I have been handed data that is interval censored where left censoring is limit of detection and right censoring is saturation of the assay. How do I estimate the means and mean standard errors of this data?
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$\begingroup$ I just though of something. If I do a survival model on each sub group by predictor level, that pretty much is the mean, if suitably adjusted for the error family. $\endgroup$– BryanApr 3 at 19:55
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$\begingroup$ It depends on what you assume about the distribution and how the censoring occurs. For instance, it's one thing to make an estimate when the censoring limits are all the same and another thing to make an estimate when the limits are variable (and might depend on the underlying values). Many papers and even books have been written about this: see, for instance, Helsel's NADA. $\endgroup$– whuber ♦Apr 3 at 19:56
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$\begingroup$ In this case, the limits are the same. Any reading below a certain OD is below quantifiable. Any reading above a different OD is saturated. These thresholds are the same for all points. I have looked at NADA, and it doesn't seem to do much with doubly-censored data. $\endgroup$– BryanApr 3 at 20:23
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$\begingroup$ That figures, because it is so oriented towards applying survival analysis techniques. A standard method uses maximum likelihood. Another is ROS (regression on order statistics), which might be simple and convenient in your application. See stats.stackexchange.com/a/130174/919 for brief accounts of both methods. $\endgroup$– whuber ♦Apr 3 at 22:43
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