MI in competing risks analysis

[melissaja...@gmail.com]

Hi Jonathan,

I want to perform MI prior to competing risks regression. I am keen to use a directly specified MICE imputation model as this seems the simplest approach. Reading your paper "Missing covariates in competing risks analysis" (2016) you mention an approach by Resche-Rigon (2012), a presentation which I can't find referenced anywhere else. Nonetheless I am after a simple adequate method which this seems to be. I am not anticipating any large covariate effects in the competing risks model.

Can I just clarify  the variables to be included in the imputation model;

- Covariates for inclusion in the final competing risks model.

- Relevant axillary variables.

- A binary event indicator for the failure event of interest.

- The Nelson-Aelen estimator of the cumulative hazard function for the failure event of interest.

- Interactions between the NA estimator and each covariate.

Am I correct that the binary event indicator and NA estimate for the competing event should not be included in the imputation model?

Thank you 

[Jonathan Bartlett]

Hi there

In general their results show you should include the event indicator for each competing risk and the corresponding cumulative hazard function (in addition to the other variables you listed).

If you are only interested in modelling the cause specific hazard for one type of failure, you can treat failures from other causes as censoring and apply the results of White and Royston for survival data. However, if the variables you are imputing are related to the cause specific hazards for some of these other causes, you will probably lose some efficiency by doing this.

Best wishes

Jonathan

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[melissaja...@gmail.com]

Thank you Jonathan your response is greatly appreciated.

Regarding the interactions to be included in the imputation model - 

Do I include interactions between each covariate and the cumulative hazard function for the competing cause of failure in addition to the interactions between each covariate and the cumulative hazard function of the failure event of interest?

[Jonathan Bartlett]

Oh yes sorry forgot to mention that. Yes, their analysis shows you get a better approximation to the implied conditional distribution of the missing covariates by including those interactions. But as I wrote, if efficiency/precision is not such a big concern, you could consider treating all the failures due to causes not of primary interest as censoring at the imputation stage (as well as at the analysis stage), and follow the results of White and Royston for imputing covariates in a Cox model survival data setting.

[melissaja...@gmail.com]

Okay excellent, thanks for that.

Just wondering how this would apply to MI for a competing risks model using propensity score methods. That is, a propensity score for receiving treatment is predicted from a number of baseline variables (some of which having missing values) using a logistic regression model, then the propensity score is used to create a matched or inverse probability of treatment weighted sample on which the competing risks model is run, which includes a variable denoting treatment as well as other covariates (which also have missing values). When creating an imputation model for such a scenario, should I include interactions between the cumulative hazard functions and variables which make up the propensity score model, or just with the variables to be included in the competing risks model? I appreciate there may not be an evidence based answer to this but your advice would be appreciated.

Thank you

[Jonathan Bartlett]

I suggest looking at this paper: https://www.ncbi.nlm.nih.gov/pubmed/28573919

If I understand correctly, there are some variables that are going into the propensity score model, say X1, and a set X2 which go into your competing risks analysis, with X2 including treatment, and these two sets are not the same. I would need to give what impact this would have some more thought...

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