# Product Limit Estimate for Non-detects Using Kaplan-Meier

### Description

Compute Product Limit Estimate (PLE) of F(x) and Confidence Limits for data with non-detects (left censored data).

### Usage

1 | ```
plekm(dd,gam)
``` |

### Arguments

`dd` |
An n by 2 matrix or data frame with |

`gam` |
one-sided confidence level |

### Details

R function `survreg`

is used to calculate Kaplan-Meier estimate
of S(z), where z = k - x and k is greater than the largest x value.
This technique of "reversing the data" to convert left censored data
to right censored data was first suggested by Nelson (1972). conf.type
= "plain" is required in survreg for correct CLs. The value of S(z)
is then used to calculate F(x). Note that if *γ* = 0.95 the 90%
two-sided CLs are calculated.

### Value

Data frame with columns

`a` |
is the value of j |

`ple` |
is PLE of F(x) at |

`stder` |
standard error of F(x) at |

`lower` |
lower CL for PLE at |

`upper` |
upper CL for PLE at |

`n` |
number of detects or non-detects |

`d` |
number of detects equal to |

### Note

In survival analysis S(x) = 1 - F(x) is the survival function i.e., S(x) = P [X > x]. In environmental and occupational situations S(x) is the "exceedance" function, i.e., S(x) = is the proportion of X values that exceed x. The PLE is the sample estimate of F(x), i.e., the proportion of values in the sample that are less than x.

### Author(s)

E. L. Frome

### References

Nelson, W.(1972), "Theory and Application of Hazard Plotting for
Censored Failure Data", *Technometrics*, 14, 945-66

Frome, E. L. and Wambach, P.F. (2005) "Statistical Methods and Software for
the Analysis of Occupational Exposure Data with Non-Detectable Values",
*ORNL/TM-2005/52,Oak Ridge National Laboratory*, Oak Ridge, TN 37830.
Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM2005-52.pdf

Schmoyer, R. L., J. J. Beauchamp, C. C. Brandt and F. O. Hoffman, Jr.
(1996), "Difficulties with the Lognormal Model in Mean Estimation and
Testing," *Environmental and Ecological Statistics*, 3, 81-97.

### See Also

`plend`

, `pleicf`

### Examples

1 2 3 4 |