SurvivalDistributions extension
EpiAwareADToolsSurvivalDistributionsExt loads when SurvivalDistributions is loaded alongside EpiAwareADTools. It is the only extension that adds distribution methods rather than AD rules, so it needs no backend loaded to take effect. The backends reach it through the gamma-CDF derivative rules the other extensions register.
What it registers
Four AD-safe hook methods for SurvivalDistributions.GeneralizedGamma:
All four go through a small internal helper, _gg_cdf(d, u) = cdf_ad_safe(d.G, u^d.gamma), except logccdf_ad_safe, which calls logccdf_ad_safe(d.G, u^d.gamma) directly. A GeneralizedGamma(σ, ν, γ) carries an inner Gamma(ν/γ, σ^γ), so routing through the inner Gamma at the transformed point u^γ reuses the Gamma methods of the hooks, which already differentiate the regularised lower incomplete gamma through _gamma_cdf. The u^γ transform and the inner shape and scale are elementary functions of ν, γ and σ, so the gradient flows through all three parameters. The constructor promotes its parameters into the inner Gamma{T}, so a Dual or tracked parameter survives into d.G and the per-backend rules do the rest. Each method handles u <= 0 before touching the inner distribution.
One public Distributions method:
logcdf(d::SD.GeneralizedGamma, t::Real) = logcdf_ad_safe(d, t)SurvivalDistributions.LogLogistic gets nothing. Its logccdf is built from log1p and exp, so it differentiates through the generic elementary fallback on every backend.
What fails without it
SurvivalDistributions defines logccdf(d, t) = logccdf(d.G, t^γ), and the stock logccdf(::Gamma) routes through StatsFuns._gammalogccdf. That has no ForwardDiff.Dual, no ReverseDiff.TrackedReal and no Mooncake method, so any numeric kernel that queries the CDF or survival of a GeneralizedGamma leaf errors under every AD backend.
The logcdf method is a separate gap. SurvivalDistributions defines logccdf but no logcdf, so a bare logcdf(GeneralizedGamma(θ...), t) falls through to the generic logcdf(d, x) = log(cdf(d, x)), reaches SurvivalDistributions' own cdf(GG, t) = 1 - exp(logccdf(d.G, t^γ)), and lands back on _gammalogccdf. It is the survival branch, not _gammalogcdf, because the whole GeneralizedGamma CDF family is defined from the survival. Under any backend it strips the Dual and throws. Only logcdf is claimed here. cdf, ccdf and logccdf are owned by SurvivalDistributions, and redefining them would be method-overwriting piracy that breaks precompilation, so they are left to the hooks.
The logcdf method is additive only while upstream claims no method of its own
SurvivalDistributions = "0.1" permits an upstream logcdf(::GeneralizedGamma, ::Real), and adding one would be non-breaking for them. If that happens, this definition becomes an overwrite, and precompiling the extension fails with "Method overwriting is not permitted during Module precompilation", naming both definitions. No test can guard ahead of it: the method table keeps one entry per signature, and the failure lands while the extension precompiles, before any test body runs. The precompile error is the signal, and the fix is to delete the method.
Upstream target
SurvivalDistributions.jl itself, which would carry these methods once the Gamma CDF is differentiable in its parameters upstream (SpecialFunctions.jl issue #531). That is the same deletion condition as the rest of the hook family.