Sensitivity missing data

In all cases and particularly where the extent of missing data is substantial, several analyses will usually be undertaken to assess the sensitivity of the conclusions to the method used to handle missing data. If the conclusions are fairly consistent across these different analyses then we are in a good position. If, however, our conclusions are seen to change, or to depend heavily on the method used for dealing with missing data, then the validity of those conclusions will be drawn into question. 

Some aspects of degree of concern currently can be considered in a quantitative evaluation. For example, EPA considers human and animal data in the process of calculating the RfD, and these data are used as the critical effect when they indicate that developmental effects are the most sensitive endpoints. When a complete database is not available, a database UF is recommended to account for inadequate or missing data. The dose-response nature of the data is considered to an extent in the RfD process, especially when the BMD approach is used to model data and to estimate a low level of response however, there is no approach for including concerns about the slope of the dose-response curve. Because concerns about the slope of the dose-response curve are related to some extent to human exposure estimates, this issue must be considered in risk characterization. (If the MOE is small and the slope of the dose-response curve is very steep, there could be residual uncertainties that must be dealt with to account for the concern that even a small increase in exposure could result in a marked increase in response.) On the other hand, a very shallow slope could be a concern even with a large MOE, because definition of the true biological threshold will be more difficult and an additional factor might be needed to ensure that the RfD is below that threshold. 

An assumption of such an imputation strategy is that the future course of the individual s condition can reasonably be predicted by the last known state. If participants in the test group drop out of the study more often than those on placebo because the test treatment has failed, such an assumption may not be realistic. It is possible that participants who dropped out for treatment failure actually got worse than when they left the study. A commonly proposed strategy is to use a number of imputation methods and see how the analysis results change as a result. If the results of this sensitivity analysis suggest that the overall conclusion remains the same, it is less important how the missing data are managed. 

It may be necessary to ask patients directly for information (e.g., number and length of time of home visits by health professionals). Missing data can be estimated using meta-analysis to combine results from other studies. Alternatively assumptions can be based on expert opinion and then tested using sensitivity analysis. If data is collected from different sources then it will be important to use simulation models to combine the data and take account of the variation. 

Robins, J.M., A. Rotnitzky, and D.O. Scharfstein. Sensitivity analysis for selection bias and unmeasmied confoimding in missing data and causal inference models. In M.E. HaUoran and D. Berry (eds.). Statistical Models in Epidemiology, the Environment and Clinical Trials, IMA Volumes in Mathematics and Its Applications. Springer, New York, 1999. 

The main advantage to PCA is that it makes no assumptions about the underlying probability distributions of the original variables. The primary disadvantage is that it is sensitive to outliers, missing data and poor correlations between variables due to poorly distributed variables. 

Once the model was complete, it was adjusted to a steady state condition and tested using historic carbon isotope data from the atmosphere, oceans and polar ice. Several important parameters were calculated and chosen at this stage. Sensitivity analysis indicated that results dispersal of the missing carbon - were significantly influenced by the size of the vegetation carbon pool, its assimilation rate, the concentration of preindustrial atmospheric carbon used, and the CO2 fertilization factor. The model was also sensitive to several factors related to fluxes between ocean reservoirs. 

Finally, it is generally recommended to use estimation approaches, combined with sensitivity analysis, for additives when data are missing, when performing an LCA case study on additive containing products, such as outlined above. Only when they are included it is possible to draw conclusions on the importance of additives over the life cycle of a product. 

Adverse effects of copper deficiency can be documented in terrestrial plants and invertebrates, poultry, small laboratory animals, livestock — especially ruminants — and humans. Data are scarce or missing on copper deficiency effects in aquatic plants and animals and in avian and mammalian wildlife. Copper deficiency in sheep, the most sensitive ruminant mammal, is associated with depressed growth, bone disorders, depigmentation of hair or wool, abnormal wool growth, fetal death and resorption, depressed estrous, heart failure, cardiovascular defects, gastrointestinal disturbances, swayback, pathologic lesions, and degeneration of the motor tracts of the spinal cord (NAS 1977). 

Data are scarce or missing on copper deficiency effects in aquatic flora and fauna and in avian and terrestrial mammalian wildlife additional studies of copper deficiency in these groups are merited. In sensitive terrestrial agricultural crops, copper deficiency occurs at less than 1.6 mg... 

If it is not possible to include a particular element in the calibration solutions, it is possible to perform a semiquantitative analysis. This uses the response of those elements which are in the calibration solution, but predicts the sensitivity (defined as cps/concentration) for the missing element(s) by interpolating between the sensitivities of known elements. By plotting sensitivity against mass for all the elements present in the calibration solutions (Fig. 9.7) and fitting a curve through the points, it is possible to predict the sensitivity of the instrument for any particular mass number, and hence use this sensitivity to convert cps to concentration at that mass number. As can be seen from the figure, however, this is a very crude approximation, and any data produced in this way must be treated with some caution. 

Only a limited number of biomedical applications have been published in the normal-phase mode, as can be seen in Table 17.4. However, the sensitivity of the methods seems to be comparable to the reversed-phase and polar-organic mode applications, although a detailed comparison is not feasible since the LOQ data are missing for the few substances that have been analyzed in both modes. The majority of the methods are based on MS detection, and APCl seems to be the predominant ionization mode for the applications in normal-phase mode. 

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