non-parametric trend analysis with data that is both left and right censored I am assessing the the presence of monotonic temporal trends in E. coli concentration data using a non-parametric approach. These data are both right and left censored (for example the lower detection limit is either one or ten depending on the dilution and the upper detection limit is 80, 201, 600, or 2419 depending on the way the counts were done). For other analyses of concentration data (I am using cenken from package NADA in R) I have dealt only with left censored data, and am wondering if code has been developed for a censored Mann-Kendall test that can handle both right and left censored data (it is my understanding is that cenken cannot handle this, but it would be lovely if I were wrong). Perhaps some survival analysis packages can do so?  
 A: Left and right censoring are both contained in the more general issue of interval censoring, i.e. when your $i^{th}$ response is only known to be contained within the interval $[l_i, r_i]$. Here, left censoring could be represented in the form $[0, r_i]$ and right censoring is represented as $[l_i, \infty)$. 
I've authored an R-package icenReg that builds regression models for interval censored data, although right now it specifically allows for two standard survival regression models (proportional hazards and proportional odds). You can use ic_sp for semi-parametric models (and if you wanted non-parametric models, i.e. the NPMLE which is a generalization of the Kaplan Meier curves, you can get this just by fitting 0 as your covariates). You can also use imputeCens for multiple imputations of the response variables, so that you can use the full responses in a model that does not allow for interval censoring. 
However, if you are not dealing with survival data, you may be interested in the tobit model. Alternatively, if you are looking for multiplicative factors rather than additive, you may want an AFT model. Currently, neither of these are supported by icenReg, but they can be fit using survival's survreg function. 
