Shane:  Just to add some practical advice on top of Rich's interpretation
of the censoring process (which is correct), my recent experiences with
analyzing below-detection limit chemical concentrations in water using
left-censoring estimators indicates that historically people have not
always indicated the below-detection limit data in a consistent fashion.
 So often people would include either a < with the detection limit value
(e.g, <5), possibly also negative values (e.g., -5, negatives could be used
as a flag for censoring if the real measurement scale is strictly positive
as it is for chemical concentrations, but it has risky potential side
effects), and possibly a separate column variable like your Censored
TRUE/FALSE.  I'm wondering if it is possible that your data format has a
mix of these approaches.  It seems like most recent statistical software
for censoring usually wants a column variable for the measured response
(Y), where observations of Y that are below (or above) detection-limit
(censored) have the detection limit (censoring) value; and then a second
column like your Censored column (either with TRUE/FALSE or 0/1 indicators).

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  cadeb@usgs.gov <brian_cade@usgs.gov>
tel:  970 226-9326



On Thu, Mar 14, 2013 at 9:20 AM, Rich Shepard <rshepard@appl-ecosys.com>wrote:

> On Thu, 14 Mar 2013, Shane Carey wrote:
>
>  Thanks for your reply. My data frame contains the value and a true/false
>> to indicate whether they are censored or not.
>>
>> So I have something like:
>>
>> Data          Censored
>> -1.2             TRUE
>> -5.5             TRUE
>> 5                 FALSE
>>
>
>  These negative values are actual values so do these have to be made
>> absolute?
>>
>
> Shane,
>
>   If your data represent chemical concentrations of some sort then, yes,
> the data must all be positive. You cannot have a chemical concentration
> less
> than zero. If the negative values are actual, then what is the reporting
> level? And what do they measure that is really a censored value?
>
>   The concept of censored data, whether right or left censored, is that
> there is no way of knowing the actual numeric value. In right-censored
> survival analyses (e.g., medical trials) the death of an individual is
> recorded. But, when the study ends for whatever reason, there are still
> subjects alive and there's no way of knowing how long after the end of the
> study they die. Ergo, their age at death is unknown or censored.
>
>   With left censored data such as chemical constituent concentrations in
> air, water, or some other medium, there is a concentration below which the
> instruments cannot distinguish it from noise. All we know is that the
> constituent is present but its concentration is somewhere between zero and
> the detection/reporting limit. Therefore, having a number that is below
> this
> detection/reporting limit is meaningless, and it cannot be negative. That's
> why it is flagged as being censored. The cenmle() function assumes these
> conditions to be true.
>
>   Please keep this thread on the mail list so others can participate and
> learn from the conversation.
>
> Rich
>
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