Technical Report No. 2-89
Allowing for random errors in radiation exposure estimates for the atomic bomb survivor data
Pierce DA, Stram DO, Vaeth MEditor’s note: Publications based on this report were published in Radiat Res 123:275-84, 1990, and J Radiat Res (Tokyo) 32S:108-21, 1991.
Summary
The presence of nonsystematic errors in the individual radiation exposure estimates for the atomic bomb survivors results in underestimation of radiation effects in dose-response analyses and also distorts estimates of the shape of the dose-response curve. Statistical methods are presented which will adjust for these biases for linear and quadratic dose-response models, provided that a valid statistical model for the exposure estimation errors is available. This latter qualification is important; less than would be desired is currently known about the nature and magnitude of the errors. Emphasis is placed on clarifying the rather subtle statistical issues involved. The methods involve downward adjustment of dosimetry system estimates, but this is not to imply that these estimates are biased; rather this is part of the dose-response analysis to remove biases in the risk estimates. Primary focus in this report is on linear dose-response models, but methods for linear-quadratic models are also indicated. Some plausible models for the exposure estimation errors are considered, with a substantial range in magnitude of errors, and sensitivity analysis of the resulting bias corrections is provided. It is found that unbiased estimates of linear excess risk for cancer mortality, for these error models, are about 5-15% greater than estimates making no allowance for such errors. The upper end of this range is reduced to about 10% if, as is commonly done, some survivors with extremely high exposure estimates are eliminated from the analysis. Since the range is not extremely wide and since the statistical issues-although difficult-seem clear enough to proceed, it is recommended that some adjustment of the type proposed here now be made in most analyses. A specific error model in the central range of those considered is tentatively proposed for such adjustments. No information specific to the new DS86 dosimetry is used in this recommendation, even though it will be important to bring such information to bear on DS86 as soon as possible. To a large extent the revision in dosimetry was intended to correct systematic errors affecting large groups of survivors, whereas the methods here pertain only to nonsystematic errors resulting largely from inadequacies in information about location and shielding of individual survivors-input common to old and new dosimetry systems. For further accrual of information regarding precision of the new dosimetry system to be most useful, it is critical that attention be given to the rather subtle statistical issues involved. In particular, it is critical to distinguish between the distribution of estimates for those at a given true exposure, and the distribution of true exposures for those having a given estimate.
The presence of nonsystematic errors in the individual radiation exposure estimates for the atomic bomb survivors results in underestimation of radiation effects in dose-response analyses and also distorts estimates of the shape of the dose-response curve. Statistical methods are presented which will adjust for these biases for linear and quadratic dose-response models, provided that a valid statistical model for the exposure estimation errors is available. This latter qualification is important; less than would be desired is currently known about the nature and magnitude of the errors. Emphasis is placed on clarifying the rather subtle statistical issues involved. The methods involve downward adjustment of dosimetry system estimates, but this is not to imply that these estimates are biased; rather this is part of the dose-response analysis to remove biases in the risk estimates. Primary focus in this report is on linear dose-response models, but methods for linear-quadratic models are also indicated. Some plausible models for the exposure estimation errors are considered, with a substantial range in magnitude of errors, and sensitivity analysis of the resulting bias corrections is provided. It is found that unbiased estimates of linear excess risk for cancer mortality, for these error models, are about 5-15% greater than estimates making no allowance for such errors. The upper end of this range is reduced to about 10% if, as is commonly done, some survivors with extremely high exposure estimates are eliminated from the analysis. Since the range is not extremely wide and since the statistical issues-although difficult-seem clear enough to proceed, it is recommended that some adjustment of the type proposed here now be made in most analyses. A specific error model in the central range of those considered is tentatively proposed for such adjustments. No information specific to the new DS86 dosimetry is used in this recommendation, even though it will be important to bring such information to bear on DS86 as soon as possible. To a large extent the revision in dosimetry was intended to correct systematic errors affecting large groups of survivors, whereas the methods here pertain only to nonsystematic errors resulting largely from inadequacies in information about location and shielding of individual survivors-input common to old and new dosimetry systems. For further accrual of information regarding precision of the new dosimetry system to be most useful, it is critical that attention be given to the rather subtle statistical issues involved. In particular, it is critical to distinguish between the distribution of estimates for those at a given true exposure, and the distribution of true exposures for those having a given estimate.