It is logically not possible to quantify the number of indirect deaths

Background: A popular statistic to quantify the impact of being exposed to a hazardous factor (e.g., alcohol consumption or air pollution) is the number of people dying prematurely due to this exposure per year. Here, a distinction is essential between deaths occurring immediately after exposure where the causal relationship is obvious (direct deaths) and deaths occurring after a relevant delay (indirect deaths). Since well-designed randomized human long-term-experiments are not feasible in this context, primarily observational data are used for these estimations. The methodological principle that causal conclusions based on observational data need to be questioned critically is a commonly dogma of common-sense, but little attention is given to the question, whether enumerating the number of indirect premature deaths due to a certain exposure is logically feasible in case all empirical problems could be circumvented, if ideal experimental data were available.

Methods: To clarify this issue, theoretical considerations - thought experiments - were performed and an unsystematic search was done for methodological literature related to this issue.

Results: It can be unambiguously demonstrated that estimating the number of indirect deaths is logically not possible, even if perfectly reliable data could be collected experimentally (Which is obviously not feasible because of ethical and practical limitations). The mathematical proof of this fact stems from Robins & Greenland (1989). This presentation aims at illustrating this important insight to the audience with without a formal-mathematical explanation.

Conclusions: Calculations deriving the number of indirect deaths caused by a certain exposure from empirical data are very popular but logically fallacious - or, phrased differently, untenable bogus quantifications.