Partitioning of excess mortality in population-based cancer patient survival studies using flexible parametric survival models.
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For this purpose we extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects.This is done by incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model.Furthermore, we illustrate how the results from the proposed model can be used to derive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence of competing causes of death.
Affiliation: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Box 281, Stockholm, Sweden. sandra.eloranta@ki.se
ABSTRACT
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Background: Relative survival is commonly used for studying survival of cancer patients as it captures both the direct and indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to the expected survival in a comparable cancer-free population. However, existing methods do not allow estimation of the impact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose we extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects. Methods: In the extended model we partition the excess mortality associated with a diagnosis of cancer through estimating a separate baseline excess hazard function for the outcomes under investigation. This is done by incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. This approach thereby enables modeling of temporal trends in e.g., excess cardiovascular mortality and remaining cancer excess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used to derive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence of competing causes of death. Results: The method is illustrated with examples where the total excess mortality experienced by patients diagnosed with breast cancer is partitioned into excess cardiovascular mortality and remaining cancer excess mortality. Conclusions: The proposed method can be used to simultaneously study disease patterns and temporal trends for various causes of cancer-consequent deaths. Such information should be of interest for patients and clinicians as one way of improving prognosis after cancer is through adapting treatment strategies and follow-up of patients towards reducing the excess mortality caused by side effects of the treatment. Related in: MedlinePlus |
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Mentions: In cancer patient survival analyses it has previously been shown that the effects of age at diagnosis and calendar period are often non-proportional. The model was extended to evaluate the need for time-dependent effects for the two covariates by including additional interaction terms with the spline variables representing the time scale. Each time-dependent effect was modelled using 3 df (with knots placed at the 0th, 33rd, 67th and 100th centiles of the uncensored log survival times) whereas the baseline effect was still modelled using 5 df. In this model, the effect of calendar period was assumed common for the two outcomes. The resulting excess mortality rates per 1,000 person-years, for women diagnosed 1978-1982 are shown in figure2. The excess CVD mortality tends to increase as a function of time since diagnosis whereas the opposite is seen for the remaining excess mortality. However, for the eldest age group, the excess CVD mortality seems to follow a U-shape the first 7 years after diagnosis which is probably reflecting that a selection of these patients are presenting with damaged vessels already at the time of diagnosis and are therefore at a higher risk for cardiac mortality even shortly after diagnosis. The excess CVD mortality rate increases with increasing age at diagnosis but is lower than the remaining excess mortality throughout follow-up. Figure3 shows the predicted EMRRs for the effect of age at diagnosis on the component parts as a function of time since diagnosis. Apart from a tendency towards a departure immediately after diagnosis the effect of age at diagnosis on excess CVD mortality remains relatively constant throughout the 15 years of observation time (p for interaction = 0.346). A more notable departure from the proportional hazards assumption is observed for the remaining excess mortality, primarily among the two eldest age groups (p < 0.001). |
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Affiliation: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Box 281, Stockholm, Sweden. sandra.eloranta@ki.se
Background: Relative survival is commonly used for studying survival of cancer patients as it captures both the direct and indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to the expected survival in a comparable cancer-free population. However, existing methods do not allow estimation of the impact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose we extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects.
Methods: In the extended model we partition the excess mortality associated with a diagnosis of cancer through estimating a separate baseline excess hazard function for the outcomes under investigation. This is done by incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. This approach thereby enables modeling of temporal trends in e.g., excess cardiovascular mortality and remaining cancer excess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used to derive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence of competing causes of death.
Results: The method is illustrated with examples where the total excess mortality experienced by patients diagnosed with breast cancer is partitioned into excess cardiovascular mortality and remaining cancer excess mortality.
Conclusions: The proposed method can be used to simultaneously study disease patterns and temporal trends for various causes of cancer-consequent deaths. Such information should be of interest for patients and clinicians as one way of improving prognosis after cancer is through adapting treatment strategies and follow-up of patients towards reducing the excess mortality caused by side effects of the treatment.