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The former method combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event [ 7- 13], so that the effects of the treatment and other factors can be interpreted separately into those on the proportion of cured patients and the failure time of uncured patients.
In this paper, to analyse data including such a long-term censored relapse-free time, we discuss a semi-parametric cure regression (Cox cure regression), which combines a logistic formulation for the probability of occurrence of an event with a Cox proportional hazards specification for the time of occurrence of the event.
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Clearly, there is a delicate balance that must be struck between the formulation of the probability axioms, and the understanding of 'bets' and 'sure loss' for the Dutch Book theorem and its converse to hold.
Several formulations of the probability of detection function have been proposed [40,41].
Practical and tractable formulations for determining the probability of progressive collapse in structures are developed.
There are, however, serious concerns regarding the adopted formulation for the calculation of the survival probability of passenger ships, particularly for ROPAX and large cruise vessels.
In this formulation, the probability of loss is minimized instead of the delay.
Our formulation implies that the probability of missingness depends on both outcome and treatment assignment.
As we will show on the analyzed data set, there may be no need for this addition, but we include it in the formulation for the sake of the generality of the response probability derivation.
The maximum likelihood framework seamlessly incorporates quantitative allele probabilities; they only require an alternative formulation for the distribution of the error term.
The above discussion, apart from probability expression of (2), establishes the mixed-integer linear programming (MILP) formulation for the MTHS problem.
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