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    • A marginal structural model by means of additive

    2018-11-05

    A marginal structural model by means of additive hazard regression was thereafter applied to mortality. Additive hazard regression is a flexible model for survival analyses with the linear dependence of the model facilitating decomposition into direct, indirect, and total effects (Lange & Hansen, 2011). The Aalen additive hazard regression is, in itself, entirely non-parametric with covariate effects varying with time (Aalen, 1989). However, a reduction of the model is feasible using the Mckeague and Sasieni (1994), whereby some coefficients are time-invariant, and the Lin and Ying (1994), whereby all coefficients except the baseline are kept time-invariant. This latter model is by analogy an additive version of the Cox regression model. These methods are implemented in the timereg package in R (Scheike & Martinussen, 2006). Standard tests (Scheike & Martinussen, 2006) for the time dependence of coefficients showed that they could be kept time-invariant, thus, the coefficients were presented as the additional number of deaths per year per 1000 breast cancer patients. Similarly, the cumulative baseline mortality could be seen to increase linearly over time, and is therefore presented as the expected number of deaths per year per 1000 patients for the reference group. Direct and indirect effect estimates as well as effect estimates for the total effects were obtained by conducting a parametric bootstrap resampling with 10,000 replications as described by Nordahl et al. (2014). To determine the plausibility of the results, a sensitivity analysis was conducted investigating education-specific changes in incidence and by adjusting for the association between education and the risk of dying from causes other than breast cancer. For the analysis of incidence, Poisson regression modeling was used. The metabotropic glutamate receptor size data contained no information on civil status and parity, as the population at risk was defined as the aggregate population stratified by education, year of diagnosis, age at diagnosis, and year relative to the start of screening in each county. To analyze the association between education and the risk of dying from causes other than breast cancer, all-cause mortality was compared to cancer-related mortality (WHO ICDv10 C00-C97), breast-cancer specific mortality (ICDv10 C50), and excess mortality by subtracting the expected mortality by education level in the general population. The data for the sensitivity analyses are discussed in Appendix C.
    Results
    Discussion The scope of this article was to study the role of cancer stage and socioeconomic inequality in mortality. This study is inherently limited in its focus given the complex relationship between SES and breast cancer incidence and mortality in the general population (Yabroff & Gordis, 2003). Indeed, the results are in line with a central tenet of Yabroff and Gordis which stated that the relationship between SES and mortality is dependent on the relation of stage distribution with SES, which changes upon the introduction of a cancer control program. The introduction of a public screening program was associated with an increase in the incidence of breast cancer that, to some degree, also had a leveling effect of incidence across education levels. In my view, this is supportive of the main findings in this study, since this suggests, but does not confirm, that groups with lower levels of attained education did indeed benefit more from the technology diffused by the introduction of the NBCSP. The estimates of incidence increase are comparable to those of a recent study investigating changes by cancer stage (Lousdal, Kristiansen, Moller, & Stovring, 2016). Since the cancer registry has almost complete coverage of breast cancer incidence (Larsen et al., 2009), it follows that one can also use the data source to evaluate cancer and breast-cancer specific mortality as opposed to total mortality. When assessing mortality among breast cancer patients, the results suggested that direct differences (not through cancer stage) in mortality after the introduction of the program were more uniform across education levels, whereas the indirect effects (those through cancer stage) remained similar to results observed in the all-cause analysis. One interpretation of this finding, although not a definitive conclusion, suggests that any previous differences in breast cancer mortality (beyond what can be observed from the relationship between SES and cancer stage) would remain in future investigations, but would be more equal than differences found in analyses examining in all-cause mortality.