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The instantaneous hazard rate of return migration at time t, conditional on survival to time t can be written as hleft(t;{x}_iright)={h}_0 t)ast exp left({x}_i^{prime}beta right) (6).
The temporal distribution of deaths and LTFU were assessed by plotting smoothed instantaneous hazard curves from product-limit analyses, using weighted kernel density estimates based on an Epanechnikov function.
An R function epi.instanthaz in the epiR package of R[ 17] was used to calculate the instantaneous hazard rate.
In the following, λ i (t) is the instantaneous hazard function of outcome to be estimated for pair P j.
Structurally, the disease progression model is a continuous time Markov Process governed by instantaneous hazard rates between each state (Ross, 1993).
Following Hogan et al.[ 2], the instantaneous hazard of infection for susceptible individuals s(t) is specified as a B-spline function of time.
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To investigate the pattern of risk over the first year of life, instantaneous hazards of failure based on the Kaplan-Meier survival function were used.
It has previously been shown that the way in which risk factors are associated with the NB hazard (instantaneous risk) may not coincide with the way these factors are associated with the cumulative incidence of NB (cumulative risk) [ 15].
This assumes that the instantaneous risk of death (hazard) for a reference value of a covariate will vary through time, but that the hazards for other values of the covariate will be a constant multiple of this baseline hazard, and this multiple will not vary through time.
For the one component model, the survival function S t) for the overall population survival time and the hazard, the instantaneous risk of death, were fitted assuming the following parametric models: Gaussian, Log-normal, Weibull and Gamma.
Another approach is to perform a visual inspection of the hazard function (instantaneous risk of death) plot to look for temporal changes suggesting a "cure" might have been achieved for some patients [ 4].
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CEO of Professional Science Editing for Scientists @ prosciediting.com