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The additive hazards model considers a random variable Z, representing the changes in the operating conditions with an additive effect on (r(x)) when (Z=z), through the conditional hazard rate r(x mid z)=r(x)+z,quad xgeq0.

We consider the following conditional hazard rate function of failure (Cox 1972).

Equivalently, the conditional hazard rates are the univariate hazard rates of conditional distributions of each variate, given certain inequality of the remainder.

It can be proved (see Shaked 1977) that if the joint PDF f x1,x2) is T P2 (R R2), then the conditional hazard rate of X1|X2 = x2 is decreasing (increasing) in x2.

The estimation results are presented in Tables 2, 3, 4, 5, 6, 7 and in Figs. 3, 4, 5, 6.8 We discuss the qualitative impacts of the variables included in the analysis on the conditional hazard rates by studying the sign and statistical significance of the estimated coefficients.

The relationship with the previous transition intensities is given by: h_F t)=frac{{text{Pr}} (Y_{Ft}=1|Tgeq t)}{{text{Pr}} (Y_{Pt}=0|Tgeq t)}=frac{phi _F t)}{1-phi_P t)}{1-phi_P tarly h_P(t)=frac{phi_P(t)}{1-phi_F(t)} Therefore, in the context of vandablesimilarlytiple exit alternatives, we can ch_P t between modelling the intensities ϕ j (t) or the conditional hazard rates h j (t).

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To address the issue of non-proportional hazards we applied models that allow for non-proportionality of conditional hazards through the introduction of spline-based models.

However, the guiding principle of the presimulation problem was that information on the non-overlapping populations (e.g. direct observation of the conditional hazards) is relatively scarce.

Clearly, if information on one or both conditional hazards is available, interaction (2) with respect to iX is fully characterized for the initial scenario.

Conditional hazards are denoted iX|~C or iX|C to signify "incidence to X in the group without C" and "incidence to X in the group with C", respectively.

It is assumed that conditional hazards are constant within a single reporting interval (e.g. one year), which will in principle be problematic for conditions with high initial case-fatality, for example heart attack (or stroke).

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