README.md

In ccb60/LCensMeans: Calculate Condtional Means of Left Censored Data

See the R Notebook "Conditional Means of Censored Distributions" for an explanation of the following functions.

Introduction

This tiny package exposes a couple of functions for estimating the conditional mean of censored values for left censored environmental data.

It is still common practice in envrionemtnal analysis to replace "non-detects" in laboratory data with essentially arbitrary values, usually zero, one half of the detection limit, or the detection limit. None of these approaches rests on any statistical foundation, and they ignore the information available from knowing that a sample concentration was below a certain value. The frequency of non-detects itself contains information relevant to estimating teh value of censored data.

We can do better.

The goal of this package is to offer a simple interface to replace non-detects with a maximum likelihood-derived estimator of the mean of unobserved (censored) observations.

It estimates those means by first calculating maximum likelihood estimates of parameters of a log normal distribution that could have produced the observed censored data, and then drawing a sample from that distribution, and calculating the mean of values that would have been censored.

The package can handle different levels of censoring for different observations.

Caveats

This package assumes data are distributed according to a lognormal distribution. While that is a good first guess for many environmetnal data sets, envrionmetnal data are often substantially more right skewed than a lognormal distribution implies. The user is cautioned to evaluate whether making the assumption of a log lormal distribution is reasonable for tehir data or not.

Explanation

The idea is to fit a maximum likelihood model to the data assuming we are looking at a censored lognormal distribution.

With a lognormal density in hand, we can estimate a conditional mean of "unobserved" observations below a detection or reporting limit by sampling from the truncated distribution and colculating a mean.

The first function ("lc_loglik") provides a likelihood function for a left-censored lognormal distribution. It is used with maximum likelihood estimation to estimate parameters for the underlying lognormal distribution. The parameters consist of a vector of concentrations and a vector of flags indicating which observations are censored, and therefore represent the applicable detection limit.

The second function estimates the conditional mean for a truncated lognormal distribution, given parameters of the lognormal distribution and a cutoff value (here, the detection limit). The third function vectorizes the second, allowing us to pass a vector of detection limits, rather than calculating this for each sample.

The last function manages the process of combining the other functions to generate a "corrected" vector of estimated concentrations, where censored values are replaced by conditional means.

ccb60/LCensMeans documentation built on Oct. 30, 2020, 3:26 a.m.