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Hi,

I'm wondering about the impact of ignoring truncation due to a covariate in a time to event analysis.

CONTEXT

• Illicit use of drugs, Time to event analysis
• Exposure X = dependence on illicit drug A (0/1)
• Event = first use of illicit drug B
• T = time from first use of A to first use of B (Note: "first use of A" is distinct from X and always precedes X=1)
• Research question: Is dependence on drug A associated with shorter time to first use of illicit drug B?
• T0 = initiation of entry into risk set (T=0 at A0) AND earliest possible initiation of exposure
  
  • Those who used B before A are not part of the target of inference
  • X = 0 prior to T0 since dependence cannot precede first use, but could change to 1 anytime thereafter
• T1 = start of study
• Eligibility criteria: Individual has started using drug A, is not yet dependent on drug A (X=0), and has never used drug B

WHAT I DID

I fit the model using the counting process approach in SAS PROC PHREG, with left truncation (T > (T1-T0)) and right censoring (at the end of the study), with X as a time-dependent covariate, and with Z representing other covariates in the model.

COMPLICATION

In this design, those who became dependent on drug A (X=1) prior to T1 were not eligible. But X is a covariate, not the outcome.

The researchers were intending to study time from first use of A to first use of B among those who had not yet become dependent on A (X=0). If X it were a time-independent covariate, this would not be a problem. It would just limit the inference to those with X=0. But in this case X is time-varying. The complication is that, since those with X=1 prior to the start of the study were not eligible, the data are truncated by the covariate. I'm not sure this is the correct terminology, but I hope the description is clear.

I don't think a competing risks analysis would work here because the event of interest and X are not independent processes, and one does not censor the other.

QUESTIONS

Does the truncation due to the covariate bias the estimated adjusted HR for X? What about the AHRs for the components of Z?

If there is bias, does anyone have a suggestion for how to handle this complication?

I either need to redo the analysis or explain in the Limitations section of the paper what is the impact of this.

Thanks in advance for any insights!

Ramzi

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Ramzi W. Nahhas, Ph.D. (Biostatistics)
Associate Professor, Department of Community Health
Department of Psychiatry (secondary)
ramzi.nahhas@wright.edu
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The population of interest is users of A who are not dependent.   It sounds like, X, dependence, is a cause of informative censoring, not a covariate.  The way I read this, if the status switches to dependent, the subject leaves the study.   So it is not a time dependent covariate in the sense that the new status is stays in the data set until the event, use of B.   

In a way it is like an adverse event.   Clearly the subjects are at risk for B, but like subjects removed for an adverse event, their final study event is unknown.   I know there is some recent work on informative censoring and dependent missing data.  

   

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Georgette Asherman
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In this study, the subjects do remain in the study even if they become dependent on drug A (X=1), and X was included as a covariate in the analysis of time to first use of drug B.

I could change the way I am doing the analysis, though, and treat X as if it censors. But I'm not sure if that addresses the problem of X=1 truncating entry into the study. I don't have any information on those individuals.

I am now thinking that, if I want to make inference about the impact of X for drug A users in general, the estimated HR for X will be an overestimate, because the individuals left out of the study are those with X=1 but without yet experiencing the event of interest. Had they been included in the study, the estimated HR would decrease.

I wonder if X can remain in the model as a covariate if I am careful about to whom the results generalize. The HRs for covariates other than X describe their impact on the time to event for drug A users who are not yet dependent on drug A. The interpretation of the HR estimate for X, then, is that it estimates how the hazard would change in the future if such a person became dependent on drug A.

Is that explanation valid?

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Ramzi W. Nahhas, Ph.D. (Biostatistics)
Associate Professor, Department of Community Health
Department of Psychiatry (secondary)
ramzi.nahhas@wright.edu
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