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Sent from my phone. Please excuse my brevity.

>

>First, as others have said please obey the mailing list rules and turn

>of

>First, as others have said please obey the mailing list rules and turn

>off html, not everyone uses an html email client.

>

>Here is your code, formatted and with line numbers added. I also fixed

>one error: "y" should be "status".

>

>1. fit0 <- coxph(Surv(futime, status) ~ x1 + x2 + x3, data = data0)

>2. p <- log(predict(fit0, newdata = data1, type = "expected"))

>3. lp <- predict(fit0, newdata = data1, type = "lp")

>4. logbase <- p - lp

>5. fit1 <- glm(status ~ offset(p), family = poisson, data = data1)

>6. fit2 <- glm(status~ lp + offset(logbase), family = poisson, data =

>data1)

>7. group <- cut(lp, c(-Inf, quantile(lp, (1:9) / 10), Inf))

>8. fit3 <- glm(status ~ -1 + group + offset(p), family = poisson, data

>= data1)

>

>The key idea of the paper you referenced is that the counterpart to the

>Hosmer-Lemishow test (wrong if used directly in a Cox model) is to look

>at the predicted values from a Cox model as input to a Poisson

>regression. That means adding the expected from the Cox model as a

>fixed term in the Poisson. And like any other poisson that means

>offset(log(expected)) as a term.

>

>The presence of time dependent covariates does nothing to change this,

>per se, since expected for time fixed is the same as for time varying.

>In practice it does matter, at least philosophically. Lines 1, 2, 5 do

>this just fine.

>

>If data1 is not the same as data0, a new study say, then the test for

>intercept=0 from fit1 is a test of overall calibration. Models like

>line 8 try to partition out where any differences actually lie.

>

>The time-dependent covariates part lies in the fact that a single

>subject may be represented by multiple lines in data0 and/or data1. Do

>you want to collapse that person into a single row before the glm fits?

>If subject "Jones" is represented by 15 lines in the data and "Smith"

>by 2, it does seem a bit unfair to give Jones 15 observations in the

>glm fit. But full discussion of this is as much philosophy as

>statistics, and is perhaps best done over a beer.

>

>Terry T.

>

>________________________________

>From: Max Shell [

[hidden email]]

>Sent: Wednesday, January 17, 2018 10:25 AM

>To: Therneau, Terry M., Ph.D.

>Subject: Re: Time-dependent coefficients in a Cox model with

>categorical variants

>

>Assessing calibration of Cox model with time-dependent

>coefficients<

https://stats.stackexchange.com/questions/323569/assessing-calibration-of-cox-model-with-time-dependent-coefficients>

>

>I am trying to find methods for testing and visualizing calibration to

>Cox models with time-depended coefficients. I have read your 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$B!$(BI simplely use data1$B!!(B<- 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!

>

>On Mon, Jan 15, 2018 at 9:23 PM, Therneau, Terry M., Ph.D.

><

[hidden email]<mailto:

[hidden email]>> wrote:

>The model formula " ~ Histology" knows how to change your 3 level

>categorical variable into two 0/1 dummy variables for a regression

>matrix. The tt() call is a simple function, however, and ordinary

>multiplication and does not have those powers. In this case you need

>to do the setup by hand : create your own 0/1 dummy variables and work

>with them.

>

>sqcc <- ifelse(dta$Histology == 'Sqcc', 0, 1)

>hrac <- ifelse(dta$Histology == 'High risk AC', 0, 1)

>fit <- coxph(Surv(time, status) ~ Sex + sqcc + hrac + tt(sqcc) +

>tt(hrac),

> data = dta, tt = list(function(x,t, ...) x*log(t),

> function(x, t, ...) x* log(t)))

>

>

>Terry Therneau

>

>PS I've rarely found x*log(t) to be useful, but perhaps you have

>already looked at the cox.zph plots and see that shape.

>

>

>Suppose I have a dataset contain three variants, looks like

>head(dta)

> Sex tumorsize Histology time status

> 0 1.5 2 12.1000 0

> 1 1.8 1 38.4000 0

>.....................

>

>Sex: 1 for male; 0 for female., two levels

>Histology: 1 for SqCC; 2 for High risk AC; 3 for low risk AC, three

>levels

>Now I need to get a Time-dependent coefficients cox fit:

>

>library(survival)

>for(i in c(1,3) dta[,i] <- factor(dta[,i])

>fit <-

> coxph(

> Surv(time, status) ~ Sex + tumorsize + Histology + tt(Histology),

> data = dta,

> tt = function(x, t, ...) x * log(t)

> )

>

>But I keep gettting this error says:

>

>Error in if (any(infs)) warning(paste("Loglik converged before variable

>", :

> missing value where TRUE/FALSE needed

>In addition: Warning message:

>In Ops.factor(x, log(t)) : ?*? not meaningful for factors.

>

>How can I fix it? I know that the "Sex" and "Histology" are both

>categorical variants. I want to have a model that have two ?(t) = a +

>blog(t) for each histology level.

>Thank you?

>

>

>

> [[alternative HTML version deleted]]

>

>______________________________________________

>

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