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    <p>The survival function at time t for a log-normal model can be represented in R with <code>1 - plnorm()</code>, where <code>plnorm()</code> is the log-normal cumulative distribution function. To illustrate, we'll first put your plot into a function for convenience:</p> <pre><code>## Function to plot aft data plot.aft &lt;- function(x, legend = c("ICU Patients", "Non-ICU Patients"), xlab = "Days since Infection", ylab="Percent Surviving", lwd = 2, col = c("red", "black"), at = c(0, 20, 40, 60, 80, 100, 120, 140, 160, 180), ...) { plot(x[, 1], x[, 2], type = "l", ylim = c(0, 1), xaxt = "n", xlab = xlab, ylab = ylab, col = col[2], lwd = 2, ...) axis(1, at = at) lines(x[, 1], x[, 3], col = col[1], lwd=2) legend("topright", legend = legend, lwd = lwd, col = col) } </code></pre> <p>Next, we'll specify the coefficients, variables, and models, and then generate the survival probabilities for the exponential and log-normal models:</p> <pre><code>## Specify coefficients, variables, and linear models beta0 &lt;- 5.00 beta1 &lt;- -0.500 icu &lt;- c(0, 1) t &lt;- seq(0, 180) linmod &lt;- beta0 + (beta1 * icu) names(linmod) &lt;- c("unexposed", "exposed") ## Generate s(t) from exponential AFT model s0.exp &lt;- dexp(exp(-linmod["unexposed"]) * t) s1.exp &lt;- dexp(exp(-linmod["exposed"]) * t) ## Generate s(t) from lognormal AFT model s0.lnorm &lt;- 1 - plnorm(t, meanlog = linmod["unexposed"]) s1.lnorm &lt;- 1 - plnorm(t, meanlog = linmod["exposed"]) </code></pre> <p>Finally, we can plot the survival probabilities:</p> <pre><code>## Plot survival plot.aft(data.frame(t, s0.exp, s1.exp), main = "Exponential model") plot.aft(data.frame(t, s0.lnorm, s1.lnorm), main = "Log-normal model") </code></pre> <p>And the resulting figures:</p> <p><img src="https://i.stack.imgur.com/MlkVA.png" alt="Exponential model"></p> <p><img src="https://i.stack.imgur.com/wL0iO.png" alt="Log-normal model"></p> <p>Note that </p> <pre><code>plnorm(t, meanlog = linmod["exposed"]) </code></pre> <p>is the same as</p> <pre><code>pnorm((log(t) - linmod["exposed"]) / 1) </code></pre> <p>which is the Φ in the canonical equation for the log-normal survival function: S(t) = 1 − Φ((ln(t) − µ) / σ)</p> <p>As I'm sure you know, there are a number of R packages that can handle accelerated failure time models with left, right, or interval censoring, as listed in the <a href="http://cran.r-project.org/web/views/Survival.html" rel="noreferrer">survival task view</a>, in case you happen to develop a preference for R over SAS.</p>
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    1. CO@jhetzel I have developed a preference for R over SAS, but I this is Phase 1 of a somewhat more complex project, and I know SAS better. Trying to minimize potential for mishaps with unknown methods and unknown code. Translating it all to R is...on the list.
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