Worked example: evidence verification latency

Question

This example models time to first entry into a source/evidence AOI. Repeated trials occur under standard and evidence_prompt conditions. Complete usable trials that never inspect the evidence AOI remain in the risk set until the observation window ends and are right censored.

Generate raw trial/event inputs

raw <- simulate_gaze_survival_inputs(
  "verification",
  seed = 20260918,
  n_participants = 36,
  trials_per_participant = 3
)

The synthetic input is deliberately not pre-censored. The survival state is constructed from the event definition and the explicit trial observation window.

Construct and validate the survival table

verification <- prepare_gaze_survival_data(
  raw$trials,
  raw$events,
  target_aoi = "source_evidence",
  event_type = "first_aoi_entry",
  condition_col = "condition_id",
  min_valid_fraction = .90,
  time_origin = "trial_start",
  event_detector = "synthetic_truth",
  aoi_specification = "fixed synthetic source/evidence AOI"
)

validate_gaze_survival_data(verification, raise_on_error = FALSE)

## [1] severity code     n        message 
## <0 rows> (or 0-length row.names)

summarise_gaze_censoring(verification, by = "condition")

##         condition n_trials n_analyzable n_observed_events n_censored
## 1 evidence_prompt       54           54                53          1
## 2        standard       54           54                49          5
##   n_review_required censoring_fraction
## 1                 0         0.01851852
## 2                 0         0.09259259

A missing target event becomes ordinary right censoring only when the observation window is complete and usable. Unresolved or poor-quality trials remain review cases.

Kaplan-Meier description

plot_gaze_survival_curve(verification, group = "condition")

Kaplan-Meier curves for time to first source/evidence AOI entry.

Lower survival at a given time means a larger proportion of trials has already inspected the evidence AOI.

Complementary event-incidence view

plot_gaze_cumulative_incidence(verification, group = "condition")

Single-event 1-KM display for time to first source/evidence AOI entry.

This is the complement of the Kaplan-Meier survival curve for one target event. Do not interpret it as a competing-risks cumulative-incidence function when multiple mutually exclusive events compete.

Empirical hazard/risk increments

plot_gaze_hazard(verification, group = "condition")

Empirical event/risk increments for the evidence-verification example.

This plot is most useful as a diagnostic view of when event increments occur relative to the risk set; it should not be oversold as a smooth underlying hazard function.

Repeated-participant Cox model

cox <- fit_gaze_mixed_cox_model(
  verification,
  "condition",
  participant_col = "participant_id",
  structure = "cluster_robust"
)

tidy_gaze_survival_model(cox)

##                term estimate_log_scale std_error hazard_ratio  conf_low
## 1 conditionstandard          -1.087844 0.2157481    0.3369423 0.2207549
##   conf_high statistic      p_value effect_measure
## 1 0.5142812 -5.042194 4.602255e-07   hazard_ratio

check_gaze_proportional_hazards(cox)

##        term rho    chisq    p_value alpha ph_flag
## 1 condition  NA 6.369666 0.01160874  0.05    TRUE
## 2    GLOBAL  NA 6.369666 0.01160874  0.05    TRUE

The hazard ratio is an instantaneous evidence-inspection-rate contrast among trials still at risk. It is not a ratio of mean latencies.

Explicit AFT sensitivity models

weibull <- fit_gaze_aft_model(
  verification,
  "condition",
  distribution = "weibull"
)
lognormal <- fit_gaze_aft_model(
  verification,
  "condition",
  distribution = "lognormal"
)

compare_gaze_survival_models(cox, weibull, lognormal)

## Warning: Information criteria are not directly comparable across Cox partial
## likelihood, coxme penalized frailty likelihood, and AFT full likelihood, or
## across different analysis-row counts. Use diagnostics and estimand-specific
## interpretation instead of ranking by AIC/BIC.

##     model        family           backend    logLik      AIC      BIC   n
## 1 model_1  cox_repeated   survival::coxph -381.0763 764.1526 766.7776 102
## 2 model_2   aft_weibull survival::survreg -138.6049 283.2098 291.2562 108
## 3 model_3 aft_lognormal survival::survreg -140.0168 286.0335 294.0799 108
##         likelihood_basis information_criteria_comparable
## 1 cox_partial_likelihood                           FALSE
## 2        full_likelihood                           FALSE
## 3        full_likelihood                           FALSE

Interpret the AFT effects as time ratios under the named distribution. Do not select Weibull versus log-normal because one gives a more favorable p-value.

Troubleshooting clinic

Stop and resolve the scientific/data contract rather than silently modifying rows when:

• the observation window is missing or incomplete;
• event time exceeds the censoring limit;
• the target is already present at time zero and the time origin is ambiguous;
• gaze quality is below the declared rule;
• event counts are too sparse for stable inference;
• proportional-hazards diagnostics are flagged;
• competing events require a competing-risks estimand.

For coxme frailty fits, report a corresponding marginal Cox PH diagnostic separately rather than pretending cox.zph() applies to the frailty object.

Reporting example

Evidence-inspection latency was analysed as a right-censored time-to-event outcome. The target event was first entry into the source/evidence AOI from trial onset. Complete usable trials without an evidence entry were retained as right-censored observations; unresolved gaze-quality trials were not recoded as censoring. We fitted a participant-clustered Cox model and reported hazard ratios with 95% confidence intervals. Proportional-hazards diagnostics and pre-specified Weibull/log-normal AFT sensitivity models were examined.

Report participants, trials, events, censored trials and percentage, review-required rows, event/AOI/time-origin definitions, gaze-quality rule, repeated-participant structure, effect estimate with 95% CI, diagnostics, sensitivity analyses, and package/backend versions.

API links

Preparation and validation: prepare_gaze_survival_data(), validate_gaze_survival_data(), summarise_gaze_censoring().

Models and diagnostics: fit_gaze_mixed_cox_model(), fit_gaze_aft_model(), check_gaze_proportional_hazards(), compare_gaze_survival_models().

Reporting and visualization: tidy_gaze_survival_model(), report_gaze_survival_model(), plot_gaze_survival_curve().