What Factors Affect Pyridium Dosage?

Reference dose (RfD, reference dose) is an indicator proposed by the EPA (U.S. Environmental Protection Agency) for the risk assessment of non-carcinogens. It is the Estimated daily average exposure dose. The population is expected to reduce the risk of non-carcinogenic or non-mutagenic effects in their lifetime to an undetectable level at this dose level throughout life.

Reference dose by

NOAEL/LOAEL Problems with reference dose NOAEL / LOAEL method

There are many problems in formulating a reference dose according to the traditional NOAEL / LOAEL method. These issues include:

(1) The traditional method does not include information on the shape of the dose-response curve, but focuses on a single point (NOAEL or LOAEL).

(2) The value of NOAEL depends on the number of experimental doses and the dose interval. The possible NOAEL values are limited to the discrete values of the experimental dose. Theoretically, the experimental non-adverse effect dose can be any value between the experimental NOAEL and LOAEL. Sometimes the true NOAEL is lower than the observed NOAEL, especially in studies where the number of animals in each dose group is limited.

(3) The change of data is not directly considered. For example, studies with more animals may detect effects at lower doses than studies with fewer animals; the result is that a small-scale study from the same species may have a higher NOAEL than a similar study But NOAEL for large-scale research. Traditional methods do not consider the mechanism of such data changes.

(4) The determination of NOAEL depends on the background incidence that affects the animals in the control group. Therefore, if the background incidence is high, the statistically significant difference between the dose group and the control group is more difficult to detect, even if it occurs The same goes for the significant effects of biology.

(5) Combined with exposure data, a reference dose based on NOAEL can be used to estimate the size of the population at risk, not the size of the risk.

In response to these problems, alternative methods have been established that attempt to solve some of these 4i feet. One such alternative, the benchmark dose method, has been the subject of extensive research over the past 10 years. The EPA Risk Assessment Forum is developing guidelines for procedures and models used in the calculation of baseline doses.

Reference dose

There are 4 basic steps involved in determining the reference dose using the baseline dose method. The first step is to select experiments and responses for baseline dose modeling. The second step is to calculate the baseline dose for the selected response. The baseline dose values should be calculated for all possible endpoints for the critical baseline dose. The third step is to choose a reference dose from these calculated reference doses. The final step is to calculate the reference dose by dividing the selected baseline dose by the appropriate uncertainty factor. The decision points associated with these steps are listed in Figure 1. The ensuing discussion summarized the key issues specific to the baseline dose method, based primarily on information from Crump et al. (1995).

figure 1

(1) Modeling of response data

The considerations for selecting experiments and responses that are suitable for baseline dose modeling are similar to those for determining the appropriate studies to use as a basis for NOAEL. A chemical may have several suitable studies that can be modeled and related health effects. Ideally, a set of baseline dose calculations for the relevant effects is performed. However, using all relevant responses to calculate the baseline dose may be resource intensive. In addition, it is difficult to interpret a large number of dose-response analysis results. When selecting data for modeling, it is appropriate to limit attention to those responses that have evidence of a dose-response relationship. Statistically, this relationship can be shown by a significant trend (increase or decrease) in response with increasing dose levels. You may also need to consider proving biological significance. Another alternative is to focus on the most critical impacts of modeling, as seen in LOAEL. However, limiting the number of modeled responses may not accurately represent the smallest baseline dose.

(2) Using classification and continuous data

A central issue when selecting data for modeling is the form of the data used. Categorical data, especially quantum data, can be used more directly in the benchmark dose method, because the data is expressed in terms of the number (or percentage) of subjects who show a definite response at a given dose. Data can also be in continuous form, where results are expressed as continuous biological endpoints, such as changes in organ weight or serum enzyme concentration. With continuous data, results are usually expressed as mean or standard deviation of the dose group, but are most valuable when data for individual animals are available. To perform dose-effect modeling of such data, the boundaries between normal and adverse reactions must be determined. Continuous data can be modeled by considering the average response of each dose group as part of the average response of the control group or as the percentage of animals exhibiting adverse reactions at each dose level. This method takes advantage of the continuity of the response data, but expresses the results in a manner directly similar to the results derived from the analysis of categorical data, such as additional risk or additional risk, rather than the change in average response. Crump (1995) provides the option to process continuous data that can be applied to the same model used for quantum endpoint analysis. This advancement improves the consistency of results across the different endpoints of any particular chemical. In any case, applying the benchmark dose method to continuous data requires professional judgement in order to determine which effect dose or class caused the abnormal (adverse) effect. Routine application of the benchmark dose method is not recommended, but can be applied when data are available and there is a reason for extensive analysis ^[2] .

(3) Select the mathematical model

Various mathematical methods have been proposed for determining the baseline dose. Figure 2 lists some dose-response models that can be used with quantum or continuous data to estimate baseline doses. The EPA benchmark dose model program includes methods using gamma, logarithmic, multilevel, normal distribution, quantum linearity, quantum quadratic, and Weibull software models using quantum data. Linear, polynomial, power, and Hill models can be used with continuous data.

figure 2

Categorical data (including quantum data) is usually used in dose-response models to include experimental doses, the number of animals in each dose group, and the number of responses in each response category. For continuous data, the experimental dose, the number of animals in each dose group, the average response in each group, and the difference in response samples in each dose group are required.

The benchmark dose method should not be applied to a data set with only 2 experimental groups (a control group and a positive dose group). In this case, many of the advantages of the reference dose method in considering the shape of the dose-response curve will be lost; such data provides very little information about the shape of the dose-response curve. The more doses available, especially at lower doses, the greater the expected advantages of the baseline dose method over the NOAEL method.

(4) Processing model fitting

Fitting the model to experimental data will yield parameter estimates that help determine the best model for the data fit. This fitting is usually done by the maximum likelihood method, which estimates the response probability (quantum data) or average response (continuous data) of each dose value. A goodness-of-fit test can be used to determine whether a model adequately describes dose-response data. Experimental data should be plotted according to the model design to provide a visual representation of the fit. In many cases, several models seem to fit the data well. In this case, other considerations can be used to choose an appropriate model. For example, the statistical assumptions supporting the model should be reasonable for the given data. For example, suppose the quantum result is a binomial distribution that follows dose-dependent expectations. This hypothesis requires that each subject responds independently and that all subjects have an equal probability of response. The continuous response of each dose value is assumed to follow a normal distribution and is also assumed to be independent. When biological factors may be important (such as intra- den correlations of developmental toxicity data), they can also be used to select appropriate models. Another biological consideration may be the existence of a hypothetical threshold. If a given impact has a desired threshold, a model that takes into account the threshold dose can be selected for modeling. The biological plausibility of the dose-response curve shape should always be a factor in the model selection process.

Even with these considerations, there may often be several different models that adequately describe the data. In this case, it is important to check the fit of the baseline response. Models with similar fits to the entire data set may have different predicted values near the baseline response. A model can be selected based on more local characteristics. For some data sets, there is no standard model that fits the data reasonably. The fit is evaluated statistically by comparing the predicted values of the model with the observed values. The goodness-of-fit statistics formalize the comparison and provide a P value in the range between 0 and 1 as a measure of fit. When using ² statistics, a larger P value indicates a better fit: a smaller P value indicates a poorer fit. Sufficiently small P-values (eg, less than 0.01 or 0.05) are generally considered to be insufficient models to describe the observed dose-response patterns.

The poor fit is usually due to the reduced response at higher doses, which is in contrast to lower doses. The trend of the effects is not consistent, and may be due to the saturation of the metabolic system associated with a competing toxic process or toxic response of interest. In this case, there are several programs available to adjust the modeling process. For example, responses at the highest doses can be excluded because these doses usually provide the least information about the response at the lower dose area of interest. When metabolic pathways are saturated, toxicokinetic data can be used to estimate the dose delivered to relevant organs. Baseline dose modeling can then be performed on the effective dose.

The appearance (graphical) examination of the model-predicted values in relation to observations is a basic practice related to all these fitting problems. This complements the formal statistical evaluation of the fit and may actually provide the same or more information. Biological plausibility is another key factor to consider when choosing the best baseline dose from several options.

(5) Measure the response of change

Crump (1984) proposed two measures of the increase in response to quantum data, namely additional risk and additional risk. The additional risk is the response probability P (d) of dose d minus the response probability P (0) of zero dose (control response). It describes the increased proportion of animals that respond in the presence of a dose. The additional risk is the additional risk divided by (1-P (0)). It describes the increased proportion of animals that responded in the presence of a dose, divided by the proportion of animals that did not respond under control conditions. These two measures differ in the way they consider the control response. For example, if a dose increases the response from 0% to 1%, both the additional risk and the additional risk are 1%. However, if one dose increases the risk from 90% to 91%, the additional risk is still 1%, but the additional risk is 10%. The choice of additional risk and additional risk is based in part on the assumption that a compound increases background risk. Use additional risk as the default because it is more conservative.

Similar measures of risk for continuous data have been proposed (Crump, 1984). The change in the first measurement response can be expressed as the difference between the mean response at dose d minus the mean response at the control. The second measure is simply the difference between the average response of the dose and the control divided by the average response of the control (ie, normalization), which represents the change as a fraction of the control response, not the absolute amount of change.

Recent considerations of continuous endpoint baseline doses suggest other options. Allen et al. And Kavlock et al. Decided to normalize the change by averaging the response times the background standard deviation to obtain a baseline dose equivalent to NOAEL. For the developmental endpoints studied by these researchers, the optimal multiplier for the standard deviation was 0.5.

It is unclear when the expressed risk measure compared to the background (ie, additional risk) is better than the measure expressed in absolute change. Additional research is needed to provide guidance on the most appropriate measure of response change in a particular situation.

(6) Choose the benchmark response

A key decision in deriving the baseline dose is the selection of the baseline response (BMR). Since the use of the reference dose is the same as the derivation of NOAEL in the reference dose, the reference response should be selected near the lower limit of the range of effects detected by the study. The dose expected to cause a 10% increase in the incidence of effects in the test population (ED ₁₀ ) is usually selected as the baseline response. For some data, ED ₅ or ED ₁ can be adequately estimated, which is a closer to true unaffected dose. However, in many cases, ED ₁₀ is the lowest risk dose that can be estimated from standard toxicity studies (Crump, 1984).

During the EPA-sponsored baseline dose seminar, participants agreed that the appropriate baseline response should be either 5% or 10%, and it seems that they also acknowledge that future research may prove that choosing one of these two values is More wise. Studies by Allen et al. And Faustman et al. Show that the baseline dose, defined as a 10% increase in response probability, is often similar to the NOAEL corresponding to the Institute for Quantum Developmental Toxicity. To derive water quality benchmarks, the EPA recommends using ED ₅ or ED ₁₀ when deriving baseline doses.

(7) Calculate the confidence interval

The baseline dose is defined as the lower confidence limit for the corresponding dose of the selected baseline response. There are several reasons for using a lower statistical confidence limit instead of the maximum likelihood estimate (MLE). Confidence limits are used to account for population variability. Some human biological responses are normally distributed within a population. Therefore, if two groups of animals are to be randomly selected from the population for study, the lowest-effect-dose responding individual in a study group may be associated with exposure. The second group is different under the same experimental conditions. Using a lower confidence interval raises the confidence that the results of a small-scale animal group can be extrapolated to the entire population.

To calculate the upper confidence limit of the response and the lower confidence limit of the effective dose, you must choose a program that calculates the confidence limit and the size of the confidence limit. The recommended method for calculating the confidence interval of a curve depends on the maximum likelihood principle. This method is the same as that used by the EPA in a cancer dose-effect model computer program. This method can be used for benchmark dose modeling using EPA Benchmark software and other commercially available benchmark programs.

Through conversion, the size of the statistical confidence limit can range from 90% to 99%. The calculation of confidence limits and the choice of confidence intervals are crucial. The EPA recommends that the baseline dose model use a one-sided 95th percentile position confidence limit. This is consistent with the size of the confidence limits used in the cancer dose-response model.

(8) Choose the reference dose as the basis for the reference dose

When multiple baseline doses are calculated, an important decision is to choose the appropriate baseline dose for the reference dose calculation process. Multiple baseline doses can be calculated when different models fit the response data for a study, when more than one response is modeled in a study, and when different baseline doses from different studies are present. When multiple benchmark doses are calculated from multiple models suitable for a single data set, the analyst can choose the smallest benchmark dose or an average to synthesize the benchmark dose. When multiple baseline doses are calculated from different responses or studies examining the same endpoint, the choice of baseline dose may also involve the selection of "critical effects" and the most appropriate species, gender, or other relevant experimental design features. Graphical representations of model outputs and experimental data, as well as an understanding of biological modes of action, can assist in the selection of baseline doses.

(9) Application of uncertainty coefficient of reference dose method

Once a single or average baseline dose is selected, the reference dose can be calculated by dividing the baseline dose by one or more coefficients of uncertainty. As a default setting, all uncertainty coefficients applicable to the traditional NOAEL-based reference dose method should be considered, with the exception of the LOAEL-NOAEL extrapolation coefficient. The size of other coefficients (such as the baseline response and confidence limits), biological considerations (such as the possibility of thresholds), the severity of modeling effects, and the slope of the dose-response curve can all affect the choice and size of the uncertainty coefficient ^[3] .