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I have a medical dataset with approx 200 variables. One of the variables is a bio-marker (concentration of a particular enzyme). It's distribution is right skew, and the problem is that values above a certain level are censored/cut off at that level. So while the mean of the variable is around 10, any values greater than 50 are recorded as 50.

I would like to impute continuous values for those censored values. I am using multiple imputation with the mice package in R at present, though other systems are available to me and I am open to other approaches. A thought I had was to recode all those censored values to be missing and then running the imputations. If any of the imputed values that were originally censored are below the cut-off, then they will then be assigned to be the cut-off value.

I'd like to know opinions about this, and/or any better methods of dealing with this.

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  • $\begingroup$ What role will that biomarker play in subsequent analyses? E.g., will it be an explanatory variable, a covariate, or a dependent variable in a regression? It's possible you could use a method that does not require imputation of values. You should favor such methods, because otherwise you're making a WAG about the shape of the censored right tail, which--because of the skewness--could contain some influential values in the analyses. $\endgroup$
    – whuber ♦
    Jun 29, 2012 at 19:27
  • $\begingroup$ @whuber, the biomarker is an explanatory variable. Normal practice in this field is to discretise it as 0-1, 1-10, 10+ or sometimes just 0-1 and 1+ (ie elevated or not elevated). I had the idea to include it as a continuous explanatory variable. Although the dataset has 200 variables, clinical guidance and prior experience suggests to use 10 of these in the final model, hence I was thinking of imputing the values >50 using some of the other variables. $\endgroup$
    – Robert Long
    Jun 30, 2012 at 21:18

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Any method of imputation including multiple imputation is a shot in the dark if you can't take acoount of how the data above 50 are distributed. Since you have 200 variables are any of them correlated with the biomarker? If you could fit a regression for the biomarker as a function of the covariates you could use that model to predict the values for the truncated ones. You could apply an error to the prediction based on the residual variance in the model to generate multiple imputations that way. It would be more sensible. Of course this assumes you can find a valid model and that the residuals have zero mean and constant variance. You would only fit then non-truncated biomarker values to construct the model.

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