Issue 37 draft: Why it works vignette with analytic solutions

[SamuelBrand1]

Description

This PR closes #37.

This draft PR creates a "why it works" vignette for the mathematics underlying the approach to inference under censoring/truncation used in primarycensoreddist.

The basic concept is to present the primary censoring window problem in terms of the survival function of the inter-event time after the end of the primary event window. This random variable can be negative therefore instead of the survival function starting at 1, it starts at the probability that the secondary event occurs after the end of the primary censor window.

This survival function can be either the target of numerical quadrature, or it might have analytically accessible solutions.

I've started adding examples of where the survival function has analytic solutions. This is WIP:

• Gamma with uniform primary window.
• Log-Normal with uniform primary window.

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.
• I have added a news item linked to this PR.
• I have reviewed CI checks for this PR and addressed them as far as I am able.

[seabbs]

Thanks for this @SamuelBrand1. From a first pass it looks great and having some analytical solutions is very exciting

To do before I've read content:

• Run: spelling::update_wordlist()
• Add yourself to the description as an author
• Follow up issues for adding R and stan support for analytical solutions + testing ( I can make these issues or happy for you to do so).
• Add the new vignette to the articles section of the pkgdown.yaml.
• Link to it (via relative links https://pkgdown.r-lib.org/articles/linking.html)

[seabbs]

Read to dos:

• Consider changing the title to the very on the noise: Why it works
• Link at the top to the getting started + provide some kind of pre intro text along the lines of here be dragons.
• Split why it works and analytical solutions into their own vignettes (?). If we do that we might need some subheadings in the articles dropdown to guide readers

[seabbs]

missing f_T def

[SamuelBrand1]

I can't edit @seabbs check list so I'll C&P here:

• Run: spelling::update_wordlist()
• Add yourself to the description as an author
• Follow up issues for adding R and stan support for analytical solutions + testing ( I can make these issues or happy for you to do so).
• Add the new vignette to the articles section of the pkgdown.yaml.
• Link to it (via relative links https://pkgdown.r-lib.org/articles/linking.html)
• Consider changing the title to the very on the noise: Why it works
• Link at the top to the getting started + provide some kind of pre intro text along the lines of here be dragons.
• Split why it works and analytical solutions into their own vignettes (?). If we do that we might need some subheadings in the articles dropdown to guide readers

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 6120812 is merged into main:

• ✔️cmdstan_fit_gamma: 7.69s -> 7.73s [-1.77%, +3.02%]
• ✔️cmdstan_fit_lognormal: 1.61s -> 1.58s [-5.63%, +1.05%]
• ✔️dprimarycensoreddist_expgrowth: 1.95ms -> 1.95ms [-1.75%, +1.92%]
• ✔️dprimarycensoreddist_weibull: 1.8ms -> 1.81ms [-0.46%, +1.86%]
• ✔️fitdistdoublecens_gamma: 639ms -> 639ms [-0.5%, +0.45%]
• ✔️fitdistdoublecens_normal: 537ms -> 536ms [-1%, +0.47%]
• ✔️pprimarycensoreddist_expgrowth: 36.3ms -> 36.2ms [-1.7%, +1.31%]
• ✔️pprimarycensoreddist_lnorm: 33.6ms -> 33.4ms [-3.72%, +2.47%]
  Further explanation regarding interpretation and methodology can be found in the documentation of touchstone.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 05daf84 is merged into main:

• ✔️cmdstan_fit_gamma: 7.64s -> 7.65s [-0.67%, +0.87%]
• ✔️cmdstan_fit_lognormal: 1.68s -> 1.67s [-2.72%, +1.22%]
• ✔️dprimarycensoreddist_expgrowth: 2.12ms -> 2.02ms [-11.94%, +2.54%]
• ✔️dprimarycensoreddist_weibull: 1.99ms -> 1.99ms [-2.15%, +1.7%]
• ✔️fitdistdoublecens_gamma: 665ms -> 673ms [-1.4%, +3.51%]
• ✔️fitdistdoublecens_normal: 554ms -> 551ms [-0.95%, +0.1%]
• ✔️pprimarycensoreddist_expgrowth: 40.8ms -> 40.8ms [-1.1%, +0.71%]
• ✔️pprimarycensoreddist_lnorm: 37.4ms -> 37.3ms [-1.4%, +0.72%]
  Further explanation regarding interpretation and methodology can be found in the documentation of touchstone.

[SamuelBrand1]

My questions towards resolving final check list items:

• Where would we want to link to this?
• Split the vignette now or in a new PR to resolve Split "Why it works" vignette into intro and analytic solutions vignette #72 ?
• What is a news item?

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 9df87c0 is merged into main:

• ✔️cmdstan_fit_gamma: 7.62s -> 7.59s [-0.95%, +0.21%]
• ✔️cmdstan_fit_lognormal: 1.6s -> 1.56s [-6.35%, +2.21%]
• ✔️dprimarycensoreddist_expgrowth: 1.89ms -> 1.91ms [-0.13%, +2.54%]
• ✔️dprimarycensoreddist_weibull: 1.82ms -> 1.81ms [-2.03%, +0.39%]
• 🚀fitdistdoublecens_gamma: 655ms -> 643ms [-3.48%, -0.35%]
• ✔️fitdistdoublecens_normal: 541ms -> 540ms [-0.85%, +0.59%]
• ✔️pprimarycensoreddist_expgrowth: 36.6ms -> 36.6ms [-1.53%, +1.06%]
• ✔️pprimarycensoreddist_lnorm: 33.3ms -> 33.1ms [-1.86%, +0.69%]
  Further explanation regarding interpretation and methodology can be found in the documentation of touchstone.

[seabbs]

Where would we want to link to this?

The getting started vignette. Can be its own issue.

Split the vignette now or in a new PR to resolve

Given this has taken a while perhaps in its PR.

What is a news item?

A new line in NEWS.md that tracks changes. May be more familiar as a CHANGELOG

[seabbs]

Interestingly I can tick your boxes but you can't tick mine. Might be about repo status. I will give you some repo permissions

[seabbs]

This is really clear now. Nice work. I think merge and deal with other changes as their own issues.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 8059534 is merged into main:

• 🚀cmdstan_fit_gamma: 7.71s -> 7.61s [-1.86%, -0.74%]
• ✔️cmdstan_fit_lognormal: 1.6s -> 1.59s [-4.08%, +2.7%]
• ✔️dprimarycensoreddist_expgrowth: 1.93ms -> 1.93ms [-1.86%, +2.43%]
• ✔️dprimarycensoreddist_weibull: 1.84ms -> 1.85ms [-1.51%, +2.61%]
• ✔️fitdistdoublecens_gamma: 662ms -> 660ms [-0.86%, 0%]
• 🚀fitdistdoublecens_normal: 557ms -> 552ms [-1.44%, -0.25%]
• ✔️pprimarycensoreddist_expgrowth: 36.5ms -> 37ms [-1.15%, +3.55%]
• ✔️pprimarycensoreddist_lnorm: 33.7ms -> 33.5ms [-4.22%, +3.06%]
  Further explanation regarding interpretation and methodology can be found in the documentation of touchstone.