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Cox Proportional Hazards Regression analysis was used to retrieve baseline survival function and to model multivariable survival data.
Results of this model are summarized by plotting the estimated probability of being waitlisted within 12 months by group and date of dialysis initiation, accounting for censoring and holding all covariates constant at their sample means; these calculations combined information from the baseline survival function and adjusted relative hazard estimates.
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Survival probabilities were derived from simple Cox regression model for mortality endpoints after estimation of baseline survival functions and from simple competing risk regression model for non-mortality endpoints.
As we have shown, obtaining a simple but adequate approximation to the baseline survival function is not difficult, and indeed can be tackled in other ways if desired (e.g. spline functions [ 45]).
In term of calibration, the inaccuracy prediction between observed and predicted survival curves may result by substantial different baseline survival function in the two populations (derivation and validation sets).
Application of the model requires ancillary quantities, in particular, the prognostic index and the baseline survival function.
We are not arguing for grouping as advantageous in the interpretation or application of the model, nor of course in the reporting of the model where we point to the need for presenting both the prognostic index and the baseline survival function.
For full cohort data this takes the form (2) S t | x = S 0 t exp βx where t represents time from study entry, S(t| x) is the probability of surviving beyond time t given covariates x and S0 t) is the baseline survival function at time t.
Individual patient data would also allow model assumptions, for example proportional hazards, to be checked as necessary, and enable the baseline survival function to be estimated.
These rely on having at least the weights of the variables included in the linear predictor, and ideally the baseline survival function.
If we knew the baseline hazard function, we could integrate it over time to compute the cumulative hazard function, H 0 (t ) = ∫ 0 t h 0 (u ) du, and hence the baseline survival function, S0 t) = exp [- H0 t)].
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