# Summary Statistic for Samples With Non-detects

### Description

Summary statistic described by The American Industrial Hygiene Association (AIHA) for occupational exposure data are calculated for samples with non-detects (aka left censored data). Parametric estimates are based on a lognormal model using maximum likelihood (ML). Nonparametric methods are based on the product limit estimate (PLE) for left censored data.

### Usage

1 | ```
IH.summary(dd,L, p = 0.95, gam = 0.95,bcol=NA)
``` |

### Arguments

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

`L` |
L is specified limit for the exceedance fraction; e.g., the occupational exposure limit |

`p` |
p is probability for Xp the 100p |

`gam` |
one-sided confidence level |

`bcol` |
Column number that contains a BY variable. This column must contain a factor and the value of each of the summary statistics is calculated for each level of the factor. Default NA |

### Details

Regulatory and advisory criteria for evaluating the adequacy of occupational exposure controls are generally expressed as limits that are not to be exceeded in a work shift or shorter time-period if the agent is acutely hazardous. Exposure monitoring results above the limit require minimal interpretation and should trigger immediate corrective action. Demonstrating compliance with a limit is more difficult. AIHA has published a consensus standard with two basic strategies for evaluating an exposure profile—see Mulhausen and Damiano(1998), Ignacio and Bullock (2006). The first approach is based on the mean of the exposure distribution, and the second approach considers the "upper tail" of the exposure profile. Statistical methods for estimating the mean, an upper percentile of the distribution, the exceedance fraction, and the uncertainty in each of these parameters are provided by this package. Most of the AIHA methods are based on the assumptions that the exposure data does not contain non-detects, and that a lognormal distribution can be used to describe the data. Exposure monitoring results from a compliant workplace tend to contain a high percentage of non-detected results when the detection limit is close to the exposure limit, and in some situations, the lognormal assumption may not be reasonable. All of these methods are described in a companion report by Frome and Wambach (2005).

### Value

A data.frame with column names based on levels of the BY variable and row names:

`mu` |
ML estimate of mean of y=log(x) |

`se.mu` |
Estimate of standard error of mu |

`sigma` |
ML estimate of sigma |

`se.sigma` |
Estimate of standard error of sigma |

`GM` |
MLE of geometric mean |

`GSD` |
MLE of geometric standard deviation |

`EX` |
MLE of E(X) the (arithmetic) mean |

`EX-LCL` |
Lower Confidence Limit for E(X) |

`EX-UCL` |
Upper Confidence Limit for E(X) |

`KM-mean` |
Kaplan-Meier(KM) Estimate of E(X) |

`KM-LCL` |
KM Lower Confidence Limit for E(X) |

`KM-UCL` |
KM Upper Confidence Limit for E(X) |

`KM-se` |
Standard Error of KM-mean |

`obs.Xp` |
Estimate of Xp from PLE |

`Xp` |
ML estimate of Xp the pth percentile |

`Xp.LCL` |
MLE of LX(p,gam) the LCL for Xp |

`Xp.UCL` |
MLE of UX(p,gam) the UCL for Xp |

`zL` |
MLE of the Z value for limit L |

`NpUTL` |
Nonparametric estimate of the UTL |

`Maximum` |
Largest value in the data set |

`NonDet` |
percent of X's that are left censored, i.e., non-detects |

`n ` |
number of observations in the data set |

`Rsq ` |
Square of correlation for the quantile-quantile (q-q) plot |

`m ` |
number X's greater than the LOD |

`f ` |
MLE of exceedance fraction F for limit L |

`f.LCL` |
LCf(L,gam) MLE of LCL for F |

`F.UCL` |
UCf(L,gam) MLE of UCL for F |

`fnp` |
Nonparametric estimate of F for limit L |

`fnp.LCL ` |
Nonparametric estimate of LCL for F |

`fnp.UCL ` |
Nonparametric estimate of UCL for F |

`m2log(L)` |
-2 times the log-likelihood function |

`L ` |
L is specified limit for the exceedance fraction; e.g., the occupational exposure limit |

`p ` |
percentile for UTL |

`gam` |
one-sided confidence level |

### Author(s)

E. L. Frome

### References

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

Ignacio, J. S. and W. H. Bullock (2006), *A Strategy for Assesing
and Managing Occupational Exposures*, Third Edition, AIHA Press,
Fairfax, VA.

Mulhausen, J. R. and J. Damiano (1998), * A Strategy for Assesing
and Managing Occupational Exposures*, Second Edition, AIHA Press, Fairfax, VA.

See complete list of references at `About-STAND`

### See Also

See Also `lnorm.ml`

, `efraction.ml`

,
`percentile.ml`

, `kmms`

### Examples

1 2 3 4 5 6 7 | ```
# Analysis for cansdata Example 1 from ORNLTM2005-52
data(cansdata)
Allcans<- round(IH.summary(cansdata,L=0.2,bcol=NA),3)
# Example using cansdata with By variable
cansout <- round(IH.summary(cansdata,L=0.2,bcol=3),3)
# combine out from both analysis
cbind(Allcans,cansout)
``` |