[R] Assessing calibration of Cox model with time-dependent coefficients

[Bert Gunter]

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Bert



Bert Gunter

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On Wed, Jan 17, 2018 at 8:24 AM, Max Shell <archerrish at gmail.com> wrote:

> I am trying to find methods for testing and visualizing calibration to Cox
> models with time-depended coefficients. I have read this nice article
> <http://journals.sagepub.com/doi/10.1177/0962280213497434>. In this paper,
> we can fit three models:
>
> fit0 <- coxph(Surv(futime, status) ~ x1 + x2 + x3, data = data0) p <-
> log(predict(fit0, newdata = data1, type = "expected")) lp <- predict(fit0,
> newdata = data1, type = "lp") logbase <- p - lp fit1 <- glm(y ~ offset(p),
> family = poisson, data = data1) fit2 <- glm(y ~ lp + offset(logbase),
> family = poisson, data = data1) group <- cut(lp, c(-Inf, quantile(lp, (1:9)
> / 10), Inf)) fit3 <- glm(y ~ -1 + group + offset(p), family = poisson, data
> = data1)
>
> Here，I simplely use data1 <- data0[1:500,]
> First, I get following error when running line 5.
>
> Error in eval(predvars, data, env) : object 'y' not found
>
> So I modifited the code by replacing the y as status looks like this:
>
> fit1 <- glm(status ~ offset(p), family = poisson, data = data1) fit2 <-
> glm(status ~ lp + offset(logbase), family = poisson, data = data1) group <-
> cut(lp, c(-Inf, quantile(lp, (1:9) / 10), Inf)) fit3 <- glm(status ~ -1 +
> group + offset(p), family = poisson, data = data1)
>
> *Is this replacing correct?*
> Second, I try to introduce the time-transform use coxph with ttparament.
>
> My code is:  fit0 <- coxph(Surv(time, status) ~ x1 + x2 + x3 + tt(x3), data
> = data0, function(x, t, ...) x * t) p <- log(predict(fit0, newdata = data1,
> type = "expected")) lp <- predict(fit0, newdata = data1, type = "lp")
> logbase <- p - lp fit1 <- glm(status ~ offset(p), family = poisson, data =
> data1) fit2 <- glm(status ~ lp + offset(logbase), family = poisson, data =
> data1) group <- cut(lp, c(-Inf, quantile(lp, (1:9) / 10), Inf)) fit3 <-
> glm(status ~ -1 + group + offset(p), family = poisson, data = data1)
> My questions is:
>
>    - Is the code above correct?
>    - How to interpret the fit1, fit2, fit3? What's the connection between
>    the three models and the calibration of the Cox model?
>    - How to generate the calibration plot using fit3? The article dose have
>    a section discuss this, but no code is provided.
>
> Thank you!
>
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>
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