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Piecewise Exponential Approximation to a Survival Distribution

Source: R/getDesignSurvivals.R
pwexpcuts.Rd

Obtains the piecewise exponential distribution that approximates a survival distribution.

Usage

pwexpcuts(S, ..., tol = 1e-04)

Arguments

S

The survival function of a univariate survival time.

...

Additional arguments to be passed to S.

tol

The tolerance for convergence of the profile log-likelihood. Defaults to 0.0001.

Value

A list with three components:

  • piecewiseSurvivalTime: A vector that specifies the starting time of piecewise exponential survival time intervals. Must start with 0, e.g., c(0, 6) breaks the time axis into 2 event intervals: [0, 6) and [6, Inf).

  • lambda: A vector of hazard rates for the event. One for each analysis time interval.

  • loglik: The sequence of the asymptotic limit of the piecewise exponential log-likelihood for an increasing number of change points.

Details

This function computes the piecewise exponential approximation to a survival distribution. The piecewise exponential model divides the time axis into \(J\) intervals defined by the change points, where each interval \([t_j, t_{j+1})\) has a constant hazard rate \(\lambda_j\). The time intervals are specified as: $$[t_1, t_2), [t_2, t_3), \ldots, [t_{J}, t_{J+1})$$ where \(t_1 = 0\), \(t_{J+1} = \infty\), and \(t_j = \tau_{j-1}\) for \(j = 2, \ldots, J\). The function starts with \(J = 2\) (1 change point) and gradually increases \(J\) by adding one change point at a time until the maximized profile log-likelihood for change points stabilizes, i.e., the relative increase in the maximum of the profile log-likelihood function is less than tol. If the relative change in the hazard rate is also less than tol, the function stops and returns the results.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


# Example 1: Piecewise exponential
pwexpcuts(ptpwexp, piecewiseSurvivalTime = c(0, 3.4, 5.5),
          lambda = c(0.0168, 0.0833, 0.0431), lowerBound = 0,
          lower.tail = FALSE)
#> $piecewiseSurvivalTime
#> [1] 0.000000 3.399971 5.500012
#> 
#> $lambda
#> [1] 0.01680000 0.08329879 0.04310000
#> 
#> $loglik
#> [1] -4.120403 -4.096664
#> 

# Example 2: Weibull
pwexpcuts(pweibull, shape = 1.37, scale = 1/0.818, lower.tail = FALSE)
#> $piecewiseSurvivalTime
#> [1] 0.0000000 0.5266367 1.2814623 2.0762636 2.8645205 3.6338592
#> 
#> $lambda
#> [1] 0.5842842 0.9756606 1.2392703 1.4363304 1.5939072 1.7628962
#> 
#> $loglik
#> [1] -1.066978 -1.058643 -1.057256 -1.057019 -1.056978
#>