Bioassays are experiments that measure the biological activity or effect of a substance, such as a drug, vaccine, or hormone. Bioassay validation is the process of ensuring that the bioassay method is reliable, accurate, and reproducible. Bioassay analysis is the process of interpreting the bioassay data and drawing conclusions about the substance's potency, efficacy, or safety.
One of the key aspects of bioassay validation and analysis is parallelism.
Parallelism refers to the assumption that the test sample and the reference sample have the same response function, meaning that they produce similar results when diluted at different concentrations. This assumption allows us to compare the test sample and the reference sample on a common scale and estimate the relative potency of the test sample.
To test for parallelism, we need to perform a statistical test that compares the slopes and intercepts of the test sample and the reference sample curves. There are different methods for testing parallelism, such as the F-test, the chi-square test, and the equivalence test. The choice of method depends on the type of bioassay, the design of the experiment, and the criteria for acceptance or rejection of parallelism.
Parallelism is important for bioassay validation and analysis because it ensures that we are measuring the true biological effect of the substance and not some other factor that may affect the response.
If parallelism is violated, it means that there is a difference in the response function between the test sample and the reference sample, which could be due to factors such as matrix interference, degradation, aggregation, or immunogenicity. This could lead to inaccurate or misleading estimates of potency, efficacy, or safety.
Therefore, parallelism is a crucial concept in bioassay validation and analysis that helps us to evaluate the quality and validity of bioassay methods and data. Actually, it can reduce the time and cost of bioassay validation and analysis, as well as increase the robustness and reproducibility of the results.
Definition of parallelism
Parallelism in bioassay is a statistical criterion that evaluates whether two dose-response curves have the same shape and differ only by a constant factor.
The components of parallelism are slope ratio, intercept ratio, and equivalence limit.
The slope ratio is the ratio of the slopes of the two curves, which measures how steeply they change with respect to the dose. A slope ratio close to 1 indicates that the test and reference curves have similar slopes, which implies parallelism. A slope ratio significantly different from 1 suggests that the test and reference curves have different shapes or directions, which violates parallelism.
The intercept ratio is the ratio of the intercepts of the two curves, which measures how much they differ at zero dose. An intercept ratio close to 1 indicates that the test and reference curves have similar intercepts, which implies parallelism. An intercept ratio significantly different from 1 suggests that the test and reference curves have different levels of response at zero dose, which violates parallelism.
The equivalence limit is a predefined range of acceptable values for the slope ratio and intercept ratio, which determines whether the two curves are considered parallel or not. An equivalence limit can be based on biological or clinical relevance or statistical criteria. A relative potency within the equivalence limit indicates that the test and reference samples have similar potencies, which implies parallelism. A relative potency outside the equivalence limit suggests that the test and reference samples have different potencies, which violates parallelism.
Parallelism in bioassay is the condition where the test sample responds like a diluted copy of the reference sample, meaning that their dose-response curves have the same shape and direction. Parallelism is an important assumption for estimating the relative potency of the test sample compared to the reference sample, which is a key parameter in bioassay analysis.
Purpose of parallelism in bioassay
Parallelism in bioassay is a
statistical method that evaluates the similarity, comparability, and potency of
biological samples.
The main objectives of testing parallelism are:
1) to assess the similarity of the dose-response curves of different
samples, such as a test sample and a reference standard. This can help to
determine if the samples have the same biological activity and mechanism of
action. This objective aims to check whether the test sample and the reference sample have sufficiently similar dose-response curves to allow for a valid comparison of potency. If the curves are not similar enough, it may indicate that the test sample has a different mechanism of action, a different level of purity, or a different stability than the reference sample. Similarity testing is usually done by applying a statistical test, such as the F-test, or the equivalence test, to compare the slopes and intercepts of the curves.
2) To assess the comparability of the relative potency estimates of
different samples, such as a test sample and a reference standard. This can
help to determine if the samples have the same amount of biological activity
per unit of mass or volume. This objective aims to check whether the test sample and the reference sample have consistent dose-response curves across different batches, lots, or time points. Comparability testing is important for monitoring the quality and consistency of biopharmaceutical products over time and across different manufacturing processes. Comparability testing is usually done by applying a statistical method, such as analysis of variance (ANOVA), to compare the potencies and parallelism parameters of different samples.
3) To assess the potency of a test sample relative to a reference standard.
This can help to quantify the biological activity of a test sample and to
establish its quality and consistency. This objective aims to estimate the relative potency of the test sample compared to the reference sample. Potency testing is essential for determining the appropriate dosage and administration of biopharmaceutical products. Potency testing is usually done by applying a mathematical model, such as a linear or nonlinear regression model, to fit the dose-response curves and calculate the ratio of potencies between the test sample and the reference sample.
Methods of testing parallelism
There is no consensus on the best method to test parallelism in bioassay. Let's compare and contrast three different methods of testing parallelism: linear regression, analysis of variance (ANOVA), and equivalence testing.
Linear regression is a method that fits a linear model to the dose-response data and tests the interaction term between the dose and the preparation. If the interaction term is not significant, it implies that the slopes of the test and reference curves are not different, and thus parallelism holds. The advantage of linear regression is that it is simple and intuitive, and it can handle continuous or ordinal responses. The disadvantage is that it may have low power to detect non-parallelism when the curves are close together or have a large variability.
ANOVA is a method that partitions the total variation in the response into different sources, such as the dose, the preparation, and the interaction between them. It then tests whether the interaction term is significant or not. If the interaction term is significant, it means that the dose-response curves of the test and reference preparations are not parallel. The advantage of ANOVA is that it can handle categorical or binary responses, and it may have higher power than linear regression when the curves are far apart or have a small variability. The disadvantage is that it may be sensitive to outliers or violations of normality.
Equivalence testing is a method that tests whether the difference between the slopes of the test and reference curves is within a predefined margin of equivalence. If the difference is within the margin, it means that the slopes are equivalent, and thus parallelism holds. The advantage of equivalence testing is that it allows the user to specify a clinically or biologically meaningful margin of equivalence, and it may have higher power than linear regression or ANOVA when the curves are close together or have a large variability. The disadvantage is that it may be difficult to choose an appropriate margin of equivalence, and it may require a larger sample size than linear regression or ANOVA.
Criteria for evaluating parallelism
Parallelism can be tested using different statistical methods, such as confidence intervals, p-values, and equivalence margins.
Confidence intervals are estimates that provide a lower and upper bound for the true effect size. P-values are probabilities that measure how likely the observed data are under the null hypothesis. Equivalence margins are predefined ranges that specify how close the test and reference samples should be to be considered parallel.
These methods have different advantages and disadvantages, and the choice of the best method depends on the type and purpose of the bioassay. If parallelism is violated, the results of the bioassay may be inaccurate or misleading.
There are different statistical methods to test for parallelism in bioassays, but they all have some common elements. First, we need to fit a dose-response curve to the data, which describes how the response variable changes with different doses of the substance. Second, we need to compare the curves of the test and reference samples and see if they are parallel or not. Third, we need to make a decision based on some criteria, such as confidence intervals, p-values, or equivalence margins.
Confidence intervals are estimates that provide a lower and upper threshold to the estimate of the magnitude of the effect. By convention, 95% confidence intervals are most typically reported. For example, if we estimate that the relative potency of the test sample is 0.8 with a 95% confidence interval of (0.7, 0.9), it means that we are 95% confident that the true relative potency is between 0.7 and 0.9. To test for parallelism using confidence intervals, we can check if the confidence interval of the relative potency includes 1 or not. If it does, it means that there is no significant difference between the test and reference samples and we can accept parallelism. If it does not, it means that there is a significant difference and we can reject parallelism.
P-values are probabilities that measure how likely it is to observe a result as extreme or more extreme than what was actually observed, assuming that the null hypothesis is true. The null hypothesis is usually a statement of no effect or no difference. For example, if we obtain a p-value of 0.01 for testing the difference between the test and reference samples, it means that there is only a 1% chance of observing such a difference or larger if there is no real difference between them. To test for parallelism using p-values, we can compare the p-value with a pre-specified significance level, such as 0.05 or 0.01. If the p-value is smaller than the significance level, it means that we have enough evidence to reject the null hypothesis and conclude that there is a significant difference between the test and reference samples and we can reject parallelism. If the p-value is larger than the significance level, it means that we do not have enough evidence to reject the null hypothesis and conclude that there is no significant difference between the test and reference samples and we can accept parallelism.
Equivalence margins are predefined ranges of acceptable differences between the test and reference samples. For example, if we set an equivalence margin of ±10%, it means that we consider the test and reference samples to be equivalent if their relative potency is within 10% of each other. To test for parallelism using equivalence margins, we can check if the confidence interval of the relative potency falls within the equivalence margin or not. If it does, it means that we can accept parallelism as the difference between the test and reference samples is within our tolerance. If it does not, it means that we can reject parallelism as the difference between the test and reference samples is beyond our tolerance.
Each method has its own advantages and disadvantages, and there is no definitive answer on which one is better or worse. The choice of method depends on various factors, such as the type of bioassay, the design of the experiment, the quality of data, and the regulatory requirements. Therefore, it is important to understand the assumptions and limitations of each method and apply them appropriately in different situations.
Challenges and limitations of parallelism
Parallelism testing also poses several challenges and limitations that need to be addressed and overcome. Some of these challenges and limitations are:
1) Variability: Bioassays are inherently variable due to biological and experimental factors, such as cell culture conditions, assay reagents, operator skills, and instrument performance. In addition, bioassay data are often subject to random and systematic errors, such as measurement noise, assay drift, operator bias, and environmental factors. These sources of variability can affect the precision and reproducibility of the dose-response curves and the parallelism assessment. In other terms, such kind of errors can affect the shape and position of the dose-response curves, and thus influence the outcome of parallelism testing. Therefore, it is important to use appropriate experimental design, quality control, and data analysis techniques to minimize the sources of variability and use appropriate statistical methods to account for the residual variability in the data.
2) Outliers: Outliers are extreme or inconsistent observations that deviate significantly from the expected pattern of the data. Outliers can arise from various causes, such as errors in sample preparation, pipetting, measurement, or data entry. Outliers can distort the shape and fit of the dose-response curves and lead to false conclusions about the parallelism status. Therefore, it is essential to detect and handle outliers properly using robust methods and criteria. To deal with outliers in bioassay data, it is advisable to use robust statistical methods that are less sensitive to outliers or to identify and remove outliers based on objective criteria.
3) Assumptions: Parallelism testing relies on certain assumptions about the data and the model used to fit the dose-response curves. For example, some common assumptions are that the data follow a normal distribution, that the variance is constant across doses, that the curves have the same slope and shape parameters, and that there is no interaction between the material and the dose. However, these assumptions may not always hold true in practice and may violate the validity of the parallelism test. Therefore, it is necessary to check and verify the assumptions before performing the parallelism test and use alternative methods if the assumptions are violated.
Examples of parallelism in bioassay
Parallelism testing can be applied to various types of bioassays, such as antibody binding, enzyme activity, and cell proliferation assays. Some examples of parallelism testing in these bioassay applications are:
a) Antibody binding: Antibody binding assays measure the ability of an antibody to bind to a specific antigen and are commonly used to evaluate the quality and consistency of monoclonal antibodies. Parallelism testing can be used to compare the binding curves of a test antibody and a reference antibody and determine if they have similar slopes and shapes. This can indicate that the test antibody has similar affinity and specificity as the reference antibody and can be used interchangeably. This can help evaluate the quality and consistency of the test antibody production and purification process.
b) Enzyme activity: enzyme activity assays, which measure the rate of a biochemical reaction catalyzed by an enzyme, are often used to monitor the production and purification of recombinant enzymes, which are also important biotechnology products. Parallelism testing can be used to compare the activity curves of a test enzyme and a reference enzyme and determine if they have similar responses to different substrate concentrations. This can indicate that the test enzyme has similar catalytic efficiency and kinetics as the reference enzyme and can perform similarly in different conditions. This can help assess the stability and functionality of the test enzyme preparation and storage conditions.
c) Cell proliferation: cell proliferation assays, which measure the growth or viability of cells in response to various stimuli, are frequently used to study the effects of drugs, toxins, hormones, or other factors on cell biology and physiology. Parallelism testing can be used to compare the proliferation curves of a test cell population and a reference cell population and determine if they have similar responses to different doses or concentrations of a stimulus. This can indicate that the test cell population has similar sensitivity and mechanism of action as the reference cell population and can be used for further experiments. This can help measure the viability and responsiveness of the test cell line and its potential for drug development.
Best practices for parallelism in bioassay
Some best practices for parallelism testing in bioassay design, execution, and interpretation include:
1) Use appropriate statistical methods and criteria to assess parallelism. Common methods include analysis of variance (ANOVA), equivalence testing, and regression analysis. Common criteria include slope ratio, confidence intervals, and p-values. The choice of method and criterion should be based on the type and purpose of the bioassay, as well as the regulatory guidelines and expectations.
2) Use adequate sample size and replication to achieve sufficient power and precision for parallelism testing. The sample size and replication should be determined by a statistical power analysis, taking into account the expected variability and effect size of the bioassay. The sample size and replication should also be consistent with the bioassay design and validation plan.
3) Use appropriate dilution schemes and concentration ranges for parallelism testing. The dilution schemes and concentration ranges should cover the linear or relevant part of the dose-response curves, as well as the lower and upper limits of quantification (LLOQ and ULOQ) of the bioassay. The dilution schemes and concentration ranges should also be optimized to minimize any potential matrix effects, interference, or degradation of the test sample.
4) Use appropriate controls and reference standards for parallelism testing. The controls and reference standards should be representative of the test sample in terms of quality, stability, and potency. The controls and reference standards should also be prepared and handled in a consistent and traceable manner, following Good Laboratory Practices (GLP) and Standard Operating Procedures (SOP).
5) Use appropriate data analysis and interpretation for parallelism testing. The data analysis and interpretation should be performed by qualified personnel, using validated software tools and algorithms. The data analysis and interpretation should also be documented and reported in a clear and transparent way, following good documentation practices (GDP) and regulatory requirements.
Conclusions and future directions
Bioassays are analytical methods that use biological systems to measure the activity or effect of a substance, such as a drug, hormone, or toxin. Bioassays are widely used in drug development, pharmacology, toxicology, and environmental monitoring. However, bioassays also pose some challenges, such as variability, sensitivity, and accuracy. One of the key factors that affect the accuracy of bioassays is parallelism. Parallelism is the assumption that the test sample and the reference sample have the same response curve shape and slope when diluted in a biological matrix. Parallelism ensures that the test sample is responding like a diluted copy of the reference sample and that the concentration of the analyte can be accurately determined by interpolation from the reference curve. Parallelism can be tested by various statistical methods, such as the F-test, the chi-square test, or the equivalence test. However, parallelism testing is not always straightforward or conclusive. There are many factors that can influence parallelism, such as matrix effects, endogenous levels, minimum required dilution, selectivity, and assay design. Moreover, there is no consensus on the best method or criteria for parallelism testing among different bioassay types and applications. Therefore, there is a need for more research and development on parallelism in bioassay to improve its reliability and validity. By addressing the challenges and opportunities in this field, we can enhance the quality and reliability of bioassay data and support the development of new biopharmaceuticals and biosimilars.
Below I list some of the prominent future directions for parallelism in bioassay:
1) Developing standardized methods and criteria for parallelism testing across different types of bioassays, such as ligand-binding assays, cell-based assays, and enzyme-linked immunosorbent assays that are more robust, sensitive, and specific for different bioassay types and analytes.
2) Exploring the effects of matrix components, such as endogenous analytes, interfering substances, and binding proteins, on parallelism and how to minimize or correct them.
3) Investigating the optimal design and analysis of parallelism experiments, such as sample size, dilution scheme, statistical tests, and equivalence margins.
4) Evaluating the impact of parallelism on bioassay validation, calibration, and quality control, and how to incorporate parallelism assessment into routine bioanalytical workflows.
5) Applying novel technologies and approaches, such as high-throughput screening, multiplexing, automation, and machine learning, to improve the efficiency and robustness of parallelism testing.
By advancing parallelism research and development, bioassay innovation and optimization can be enhanced, leading to better quality and safety of biopharmaceutical products and environmental monitoring.
References
Fleetwood K, Bursa F, Yellowlees A. Parallelism in practice: approaches to parallelism in bioassays. PDA J Pharm Sci Technol. 2015 Mar-Apr;69(2):248-63. doi: 10.5731/pdajpst.2015.01016. PMID: 25868991.
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