Objectives:
Our longitudinal frailty modelling in ageing mice (12 to 27 months) was affected by substantial late-stage data censoring due to scheduled tissue collection or intervention related dropout, particularly at the 24- and 27-month time points. During longitudinal frailty model building, a likelihood based M3 method was combined with a cut-off threshold based on the minimum observed frailty index at 24 months was necessary. However, the results of the NONMEM analysis were not consistent with the comparative statistical analysis previously published. Therefore, this study aimed to quantitate the impact of late-stage data censoring on parameter recovery, accuracy and robustness, and to confirm which parameters could robustly be estimated from the original trial data.
Methods:
Virtual populations of varying sample sizes (N=33, 66, and 99) were simulated using the final structural longitudinal frailty model i.e., a sigmoidal Emax frailty progression model. This model included baseline frailty (E0), time to reach half-maximal effect (ET50), a Hill coefficient, and maximum frailty increase (Emax) parameters. Between subject variability (BSV) was initially set at 30% for E0 and ET50, and additive and proportional residual unexplained variability (RUV) set to 0.0173 and 0.23 respectively. Simulated datasets were systematically right censored at 24 and 27 months using an empirical minimum frailty index at 24 months i.e., ULOQ. Five progressives censoring scenarios at 24 and 27 months were evaluated: 80/40%, 60/30%, 50/20%, 30/15%, and 10/5% respectively. Using the structural longitudinal frailty model, parameters were estimated using both the M3 method with Laplacian estimation and a standard non-M3 approach where censored observations were omitted (Method=FOCE). Robustness was assessed using percentage parameter bias (+/- 15%) and precision across SSE replicates.
Results:
Parameter robustness performance increased with increasing sample size, with as expected the largest virtual population (N=99), demonstrating the highest stability and accuracy for the M3 method. Relative to the true simulation reference values, the estimation biases for the complete, uncensored dataset in the N=99 cohort was less than +/- 10% for all three parameters, E0, ET50, and Emax. Under progressive censoring, the M3 method maintained stable and robust estimation across all parameters. For the Emax, M3 bias remained consistently less than +/- 10% whereas the non-M3 approach showed severe, progressive underestimation, with bias reaching ~-30%. This indicates that ignoring censored late-stage observations leads to systematic flatting of the frailty trajectory and underestimation of maximum frailty burden. Similarly, ET50 estimation was well-preserved under the M3 method (bias less than +/- 10%) while the non-M3 approach collapse drastically to a bias of <-25%. E0 as expected was comparable between both methods due to no censoring in the early and mid-study data points.
Conclusions:
Late-stage censoring challenges the ability to get precise parameter estimates in longitudinal frailty models, resulting in systematic underestimation of the maximum disease burden (Emax) and the progression rate (ET50). However, the M3 method successfully preserves the full trajectory and parameter estimation even under extreme data loss (10/5%), particularly when using the largest virtual population (n=99). Given the original study design (N=33), these results indicate that by utilising the M3 workflow and ULOQ approach, we can robustly trust the estimates for E0 only.