Dynamic prediction: A challenge for biostatisticians, but greatly needed by patients, physicians and the public

Abstract

Prognosis is usually expressed in terms of the probability that a patient will or will not have experienced an event of interest t years after diagnosis of a disease. This quantity, however, is of little informative value for a patient who is still event-free after a number of years. Such a patient would be much more interested in the conditional probability of being event-free in the upcoming years, given that he/she did not experience the event in the s years after diagnosis, called "conditional survival." It is the simplest form of a dynamic prediction and can be dealt with using straightforward extensions of standard time-to-event analyses in clinical cohort studies. For a healthy individual, a related problem with further complications is the so-called "ageconditional probability of developing cancer" in the next t years. Here, the competing risk of dying from other diseases has to be taken into account. For both situations, the hazard function provides the central dynamic concept, which can be further extended in a natural way to build dynamic prediction models that incorporate both baseline and time-dependent characteristics. Such models are able to exploit the most current information accumulating over time in order to accurately predict the further course or development of a disease. In this article, the biostatistical challenges as well as the relevance and importance of dynamic prediction are illustrated using studies of multiple myeloma, a hematologic malignancy with a formerly rather poor prognosis which has improved over the last few years. K E Y W O R D Sage-conditional probability of developing cancer, conditional survival, dynamic prognosis, landmark regression models, time-dependent bias 822In doing so, we consider only absolute CS since this is the quantity of major interest in a clinical context. From a public health or epidemiologic perspective, however, relative CS, defined as the ratio of survival probabilities with the denominator derived from an age-adjusted normal population, may also be a highly relevant quantity (Shack, Braynt, Lockwood, & Ellison, 2013), which is sometimes also used for a statistical definition of cure (Baade, Youlden, & Chambers, 2011).On the other hand, for a healthy individual it might be of interest to know the probability of developing a certain disease, for example, a specific type of cancer. Quantities that are regularly published are age-specific incidence rates. These, however, cannot be directly translated into probabilities since death from other causes, for example, cardiovascular death, constitutes a competing event. Thus, the framework of multistate competing risks models has to be used to account for this fact. In a similar way as argued for CS, the resulting probabilities are of little value for an individual who is still alive and healthy at some age . Here, age-conditional probabilities of developing or dying from cancer are of interest for healthy individuals and today these are frequently reported by tumor registers and/or national statistical offi...

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