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Re: st: Cox regression using a shared frailty model in multiply imputed data
From
Stas Kolenikov <[email protected]>
To
"[email protected]" <[email protected]>
Subject
Re: st: Cox regression using a shared frailty model in multiply imputed data
Date
Wed, 12 Feb 2014 08:29:05 -0500
My guess is that theta is parameterized differently (e.g., as a log),
and -mi- does not know about it. So it just shows the coefficients
from the main equation.
-- Stas Kolenikov, PhD, PStat (ASA, SSC)
-- Principal Survey Scientist, Abt SRBI
-- Opinions stated in this email are mine only, and do not reflect the
position of my employer
-- http://stas.kolenikov.name
On Tue, Feb 11, 2014 at 8:53 AM, Justin Schaffer
<[email protected]> wrote:
> Hello, first time poster here (please excuse my ignorance).
>
> Stata (using Stata 13) will allow me to create a Cox regression model
> with shared frailty on a multiply imputed dataset. However, it does
> not give me an estimate of theta after running the command as it does
> when I run the regression model with shared frailty on non-imputed
> data. Can someone explain why this is, and whether I am violating some
> obscure law of statistics when I create a Cox regression model with
> shared frailty on my imputed dataset? I assume that estimating the
> standard error of theta is not statistically valid on an imputed
> dataset which is why the theta value is not shown, but to be honest, I
> am out of my league here. One option I'm considering is running the
> regression on each of my imputed data sets after creating a separate
> file for each imputed dataset (using mi set flongsep) and then
> averaging the theta values and estimating the standard error using
> Rubin's rules (although I have no clue if this is statistically
> valid). Notably, the variable that I regress on as well as the
> "random" variable of my shared frailty model need not be imputed (i.e.
> in the example below I run a Cox regression with shared frailty on the
> variable "age" with the variable "hosp_id" as my random effect
> variable, although neither "age" nor "hosp_id" were actually imputed
> in my dataset).
>
> Example:
>
> stset daysAlive, fail(dead)
> sts generate nelsonAalen = na
>
> mi set wide model01
> mi register regular age hosp_id nelsonAalen dead
> mi register impute imputed_variable
> mi impute chained (pmm) imputed_variable = age hosp_id dead
> nelsonAalen, add(20) augment chaindots burnin(10) rseed(1234)
>
> mi stset daysAlive, fail(dead==1)
>
> //Cox model with shared frailty on imputed dataset
> mi estimate, hr dots: stcox age, shared(hosp_id)
>> Imputations (20):
>> .........10.........20 done
>>
>> Multiple-imputation estimates Imputations = 20
>> Cox regression: Breslow method for ties Number of obs = 3174
>> Average RVI = 0.0000
>> Largest FMI = 0.0000
>> DF adjustment: Large sample DF: min = .
>> avg = .
>> max = .
>> Model F test: Equal FMI F( 1, .) = 31.39
>> Within VCE type: OIM Prob > F = 0.0000
>>
>> ------------------------------
> ------------------------------------------------
>> _t | Haz. Ratio Std. Err. t P>|t| [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>> age | 1.030194 .0054693 5.60 0.000 1.01953 1.040969
>> ------------------------------------------------------------------------------
>
> //Cox model with shared frailty on non-imputed dataset
> stcox age, shared(hosp_id)
>> failure _d: dead == 1
>> analysis time _t: daysAlive
>>
>> Fitting comparison Cox model:
>>
>> Estimating frailty variance:
>>
>> Iteration 0: log profile likelihood = -8334.2065
>> Iteration 1: log profile likelihood = -8334.2065 (backed up)
>> Iteration 2: log profile likelihood = -8333.3181
>> Iteration 3: log profile likelihood = -8333.2928
>> Iteration 4: log profile likelihood = -8333.2927
>>
>> Fitting final Cox model:
>>
>> Iteration 0: log likelihood = -8369.2282
>> Iteration 1: log likelihood = -8333.5078
>> Iteration 2: log likelihood = -8333.2927
>> Iteration 3: log likelihood = -8333.2927
>> Refining estimates:
>> Iteration 0: log likelihood = -8333.2927
>>
>> Cox regression --
>> Breslow method for ties Number of obs = 3174
>> Gamma shared frailty Number of groups= 60
>> Group variable: hosp_id
>>
>> No. of subjects = 3174 Obs per group: min= 1
>> No. of failures = 1138 avg = 52.9
>> Time at risk = 2951413 max= 283
>>
>> Wald chi2(1) =31.39
>> Log likelihood = -8333.2927 Prob > chi2 =0.0000
>>
>> ------------------------------------------------------------------------------
>> _t | Haz. Ratio Std. Err. z P>|z| [95% Conf.Interval]
>> -------------+----------------------------------------------------------------
>> age | 1.030194 .0054693 5.60 0.000 1.01953 1.040969
>> -------------+----------------------------------------------------------------
>> theta | .0391666 .0190069
>> ------------------------------------------------------------------------------
>> Likelihood-ratio test of theta=0: chibar2(01) = 11.50 Prob>=chibar2 =0.000
>>
>> Note: standard errors of hazard ratios are conditional on theta.
>
> Many thanks in advance for any statistical advice you gurus have to offer.
>
> Sincerely,
>
> JMS
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