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# Re:Re: st: confidence intervals of predicted risk after stcox

 From petretta@unina.it From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re:Re: st: confidence intervals of predicted risk after stcox Date Wed, 31 Oct 2012 10:21:49 +0100 Date Tue, 30 Oct 2012 16:09:05 -0400

```Many thanks to Steve Samuels for the explanation.
I apologize for the previous private replay.
Mario

Mario wrote to me privately. When this happens I refer the writer to the
FAQ paragraph that starts "Do not request private replies...".

My problems are:

1. If i gen survival probability and not risk, the upper and lower
limits of ci seem inverted:

```
They should be inverted. You previously computed CIs for the failure ("risk") curve, now you are computing the CIs for the survival curve. A high risk for failure implies a low risk for survival and vice-versa. This is mathematically so because F = 1 -S, as you
```previously calculated. Thus the upper and lower limits for the two curves are
switched.

[Show Quoted Text - 33 lines][Nascondi Testo quotato]
Gen survlb15 = base15^exp(lb)
gen survub15 = base15^exp(ub)
gen surv15 = base15^exp(xb)
sum survlb15 surv15 survub15

variable |       obs        mean    std. Dev.       Min        max
-------------+--------------------------------------------------------
survlb15 |        48    .7716674    .2110915    .381534   .9887756
surv15 |        48    .5276728     .343838   .0012602   .9593767
survub15 |        48    .2910488    .3057171   8.11e-21   .8586743

2. To compare the survival result at 15 months obtained in subjects
with age40 = 20 and drug = 3, i used the stata command survci
(-survci- sj11-4: St0217_1 ? Initially written by yulia marchenko of
statacorp  and thereafter adjourned by matthew cefalu (the stata
journal (2011), number  1, pp. 64?81 pointwise confidence intervals
for the covariate-adjusted survivor function in the cox model).

The code i used is:
Survci, at(age40=20 drug=3) outfile(age20_drug3).

The results of survci at 15 months are:
_t     _d        _surv       _se          _lb                _ub
15     1        .85324285   .07846486   .6101214      .95029744

those of my code are the same as regard surv15 but very different as
regard the confidence intervals (lower and upper)

surv15             survlb15              survub15
.8532429          .9722255                4089079

There are two mistakes here.
1. The minor one is that the -survci- gives CIs for someone
with   with age = 20 and drug = 3, whereas the *15 values
you show are averages over the entire sample. There's no
reason to expect similarity.

2. The major mistake is that your original CIs reflect only variability of
the estimated betas, whereas -survci-  properly takes into account the fact
that the baseline survival probability is also an estimate.

Steve

[Show Quoted Text - 59 lines][Nascondi Testo quotato]
-----------------------------------------

date: Fri, 26 oct 2012 17:15:04 -0400
from: Steve samuels <sjsamuels@gmail.Com>
subject: Re: St: Confidence intervals of predicted risk after stcox

mario, when i run your code, and sum the new variables, i get:

Variable |       obs        mean    std. Dev.       Min        max
- -------------+--------------------------------------------------------
lb15 |        48    .2283326    .2110915   .0112244   .6184661
risk15 |        48    .4723272     .343838   .0406233   .9987398
ub15 |        48    .7089512    .3057171   .1413257          1

i see nothing strange about them. What is it that does not make sense to you?

Steve

on oct 26, 2012, at 6:45 am, petretta@unina.It wrote:

Hi all,

i use stata/ic 12.1 for windows (32-bit).

I run a cox model to calculate for each patient the predicted probability
of event at 15 months, using predict xb, predict basesurv and adjiusting
the baseline risk

webuse cancer, clear
gen age40=age-40
stcox age40 i.Drug
predict xb, xb
predict basesurv, basesurv
sum basesurv if _t<16
scalar base15 = r(min)
gen risk15 = 1 - base15^exp(xb)

i ask if it is possible to have also the 95% confidence intervals of these
estimate.

I try:

Predict se_xb, stdp
gen lb = xb - invnormal(0.975)*se_xb
gen ub = xb + invnormal(0.975)*se_xb
gen lb15 = 1 - base15^exp(lb)
gen ub15 = 1 - base15^exp(ub)

but the results seems do not have sense.

Mario petretta
dpt. of internal medicine, cardiology and heart surgery
naples university federico ii -italy

Mario, when I run your code, and sum the new variables, I get:

Variable |       Obs        Mean    Std. Dev.       Min        Max
- -------------+--------------------------------------------------------
lb15 |        48    .2283326    .2110915   .0112244   .6184661
risk15 |        48    .4723272     .343838   .0406233   .9987398
ub15 |        48    .7089512    .3057171   .1413257          1

I see nothing strange about them. What is it that does not make sense to you?

*
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Mario Petretta
Dipartimento di Medicina Clinica Scienze Cardiovascolari e Immunologiche
Facoltà di Medicina e Chirurgia
Università di Napoli Federico II
081 - 7462233

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```