Differences for the age group estimates are slightly larger
Differences for the age-group estimates are slightly larger (Table 2A, Table 2B), however most of them are lower or close to 1 percentage point. For females, the median and mean value for absolute differences with the AIC model are equal to 0.083 and 0.229 percentage points respectively. Differences for the younger groups are higher but this AZD7687 can be partly explained by the smaller number of patients in these groups.
Age-specific estimates are, due to their nature, more sensitive to the number of knots, and more caution is needed when we choose df for the splines. However, the median and mean absolute differences between the reference model and the selection criteria remain very low. Differences with the AIC model for females have a median of 0.108 and a mean of 0.271 percentage points. Similarly, the median and mean absolute difference with the BIC model are equal to 0.106 and 0.140 percentage points respectively. Age-specific estimates for females with colon cancer are given in Fig. 2. The 5-year relative survival of a patient diagnosed at the age of 55 and 85 years old vary the most under different scenarios in comparison with the other ages. A similar pattern was observed for the 1-year relative survival estimates (Appendix B, Fig B1). More than 3 df might be needed to model the baseline excess hazard (Fig. 2). However, the estimates are not over-sensitive to the number of df and differences in relative survival estimates between the reference model and the models chosen by AIC (i.e. model with 6,3,5 df for the baseline excess hazard, the main and the time-dependent effect of age respectively) and BIC (i.e. model with 4,3,2 df for the baseline excess hazard, the main and the time-dependent effect of age respectively) criteria are small (Table 2A).
A bigger variation is observed in 5-year age-specific estimates for prostate cancer (Fig. 3). The largest differences are seen among different df for the main effect of age and for 75 and 85 years old estimates. The selection criteria suggest that a more complicated model will be more appropriate. The AIC chooses the model with 7,4 and 4 df for the baseline excess hazard, the main and the time-dependent effect of age respectively. The equivalent df for the BIC are 7,3 and 3 respectively. However, the differences between the reference model and the models chosen by the selection criteria remains lower than 1 percentage point for all ages (Table 2B). Smaller differences were observed for 1-year relative survival (Appendix B, Fig B2).
The results are also presented in web-based interactive graphs available at http://pclambert.net/interactivegraphs/model_sensitivity/model_sensitivity, a snapshot of which can be found in Fig. 4. Users can compare the estimates for a range of models by clicking a box. Both estimates of relative survival and excess hazard functions over years since diagnosis are given and there is also an option to choose marginal or age-specific estimates. For example, by moving the slider in the age histogram that can been seen in the bottom of Fig. 4, estimates of relative survival for a 70 years old female with colon cancer are presented.
Discussion We performed sensitivity analyses to assess the sensitivity of estimates obtained from FPMs on the number of knots chosen for the splines by using relative survival as an example. Even though we used relative survival to conduct the sensitivity analysis, our conclusions can also be applied to other settings such as FPMs that do not incorporate the expected mortality. We have also developed web- based interactive graphs that allow the comparison of estimates from different models. We advocate the use of interactive graphs for reporting findings as Saturation hybridization allow for additional exploration and improve understanding of results [, , ].