,-0.0010949913193486, -0.001193314249806, -0.0012996656659587,-0.00141457798197374, -0.00153859794267898, -0.00167228258800459,-0.00181619405586472, 0.844594565230258, 0.856774199246587,0.868144364095382, 0.878738700796645, 0.888592208066634,0.897740830817022, 0.906221056637379, 0.914069534310229,0.92132272464159, 0.928016590318475, 0.934186328384788, 0.939866146372578,0.94508908115546, 0.949886858166262, 0.954289787671259, 0.958326694236121,0.962024875270718, 0.965410084524652, 0.968506536556353,0.971336928460753, 0.973922475470259, 0.976282957407176,0.999991663016519, 0.999992483777835, 0.999993224038698,0.999993891661212, 0.99999449374333, 0.999995036692715, 0.999995526293503,0.999995967766653, 0.999996365824493, 0.999996724720012,0.999997048291405), Upper = c(0.00192559125486019, 0.0021290929231605,0.002353854583451, 0.00260206322087845, 0.00287612579886485,0.0031786905940918, 0.00351267046330581, 0.0038812681906283,0.00428800406992909, 0.00473674588152455, 0.973680786215416,0.978933221853291, 0.983459415806071, 0.987335575063791,0.990633547240022, 0.993420256506086, 0.995757394540955,0.997701314650881, 0.999303082445333, 1.00060864263866, 1.0016590679541,1.00249086226308, 1.00313629571533, 1.00362375455961, 1.00397809257467,1.00422097454016, 1.00437120503212, 1.00444503810023, 1.00445646515518,1.00441747974444, 1.00433831889898, 1.00422768145719, 1.00000512470502,1.00000463966138, 1.00000420003213, 1.00000380162202, 1.00000344061673,1.00000311354906, 1.00000281726804, 1.00000254891066, 1.00000230587612,1.00000208580231, 1.00000188654425), model = c("mod3", "mod3","mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3","mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3","mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3","mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3","mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3", "mod3","mod3")), .Names = c("dose", "probability", "Lower", "Upper","model"), row.names = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L, 99L, 100L, 101L,102L, 103L, 104L, 105L, 106L, 107L, 108L, 109L, 110L, 111L, 190L,191L, 192L, 193L, 194L, 195L, 196L, 197L, 198L, 199L, 200L), class = "data.frame")

Which results in:

.

EDIT 9/1/17: below, user dww has also provided a method of doing this in r base graphics using the package plotrix

Answer 1

How about something like this:

df$dose[1] <- 0.000001

df$facet <- ifelse(df$dose == min(df$dose), 1, 2)
ggplot(df, aes(x=dose,y=probability, group=model))+
  geom_point(data = subset(df, facet == 1)) +
  geom_ribbon(aes(ymin=Lower,ymax=Upper,x=dose,
                  fill=model, col=model,alpha=2))+

  #Axis log transformation:
  annotation_logticks(scaled = TRUE,sides="b") +
  scale_x_log10(breaks = c(0.000001, 10^(0:10)), 
                labels = c(0, math_format()(0:10))) +
  #Axes labels:
  labs(x="dosage (log scale)", y="response",size=1) +
  facet_grid(~facet, scales = 'free', space = 'free') +
  theme(strip.background = element_blank(),
        strip.text = element_blank())

Answer 2

you could use plotrix for your broken axis:

library(plotrix)
plot(df$dose, df$probability, log='x', xlim=c(0.1,1e4), xaxt='n', col=NA)
axis(1, at=10^(-1:4), labels=c(0, 10^(0:4)))
axis.break(breakpos = 0.4)
polygon(c(df$dose, rev(df$dose)), c(df$Lower, rev(df$Upper)), col = rgb(0.8,0.1,0.1,0.5))
points(0.1,0, pch=19, cex=0.5)

Breaking this down:

1. We use xlim in the plot command to start the axis one order of magnitude below the actual data points.
2. We set the laels in the axis command to label the lowest point on the x axis as zero (even though it is actually at x=0.1)
3. We then insert an axist break between the first two labels
4. Finally we plot a point at (0.1, 0), which will appear to be at (0,0) because we inserted the axis break and labelled the axis to be zero here.