Issue 57: Polish get started vignette

[athowes]

Description

This PR closes #57.

• Move loading packages to where the loading packages is mentioned
• Alter the "Finally, in Section ??, we demonstrate that the fitted delay distribution accurately recovers the underlying truth." (I merged two sections)
• Ideally the Table 2.1 caption should be altered to work like figure captions rather than this strange thing. I feel like this is possible but requires trying a few things out. Basically I'd like to be using (ref:...)
• The section at the end still has "Figure 2.2 shows…" and an empty figure caption that need to be filled out
• Attend to all comments of @parksw3 in Polish getting started vignette #57 (comment)
  • Define what we mean by primary vs secondary event
  • Add more citations: I don't think we need to do this
  • Explain Figure 1.4 a bit more carefully
  • Figure 2.1 change to density: unsure we should do this

Checklist

• My PR is based on a package issue and I have explicitly linked it.
• I have included the target issue or issues in the PR title in the for Issue(s) issue-numbers: PR title
• I have read the contribution guidelines.
• I have tested my changes locally.
• I have added or updated unit tests where necessary.
• I have updated the documentation if required.
• My code follows the established coding standards.
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[athowes]

Figure 2.1: Just so I know I'm understanding this properly, do the orange bars represent full data without censoring? I wonder if it makes more sense to plot them with density plots (alongside the true density) since they're continuous data? We could also consider plotting something like the mean (vertical line) to show the bias.

Agree - I think we don't then plot correctly discretised dists which we probably should.

Regarding this point, even if the data can be any value (continuous) I think a histogram can still be preferred to a density as a density relies on some KDE parameters (and so ultimately is a model of the data rather than a "true" representation, while a histogram is more of a "true" representation).

For this reason not clear to me that it's better to move to density. I do perhaps see that you'd want the histogram bins to line up with "daily" if that's what you mean also?

[athowes]

I'm ready for this to be reviewed / merged.

Let me know if you'd like to push back on the histogram / density plot point.

[athowes]

I found a bug in my code (I used obs_cens_trunc rather than obs_cens_trunc_samp) and have updated the barplot to be at a daily level (using geom_col):

I have not yet updated away from using the "full data" (towards using the "censored data" as suggested by Sam / above). Here the orange bars are showing a different bias as to before in the rendered version.

I could still be convinced (I should read your paper properly) but as an outsider it looks like the differences between the orange bars here and the theoretical density is just the sampling variability rather than some bias.

Anyway, this is mostly academic because I think the plot now does the job it was intended to do (show that the censored, truncated, sampled data will produce something bad if you use it).

[athowes]

Here's my light investigation into the discussion about histograms being biased. To me, the final one with highest sample size looks pretty good / unbiased.

set.seed(123)

plot_hist <- function(n) {
  data.frame(value = rnorm(n, mean = 0, sd = 1)) |>
    ggplot(aes(x = value)) +
    geom_histogram(aes(y = ..density..), bins = 30, color = "black", fill = "grey90") +
    stat_function(fun = dnorm, args = list(mean = 0, sd = 1), color = "firebrick", size = 1) +
    labs(title = paste0("Sample size: ", n), y = "", x = "") +
    theme_minimal()
}

plots <- lapply(10^{0:5}, plot_hist)
patchwork::wrap_plots(plots)

[seabbs]

Here's my light investigation into the discussion about histograms being biased. To me, the final one with highest sample size looks pretty good / unbiased.

Make it strictly positive and use bin sizes that are relatively big vs the mean + I suggest having another look at @parksw3 work on censoring.

I am not clear we want to close #57 without either a new issue addressing this plot or updating it to use actually observed data as discussed. If making a new issue can move above investigation to it.

[seabbs]

I suggest moving to plotting the retrospective observed data here and opening an issue for exploring how to plot the underlying continuous data in a way that everyone agrees is correct.

[athowes]

The main reason I don't like using obs_censored is thinking about changing this text:

If we had access to the data obs, then it would be simple to estimate the delay distribution. However, with only access to obs_cens_trunc_samp, the delay distribution we observe is biased (Figure 2.1) and we must use a statistical model.

Let's say I swap to "if we had access to obs_censored, then it would be simple..". In this case why is the epidist package designed to adjust for censoring? This text would suggest that censoring is unimportant as a distortion of the underlying process. Perhaps here truncation is the bigger effect, but I'd prefer not to suggest censoring is irrelevant. For a sufficiently large interval (let's say we censor the observations here into weeks) then censoring would be the bigger effect.

[athowes]

Here's an update using the lognormal rather than normal:

set.seed(123)

plot_hist <- function(n) {
  meanlog <- 1.8
  sdlog <- 0.5
  
  data.frame(value = rlnorm(n, meanlog = meanlog, sdlog = sdlog)) |>
    ggplot(aes(x = value)) +
    geom_histogram(aes(y = ..density..), bins = 50, color = "black", fill = "grey90") +
    stat_function(fun = dlnorm, args = list(meanlog = meanlog, sdlog = sdlog), color = "firebrick", size = 1) +
    labs(title = paste0("Sample size: ", n), y = "", x = "") +
    theme_minimal()
}

plots <- lapply(10^{0:5}, plot_hist)
patchwork::wrap_plots(plots)

[athowes]

Here is that plot with all the proposed possibilities:

[athowes]

I've moved this to using the retrospective data.

[seabbs]

This looks good I think. One question about intent as I am slightly not following and another about package dependencies.

[seabbs]

LGTM