Table 1.
Estimates of the Hazard Ratio and the upper (UCI) and lower (LCI) confidence intervals of the treatment effect of Gefitinib in the IPASS trial.
Fig 1.
Bounds of the Gauss Lobatto (GL) approximation error for the integration of survival data.
A) relationship between (log) MST and the logarithm of the Maximum Hazard rate function for survival distributions with a cubic polynomial log baseline hazard function (B) Box plots of the GL error as a function of the number of nodes in the quadrature rule (C) GL error as a function of the length of the integration interval (taken equal to be equal to the MST for each distribution examined) for different orders of the quadrature rule (D) GL error as a function of the maximum value of the hazard rate for different orders of the quadrature rule.
Fig 2.
Standardized Bias (top row), Mean Square Error (MSE, second row), p-value coverage (third row) and average confidence interval (CIL) coverage (bottom row) for the survival probabilities from four different baselines of the Gompertz, Weibull and Lognormal distributions.
500 datasets of 300 individuals were simulated for each combination of baseline hazard, parameters and censoring percentage (either 30% or 70%) and were subsequently analyzed with the Kaplan Meier method (blue) and the Poisson GAM (red). The three horizontal black lines in the p-value coverage graph give the nominal coverage (0.95) and ± 2 SE(0.95). Coverage is considered acceptable if the p-values fall within the upper and lower horizontal lines.
Fig 3.
Standardized Bias (top row), Mean Square Error (MSE, second row), p-value coverage (third row) and average confidence interval (CIL) coverage (bottom row) of the Hazard Ratio (HR) from four different baselines of the Gompertz and Weibull.
500 datasets of 300 individuals per arm (total 600 patients) were simulated for each combination of baseline hazard, parameters, HR and censoring percentage (either 30% or 70%). These were subsequently analyzed with the Cox proportional hazards model (Cox, blue) and the Poisson GAM (PGAM, red). The three horizontal black lines in the p-value coverage graph give the nominal coverage (0.95) and ± 2 SE(0.95). Coverage is considered acceptable if the p-values fall within the upper and lower horizontal lines.
Fig 4.
Standardized Bias (top row), Mean Square Error (MSE, second row), p-value coverage (third row) and average confidence interval (CIL) coverage (bottom row) of the Restricted Mean Survival Time (RMST) from four different baselines (A-D) of a general lifetime distribution.
500 datasets of 300 individuals per arm (total 600 patients) were simulated for each combination of baseline hazard, parameters, deviation from the baseline log-hazard (Proportional (PH), Linear, Quad(ratic) and Linear-Quadratic (LQ)) and censoring percentage (either 30% or 70%). These datasets were subsequently analyzed with the Poisson GAM to generate predictions for the Restricted Mean Survival Time (RMST). The three horizontal black lines in the p-value coverage graph give the nominal coverage (0.95) and ± 2 SE(0.95). Coverage is considered acceptable if the p-values fall within the upper and lower horizontal lines.
Fig 5.
Kaplan Meier curves and superimposed smooth survival curves estimated by Poisson GAM regression in the IPASS trial.
Black: carboplatin/paclitaxel arm and Blue: gefitinib arm. The smooth lines are the PGAM survival estimates for the corresponding trial arms. The step functions are the Kaplan Meier curves.
Fig 6.
Measures of treatment efficacy in the IPASS trial using proportional hazards (PH) and non proportional hazards PGAMs of two different numerical integration orders: a 10 node Gauss Lobatto (GL10) and a 20 node Gauss Lobatto (GL20) rule.
ARD: Absolute Risk Difference, RR: Relative Risk, HR: Hazard Ratio, RMST: Restricted Mean Survival Time. Dotted lines are the associated 95% pointwise confidence interval of the GL10 PGAM.
Table 2.
Estimates of the Hazard Ratio and associated 95% CI in the HEMO trial.
Fig 7.
Baseline hazard functions in the 15 centers of the HEMO trial produced by a 10 node Gauss Lobatto quadrature rule.
Fig 8.
Log hazard rate function for the interaction between calendar time and duration of ESRD at the beginning of HEMO.
This was estimated via a tensor based smooth in a stratified by center PGAM adjusting for all prespecified baseline covariates in HEMO, a general (not linear) interaction between baseline albumin concentration and observation time, the combined effects of albumin and disease duration (as a tensor product smooth) and the modification of the latter by high flux dialysis.
Fig 9.
Log hazard rate function for the interaction between albumin and duration of ESRD at the beginning of HEMO and flux.
This was estimated via a tensor based smooth in a stratified by center PGAM adjusting for all prespecified baseline covariates in HEMO, a general (not linear) smooth interaction between baseline albumin concentration and observation time, the interaction between albumin and disease duration (as a tensor smooth) and the triple interaction between albumin, disease duration and high flux arm assignment (shown in the Fig). A 10 node Gauss Lobatto quadrature rule was used to numerically integrate the cumulative hazard function.
Fig 10.
Adjusted measures of treatment efficacy in the HEMO trial using the corrected group prognosis method in the subgroups patients with albumin less than 3.5 g/dl, greater than 3.5 g/dl and the entire HEMO sample.
A 10 node Gauss Lobatto quadrature rule was used to numerically integrate the cumulative hazard function. ARD: Absolute Risk Difference, RR: Relative Risk, HR: Hazard Ratio, RMST: Restricted Mean Survival Time. Dotted lines are the associated 95% pointwise confidence interval of the GL10 PGAM.
Table 3.
Options for parametric, flexible modeling of survival data.