Misinterpretation of time-to-first event curves can lead to inappropriate treatment

From the authors:

We thank B. Hartley and co-workers for their correspondence on our analysis of the IMPACT triple therapy trial [1]. We welcome this opportunity to correct some misunderstanding of the computation of monthly rates of exacerbation, when converted from the cumulative incidence curve, as applied to the IMPACT trial.

The rate of a first exacerbation for a given month of follow-up is based not only on the gradient of the survival function as the numerator, as understood by B. Hartley and co-workers, but must also include the survival function as the denominator denoting the subjects at risk of an exacerbation [2]. Thus, the monthly rate is approximated by the difference between the cumulative incidence value at the end of each month with that at the beginning of that month, divided by the survival at the beginning of the month. Using the notation of B. Hartley and co-workers (somewhat confusing since S(t) is typically used to denote the survival function, not the cumulative incidence function as employed in their correspondence), the “rate” at a given point in time (hazard function) is:The corresponding average rate over a given time interval t₁ to t₂ is given by:This is the monthly rate of exacerbation displayed in our figure for the long-acting muscarinic antagonist (LAMA)–long-acting β-agonist (LABA) and triple therapy groups, approximated from the cumulative incidence curves, for the IMPACT trial [1]. It clearly shows that the first month's surge in the rate of exacerbation in the LAMA–LABA group is real, with no differences in the subsequent rates between the two groups during the following 11 months. Thus, contrary to the claim of B. Hartley and co-workers, this proper calculation of the rate supports the conclusion that the difference in the rate of exacerbation between the two groups is due to the first month's surge.

This pattern of an early surge, known as “depletion of susceptibles”, can be informative to understand a treatment's effect [3]. This sudden surge is not unexpected in the IMPACT trial with the abrupt withdrawal of inhaled corticosteroids (ICS) imposed at randomisation and its inclusion of a patient population with a history of asthma, over-represented by frequent exacerbators with milder airflow limitation [4].

Rather than this mathematical sophistication, it would have been more straightforward and certainly more informative if B. Hartley and the authors of the IMPACT trial had simply provided estimates for these monthly rates of an exacerbation directly from the trial data available to them. The authors could then confirm the surge with the actual trial data, and also investigate the role of prior ICS use that was abruptly discontinued at randomisation, as well as prior asthma diagnosis, frequent exacerbator phenotype, GOLD stage and eosinophilia, on this surge. Such analyses would provide valuable data for a better precision medicine targeting of the right treatment for the right patient [5]. Most importantly, this would also allow to prevent unnecessary harms from ICS to those patients who would not benefit from triple therapy.

Shareable PDF