Functions & Formulae

Takes each arm's mean QALYs among participants still followed, the proportion of each arm lost to follow-up, an assumed shift delta in the mean QALYs of those lost from the new treatment arm, a ratio r that sets the shift for those lost from usual care at r times delta, the incremental cost and a cost-effectiveness threshold, and returns the delta-adjusted QALY gain and ICER under that shift and the tipping-point shift at which the conclusion changes. The arm mean over everyone randomised, E_bar, is one minus p times E_obs plus p times (E_obs plus delta), which equals E_obs plus p times delta. That is the two-part mixture of HE-FM-LOCF-001 with tau read as p, mu_end as E_obs and mu_last as E_obs plus delta, so its bias_mu, tau times (mu_last minus mu_end), becomes p times delta. The QALY gain under shifts in both arms is Delta_tilde of HE-FM-LOCF-002 with the same reading in each arm, the observed gain plus p_T times delta_T minus p_C times delta_C, here with delta_T equal to delta and delta_C equal to r times delta. The ICER under a shift is HE-FM-ICER-001 and the gain needed at the threshold, Delta_C / lambda, is H_d of HE-FM-CET-002. These live records are cited, not restated, and HE-CF-LTFU-001 runs them in sequence for the article's scenarios. The inverse probability of censoring weights of HE-FN-DCEN-001 and HE-FM-DCEN-001 to HE-FM-DCEN-004 assume that censoring is unrelated to the unseen outcome once measured covariates are allowed for, and the administrative censoring time of HE-FM-ADMC-001 is set by design, so neither represents a departure from missing at random. This package adds the shift at which the delta-adjusted QALY gain falls to Delta_C / lambda. Notation follows the Loss to Follow-Up article.