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Re: st: Cox regression using a shared frailty model in multiply imputed data
From
Justin Schaffer <[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 12:51:10 -0800
I appreciate the thoughts... It just seems a little fishy to me that other Cox extensions (like time varying covariates) work smoothly (i.e. Stata displays the tvc coefficient) when using them with multiple imputation but the same is not true for shared frailty (I showed in my follow-up post that when using a Cox model that had both a shared-frailty model and a time varying covariate, Stata correctly spit out its estimate of the time varying covariate, but not of theta).
To be honest , I'm hoping for a bit more of an authoritative stance as to why Stata won't give me theta (rhyme intended), and whether I can/should figure out theta on my own (as well as the likelihood ratio test of theta) by manually running the cox regressions on my imputed datasets.
I can't be the first person to run a Cox regression with shared frailty on an imputed dataset. Someone must have run into this issue before me, and come up with a workaround, or figured out how to get Stata to give them theta.
Thanks,
Justin
> On Feb 12, 2014, at 5:29 AM, Stas Kolenikov <[email protected]> wrote:
>
> 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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