Re: st: Dropping right-censored spells in the Cox model

[Nicole Boyle <nicboyle@gmail.com>]

"Say you're conducting small study"
should be
"Say you're conducting a small study"

"declined participation in one HIS/HER studies"
should be
"declined participation in one of HIS/HER studies"

"DeclinationTherefore, eliminating these subjects"
should be
"Therefore, eliminating these subjects"

My apologies. I was highly caffeinated.

Nicole

On Sat, Sep 14, 2013 at 6:28 PM, Nicole Boyle <nicboyle@gmail.com> wrote:
> Hi Kai,
>
> I'll take a stab at this.
>
> I'm going to assume that those "censored spells" you're considering
> dropping do not include those that are censored due to the competing
> risk, but only include noninformative censorship: For subjects
> censored at time "c," probability of survival past some future time
> t>c is the same as probability of survival past t for subjects who
> were merely known to have survived past c. I'm also assuming those
> "censored spells" you're referring to don't include administratively
> censored subjects.
>
> Given the assumption of noninformative censorship in conjunction with
> a central property of Cox regression, I do NOT think dropping censored
> observations is a good idea.
>
> Important to Cox regression is the maximum partial-likelihood
> estimator property, which dictates that hazard estimates are computed
> only at times of failure, using the risk pools available at each of
> these failure times for these computations. All those contributing to
> the "at risk" pool at time=t are not weighted any differently at
> time=t with regards to future failure or future censorship.
>
> Since subjects censored at time=t are considered just as likely to
> fail in the future as subjects NOT censored at time=t, and because
> censored subjects by definition NEVER fail in the data, dropping
> censored subjects from the study reduces the "# at risk" denominator
> from each failure time (where censored observations would have
> normally contributed to this denominator prior to censorship) while
> keeping the "# failed" numerator intact. This will very likely bias
> results.
>
> I suggest that instead of thinking about the data in terms of [total #
> failed] / [total # at risk], which is more of a risk ratio or odds
> ratio mentality, consider thinking of each failure time as an
> independently conducted prevalence estimate.
>
> _Here's an example to clarify_
> Say you're conducting small study, and the ONLY data involves one
> instantaneous prevalence calculation:
> [# dead at this particular moment] / [# at risk for death at this
> particular moment]
>
> Now, imagine one month has gone by since you performed the
> calculation. A colleague (involved in a completely unrelated study)
> informs you that 50% of your original "at risk" sample has now just
> declined participation in one HIS/HER studies.
>
> If YOUR study only concerns the original prevalence calculation, would
> it make sense to drop those subjects unavailable to your colleague's
> study from your original prevalence calculation? Since their
> declination from your colleague's study has no bearing on whether they
> were dead or alive in YOUR study one month ago, it makes no sense to
> drop them. They contributed valuable information.
>
> But furthermore, removing them might be harmful. Only those subjects
> who were alive (not in the "# dead" numerator) in your prevalence
> calculation are the ONLY subjects in your study capable of declining
> study involvement one month later. DeclinationTherefore, eliminating
> these subjects BY DEFINITION biases your prevalence calculation.
>
>
> So, in conclusion:
> The likelihood of censorship at time=t is independent of the
> likelihood of failure at time>t. However, the likelihood of failure at
> time=t is NOT independent of the likelihood of censorship at time>t.
>
> If you discount subjects' past survival contributions based on future
> censorship, you will be at risk of artifactually "powering" your
> resulting HRs. Given the 50% censorship you've mentioned, this
> increased "power" will surely result when dropping this many subjects,
> and may result in more "powerful" HRs or even a change in HR
> direction.
>
> Nicole
>
> On Sat, Sep 14, 2013 at 7:37 AM, Kai Huang <demonsecret@hotmail.com.hk> wrote:
>> Dear all,
>>
>> I have estimated competing-risks Cox models on unemployment spells. The estimates are not very significant probably due to the small number of spells. I wonder whether the high proportion of censored spells in the model (50%) matter. Does it make sense if I drop all the right-censored spells and estimate the models with all spells being completed? Thank you very much in advance.
>>
>> Best regards,
>> Kai Huang
>>
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