Sensitivity analysis, missing data, and hypothesis testing

[wvguy8258]

Hi,

I have a large data set with with less than 10% missing values (missing response, but all predictor variables present). It is a near certainty that these values are not missing at random, dependent upon the missing value. The response is survival time of a land parcel with 'death' being development of the parcel. Predictors are things like average topographic slope in the parcel etc. I plan to fit a hazard model to the data to test hypotheses related to the sign and magnitude of slope coefficients. I've read a bit about methods for dealing with missing data, but I feel that because I am primarily interested in testing hypotheses that a simpler method may be available that I haven't yet seen in print. I am here asking for advice on the feasibility of the simple idea to follow, how it can be improved, and if anyone has any pertinent references to share.

The survival time is bounded. I am taking the beginning of colonization of the area as the beginning of the study period and the present as its end. So, the response variable is bounded between zero and 2009-time of first colonization. Let's say I have a very simple hypothesis that the slope coefficient of topographic slope is less than zero, so my null hypothesis is that it is greater than or equal to zero. It seems that I could pick values for the missing data so as to minimize the chance of rejecting this null hypothesis. If I still find evidence to reject the null under this extreme example, then it is reasonable to conclude that the full data set, if missing values were also observed, would likewise lead to this rejection. So, in the example of topographic slope I would assign missing data values that would give the largest slope coefficient (and the smallest variance at a high parameter estimate? less sure of how to think here) possible given the observed data. First, are there any logical pits I am falling into here? This seems rather straightforward with only one predictor in the model, but I suspect that a multivariate model will complicate things. Should each hypothesis considered (corresponding to each slope coefficient of interest) be considered separately? Meaning, should I concoct a series of missing values to try and not reject the null associated with hypothesis 1, start over and do the same thing for hypothesis 2, etc? Or should this be done at once? If you think this is all a bad idea, in a few words, how would you go about modeling the data I've described? Thanks. -seth

 

[Enuma_Elish]

Yours is a non-standard method but I don't see a logical pitfall. For multivar analysis my guess is you can do it separately for each parameter you are testing; or you can set up a joint test (e.g. an F test) that encompasses all of the individual tests, and then assign values to minimize that single, overarching test statistic.

Another approach may be to use a censored data ("Tobit") model.

 

[wvguy8258]

Thank you, I have been reading some about models for censored data.

 

[Enuma_Elish]

When you look at the observed characteristics of the "missing" observations, do you see a marked difference from the sample mean?