I realize I haven’t posted here something that has informed my thinking for a while.
This paper is very interesting in assessing the efficacy of contact tracing apps. It does so by properly assessing the counterfactual (i.e. no app deployed) and thus decomposing the proposed interventions with more granularity.
In particular it shows that most of the utility of such app is derived not from the notifications, but from the other interventions put in place alongside, with the main benefit actually derived from the “isolation-upon-symptoms” policy. This is important, as many of the recipients of an app notification might be warned indeed before contact tracers find them, but - had the app not been deployed - would have started having symptoms a tad later anyways. So if you analyze efficacy of the app, you have to be very careful in setting your counterfactuals.
Once those other measures are separated, the paper also quantifies the utility of the app “on top” of those other measures. Essentially it says you can only hope for a reduction on the order of 0.05 in Reff, short of a completely unrealistic installation base in the population. The paper also points out their result is at first glance very different from much more influential papers on the efficacy of contact tracing apps, based on predictive models. They then go on to explain, in Section 6.4, that this is actually the result of the counterfactual mistake explained above: the results in those other papers are being misunderstood, as what appears useful is not just the app but the app and the “isolation-upon-symptoms” policy.
In any case, this formulation as a reduction of R_eff is very useful, since it matches how this other paper formulates its own results. The latter tries to quantify the reduction of R_eff associated to non pharmaceutical interventions. For instance, it finds out that closing nightclubs contributes to a reduction of R_eff of around 0.15 in Switzerland (compared to fully open, post lockdown). One (very preliminary) interpretation of this result is that the risk of opening of nightclubs would not be compensated by the benefit of SwissCovid.