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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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