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For those interested in getting access to the Excel spreadsheet used in this blog, please download it at this link ). Location of Excel spreadsheet developed by Hoyle and Henley (Update : I learned that Martin Hoyle is not hosting this on his Exeter site due to a recent change in his academic appointment.

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Additionally, we will learn how to extrapolate the survival curve beyond the time period used to generate the Weibull parameters for cost-effectiveness studies that use a lifetime horizon. In the next blog, we will discuss how to use the Weibull parameters to generate a survival curve using a Markov model. Plot(km, xmax=600, xlab='Time (Days)', ylab='Survival Probability')įrom Figure 11, we also have the lambda (λ=0.002433593) and gamma (γ=1.722273465) parameters which we’ll use to simulate survival using a Markov model. Km <- survfit(Surv(times_start, times_end, type='interval2')~ 1) # consider adding this (from Arman Oct 2016) to plot KM Sd(means) # standard deviation of mean survival Means <- (1/lambdas)^(1/gammas) * gamma(1+1/gammas) # mean times for Weibull distrubtion Gammas <- 1/exp(log_scales) # g for Weibull, where S(t) = exp(-lt^g) Lambdas <- 1/ (exp(intercepts))^ (1/exp(log_scales)) # l for Weibull, where S(t) = exp(-lt^g) Log_scales <- sim_parameters # log scale parameters Intercepts <- sim_parameters # intercept parameters Sim_parameters <- mvrnorm(n=simulations, summary(model)$table, summary(model)$var ) # simulates simulations from multivariate normal Simulations <- 10000 # number of simulations for standard deviation of mean # Simulate variability of mean for Weibull T(chol(summary(model)$var)) # Cholesky matrix # For the Probabilistic Sensitivity Analysis, we need the Cholesky matrix, which captures the variance and covariance of parameters (1/lambda)^(1/gamma) * gamma(1+1/gamma) # mean time for Weibull distrubtion Gamma <- 1/exp(log_scale) # g for Weibull, where S(t) = exp(-lt^g) Lambda <- 1/ (exp(intercept))^ (1/exp(log_scale)) # l for Weibull, where S(t) = exp(-lt^g) # output for the example of the Weibull distribution Log_scale <- summary(model)$table # log scale parameter Intercept <- summary(model)$table # intercept parameter 2*summary(model)$loglik + 2*log(n_patients) # BIC for 2-parameter distributions 2*summary(model)$loglik + 2*2 # AIC for 2-parameter distributions 2*summary(model)$loglik + 1*log(n_patients) # BIC exponential 2*summary(model)$loglik + 1*2 # AIC for exponential distribution

N_patients <- sum(n_events) + sum(n_censors)

Model <- survreg(Surv(times_start, times_end, type='interval2')~1, dist='loglogistic') # Loglogistic function, interval censoring Model <- survreg(Surv(times_start, times_end, type='interval2')~1, dist='lognormal') # Lognormal function, interval censoring Model <- survreg(Surv(times_start, times_end, type='interval2')~1, dist='logistic') # Logistic function, interval censoring Model <- survreg(Surv(times_start, times_end, type='interval2')~1, dist='weibull') # Weibull function, interval censoring Model <- survreg(Surv(times_start, times_end, type='interval2')~1, dist='exponential') # Exponential function, interval censoring choose one of these function forms (WEIBULL was chosen for the example) #code does not apply because 0 at risk at last time point # adding times for patients at risk at last time point Times_end <-c( rep(end_time_censor, n_censors), rep(end_time_event, n_events) ) Times_start <-c( rep(start_time_censor, n_censors), rep(start_time_event, n_events) ) Setwd('insert the folder path where the data is stored')

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Update directory name and text file name in line below I use Stata's data library for convenience.) Open Stata and enter the following in the command line: (You can use any published Kaplan-Meier curve. We will use an example dataset from Stata’s data library. Generate a Weibull curve that closely resembles the survival function and whose parameters can be easily incorporated into a simple three-state Markov model Specifically, I will describe how to:Ĭapture the coordinates of a published Kaplan-Meier curve and export the results into a *.CSV fileĮstimate the survival function based on the coordinates from the previous step using a pre-built template This blog provides a practical, step-by-step tutorial to estimate a parameter method (Weibull) from a survival function for use in CEA models.

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Extrapolation to a lifetime horizon is possible using a series of methods based on parametric survival models (e.g., Weibull, exponential) but performing these projections can be challenging without the appropriate data and software. However, these Kaplan-Meier curves may only provide survival data up to a few months to a few years. Data for mortality are normally derived from survival curves or Kaplan-Meier curves published in clinical trials. In cost-effectiveness analysis (CEA), a life-time horizon is commonly used to simulate a chronic disease.

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