The impact of proportional changes in age-specific mortality on life expectancy when the mortality rate is a log-linear function of age

Væth, Michael; Skriver, Mette Vinther; Støvring, Henrik

doi:10.4054/demres.2018.39.23

Cited by 5 publications

(2 citation statements)

References 12 publications

(9 reference statements)

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“…The linear relationship was first established theoretically for standardized mortality ratios, when hazard rates increase log-linearly and are proportional. 6 However, we found that the difference in mean survival could be empirically predicted from the HR even when the assumption of log-linear hazard rates was violated for the included cancers. For cancers with a log-linearly increasing hazard rate following diagnosis, the approximation should be expected to improve.…”

Section: Discussionmentioning

confidence: 83%

“…Our investigation is motivated by 2 considerations: first, we have in 2 recent studies established that there is a very accurate linear relation between the logarithmic standardized mortality ratio (log SMR) and the (residual) life expectancy of populations. 6 Theoretically, the relationship was derived when survival follows a Gompertz distribution (log-linearly increasing hazard), but the robustness of empirical associations 7 suggests that the linearity may persist even when this assumption is not fulfilled, as is the case among cancer patients after diagnosis. Cancer patients will typically face substantially increased mortality (hazard rates) in the first years after diagnosis, after which their mortality will gradually resemble the general population of the same age and sex.…”

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confidence: 99%

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Predicting Difference in Mean Survival Time from Reported Hazard Ratios for Cancer Patients

et al. 2019

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Background. Gain in mean survival time from new cancer treatments is a core component of cost-effectiveness analyses frequently used by payers for reimbursement decisions. Due to limited follow-up time, clinical trials rarely report this measure, whereas they often report hazard ratios comparing treatment groups. Aim. We aimed to explore the empirical relationship between gain in mean survival time and the hazard ratio for cancer patients. Methods. We included all patients in Norway diagnosed from 1965 through 2004 with late-stage cancer at the point of diagnosis and with one of the following cancers: stomach, colon, rectal, pancreas, lung and trachea, kidney excluding renal pelvis, and metastasized breast and prostate. Patients were followed until emigration, death, or June 30, 2016, whichever came first. Observed mean survival times and hazard ratios were obtained in subcohorts defined by patients’ sex, age, cancer type, and time period of diagnosis, which had nearly complete follow-up. Based on theoretical considerations, we fitted a linear relationship between observed differences in mean survival and logarithmic hazard ratios. For validation, we estimated differences in mean survival from hazard ratios of bootstrap samples with artificially induced censoring and compared with fitting a Weibull distribution. Results. The relationship between differences in mean survival time and corresponding logarithmic hazard ratios was linear for each of the included cancers. The predicted differences in mean survival of the empirical approach generally had smaller bias than the Weibull approach. Conclusion. For cancer diagnoses with poor prognosis, differences in mean survival times could be predicted from corresponding hazard ratios. This hazard ratio–based approach outperforms or is similar to fitting Weibull models to data with incomplete follow-up, while making fewer assumptions.

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Section: Discussionmentioning

confidence: 83%

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confidence: 99%

Predicting Difference in Mean Survival Time from Reported Hazard Ratios for Cancer Patients

et al. 2019

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Transmission Dynamics of Tuberculosis with Age-specific Disease Progression

Chan

Yuan

et al. 2022

Bull Math Biol

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The Mechanism Underlying Change in the Sex Gap in Life Expectancy at Birth: An Extended Decomposition

2019

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The relationship between differential mortality rates and differences in life expectancy is well understood, but how changing differential rates translate into changing differences in life expectancy has not been fully explained. To elucidate the mechanism involved, this study extends existing decomposition methods. The extended method decomposes change in the sex gap in life expectancy at birth into three components capturing the effects of the sex difference in mortality improvement (ρ-effect), life table deaths density by age (f-effect), and remaining life expectancy by age (e-effect). These three effects oppose and augment each other, depending on relative change in sex-differential mortality rates. The new method is applied to period data for 35 countries and cohort data for 25 countries. The results demonstrate how the mechanism, involving the three effects, operates to determine change in the sex difference in life expectancy. We observe the pivotal importance of the f-effect, which is predominantly negative because of lower female mortality, in favoring narrowing rather than widening of the sex gap, in shifting the overall effect to younger ages, and in exaggerating fluctuations due to crisis mortality. The new decomposition provides a more detailed basis for substantive analyses examining change in differences in life expectancy.

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The impact of proportional changes in age-specific mortality on life expectancy when the mortality rate is a log-linear function of age

Cited by 5 publications

References 12 publications

Predicting Difference in Mean Survival Time from Reported Hazard Ratios for Cancer Patients

Predicting Difference in Mean Survival Time from Reported Hazard Ratios for Cancer Patients

Transmission Dynamics of Tuberculosis with Age-specific Disease Progression

The Mechanism Underlying Change in the Sex Gap in Life Expectancy at Birth: An Extended Decomposition

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