Prognostic Probability Functions from Clinical-Trial Data
In the eminent intervention-prognostic cohort study (experimental) addressed in Chap. 19 above, the data were synthesized in a manner that represents the prevailing state-of-the-art in clinical trials at large; for, the core results on the various outcomes were derived by means of Cox regression, and they were, thus, treatments-comparing “hazard ratios” – incidence-density ratios, that is – for the various entities of the investigators’ concern. Very notably, prognostic probabilities were not addressed in that particular study, nor are they being addressed in other clinical trials, as the Cox model (for “proportional hazards”) does not provide for this. But, as we show in this Chapter, prognostic probabilities, including their functional dependence on prognostic time (jointly with treatment and prognostic indicators), actually can be studied in another theoretical framework for clinical trials (and their quasi-experimental counterparts). In this approach to clinical-trial data, theory of the other species causal gnostic studies – etiognostic studies (singular in their true essence; Sect. 15.6.2) – is brought to bear on intervention-prognostic studies. This brings logistic-regression models into preeminence in the data-synthesis of intervention-prognostic cohort studies (Sect. 15.6) and in prognostic non-cohort studies (non-experimental; Chap. 21).
KeywordsCox regression Alternative sampling Incidence density proper Logistic regression Examples Basic models Augmented models Model fitting
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