Canonical empirical examples: what can and cannot be compared

The active freqTLS case-study sequence mirrors the pinned bayesTLS supplement. The table keeps endpoint, response family, threshold, and reference time visible because CTmax values defined for different endpoints, thresholds, or durations are not automatically comparable.

cases <- data.frame(
  Case = c(
    "Zebrafish oxygen", "Cereal aphids", "Snow-gum PSII",
    "D. suzukii mortality", "D. suzukii awake/coma"
  ),
  Dataset = c("zebrafish_o2", "aphid_tdt", "snowgum_psii",
              "dsuzukii", "dsuzukii"),
  Endpoint = c("survival", "survival", "retained PSII",
               "mortality/survival", "awake/coma"),
  Family = c("beta-binomial", "beta-binomial", "Beta",
             "beta-binomial", "beta-binomial"),
  Threshold = c("relative midpoint", "relative midpoint", "relative midpoint",
                "relative CTmax/z; absolute LT50 point check", "relative midpoint"),
  `t_ref (min)` = c(60, 60, 60, 240, 60),
  Report = rep("CTmax and z (not Tcrit)", 5),
  check.names = FALSE
)
knitr::kable(cases)

Case	Dataset	Endpoint	Family	Threshold	t_ref (min)	Report
Zebrafish oxygen	zebrafish_o2	survival	beta-binomial	relative midpoint	60	CTmax and z (not Tcrit)
Cereal aphids	aphid_tdt	survival	beta-binomial	relative midpoint	60	CTmax and z (not Tcrit)
Snow-gum PSII	snowgum_psii	retained PSII	Beta	relative midpoint	60	CTmax and z (not Tcrit)
D. suzukii mortality	dsuzukii	mortality/survival	beta-binomial	relative CTmax/z; absolute LT50 point check	240	CTmax and z (not Tcrit)
D. suzukii awake/coma	dsuzukii	awake/coma	beta-binomial	relative midpoint	60	CTmax and z (not Tcrit)

Scientific questions

• Oxygen-gradient zebrafish compare diploid normoxia and hyperoxia; hypoxia is excluded because z is weakly identified.
• Cereal aphids compare species at age 6, then extend to all heat-branch ages.
• Snow-gum PSII compares Dark and Light recovery with a plant random intercept on CTmax.
• D. suzukii mortality reports the direct model’s relative CTmax and z, then cross-checks the four-hour absolute LT50 as an ML point. Its exact-model bootstrap interval is not reported because too few refits converged.
• D. suzukii awake/coma uses the first cell duration and excludes duration zero because log10(duration) cannot represent it; those controls are not evidence against up. Censored time-to-coma and hurdle productivity remain bayesTLS-only.

Reading estimates across cases

z is expressed in degrees per order-of-magnitude change in tolerated duration, but endpoint and model differences still matter. CTmax is explicitly tied to t_ref and the threshold. In particular, the four-hour mortality value must not be ranked against one-hour relative-midpoint values as if all rows measured one common trait. Cross-case displays must retain the columns above.

freqTLS adds Confidence Eyes, profile/Wald/bootstrap confidence intervals, likelihood contrasts, and explicit identifiability diagnostics. Those are frequentist extensions to the shared scientific examples, not substitute case studies.