Web-based Supporting Materials for
The impact of additional life-table variables on excess mortality estimates
by Nathalie Grafféo, Valérie Jooste and Roch Giorgi.
Web-Appendix A: Extended Discussion
In this article, simulation studies were conducted to assess the impact of an additional life-table
variable on the estimates of excess mortality. The two first scenarios assessed (1) the
performance of the excess hazard model in simple situations; and (2) the impact of the lack of an
additional life-table variable in a simple case. In the following scenarios, simulations of plausible
situations were carried out, and are discussed below.
Scenario 3 would correspond to the use of data from a single Département with a national life
table instead of the use of a Département-specific life table. By using inappropriate life table in
the estimation step of the simulation, we obtained an important impact on the estimation of the
effect of age and this impact was even stronger when the mortality rates used in the estimation
step were lower than the ones used in the generation step. These results are consistent with
findings by Dickman et al. [1] that the misuse of a life table not stratified by the socioeconomic
status in a relative survival analysis augmented the difference in survival between different social
classes. Indeed, if we consider a population from a low (conversely, high) social class having
lower (conversely, higher) mortality rates than the general population (say, mortality rate
differences -0.30 and +0.30, respectively, between low social class and high social class vs. the
general population), then, the difference between the estimates of the effects of age in the low
and the high class would be equal to the difference between the true effects of age plus a positive
term. Considering that this situation corresponds to the one explored in Scenario 3, this difference
would be equal to 0.0163+0.0078=0.0241 (Cf. Table II of the original article).
Scenario 4 would exemplify a situation where the analysis would be based on data from several
Départements and the use of a national life table instead of a life table stratified by Département.
In our simulation, the increase in the spaces between the expected mortality rates at each level of
the additional life-table variable and the corresponding overall mortality rates resulted in an
increased impact on the estimates of the effects of the covariates on the excess mortality. In the
same time, there was an underestimation of the baseline excess hazard function. This can be
explained by the predominance, in the global population, of people missing the additional lifetable variable (84% with modality 0 in the general population) and having lower mortality rates
than the general population. But one may notice that two mortality rates (e.g., in men from two
states of the USA) were hardly proportional, except some age classes (e.g., between 40 and 60
years old, for black and white American men). This is why we studied, in Scenario 5, cases where
the linear representations of the mortality rates intersected. The impact on the estimates of the
effects of both age and the additional variable was higher when mortality rates intersected at
young than at older ages (> 70 years). In fact, the former case means always higher expected
hazard rates in the global population than in the population presenting the additional life-table
variable. This contradicts the fact that the log hazard ratio for the additional variable was positive.
Web-Appendix B: Figures
Figure1. Estimates of the Baseline Hazard Function in Scenario 3 exploring the impact of
the lack of an additional life-table variable in case of variations of the expected mortality
hazard rates for a single fixed modality of X.
Panels (a), (b), (c) and (d) show examples of the translation parameter, Δ0, equal to -0.30, -0.10,
+0.10, and +0.30, respectively. Bold curves represent the ‘true’ functions, dashed curves the
mean of the 1000 cubic-spline estimates. In Scenario 3: (1) life tables stratified by a binary
variable X were used in the survival data generation step; (2) a life table not stratified by X was
used in the estimation step; (3) X was fixed to 0; and (4) the values used for survival data
generation differed from those used for estimation by 10
0
.
Figure2. Estimates of the Baseline Hazard Function (BHF) in Scenario 4 exploring the
impact of the lack of an additional life-table variable in case of opposed variations of the
expected mortality hazard rates according to the modality of X.
Dashed curves represent 3 examples of distances (Δ0, Δ1) between the representations of the
mortality rates, on a logarithmic scale, related to X=0 and X=1. In Scenario 4: (1) life tables
stratified by a binary variable X were used in the survival data generation step; (2) a life table not
stratified by X was used in the estimation step; and (3) the mortality rates for people having
modality X equal to 0 (conversely, 1) differed from the mortality rates used for estimation by
10  0 (conversely, 10 1 ).
REFERENCES
1. Dickman PW, Auvinen A, Voutilainen ET, Hakulinen T. Measuring social class differences
in cancer patient survival: Is it necessary to control for social class differences in general
population mortality? A Finnish population-based study. Journal of Epidemiology and
Community Health 1998; 52:727-734. DOI:10.1136/jech.52.11.727