Why Evidence From One Strength May Support Another
A product may be marketed in several strengths even though conducting an in vivo bioequivalence study for each one is unnecessary or impractical. Regulators may allow evidence from a study at one strength to support additional strengths when the strengths are sufficiently comparable: their formulations and manufacture are appropriately related, their dissolution behavior is similar, and the pharmacokinetic evidence can reasonably be extrapolated across the relevant doses.
This is not an automatic consequence of showing bioequivalence at one strength. The waiver concerns whether a study at another strength can be omitted; it does not mean that the untested strength has been independently demonstrated bioequivalent by a clinical comparison. The earlier material on FDA, EMA, and WHO BE standards describes why requirements can vary by authority. Product-specific requirements and current regional guidance take precedence over any general checklist.
The bridge generally has three connected parts. First, the strengths must have a sufficiently similar formulation and manufacturing process. Second, the tested strength must be suitable for extrapolation across the proposed dose range, including consideration of dose proportionality or pharmacokinetic linearity where relevant. Third, in vitro dissolution should support comparable drug release across strengths. The precise evidence required, and permitted exceptions, depend on the product and regulator.
Formulation and Manufacturing Relationships
A common starting point is to compare the qualitative and quantitative compositions of the strengths. Qualitative similarity means the same excipients are used, subject to any permitted differences. Quantitative proportionality means the amounts of active ingredient and excipients change in a consistent relationship across strengths. Exact proportionality is one clear case: if the active ingredient doubles, the amount of each other component also doubles. Some guidance allows defined alternatives, such as certain excipients held constant or strengths assessed in proportionality groups, but those alternatives must be justified rather than presumed acceptable.
Manufacturing matters because two tablets with similar ingredient lists need not release drug similarly if their processes or physical properties differ. Relevant considerations can include the manufacturing process, equipment or process changes, granulation, compression, and other product attributes that affect dissolution. A claim that strengths share a formulation name is not a substitute for showing that their manufacture and resulting performance are comparable.
Worked Example: Checking Proportional Tablet Compositions
Suppose a hypothetical immediate-release product has 5 mg, 10 mg, and 20 mg strengths. The ingredient amounts per tablet are:
| Ingredient | 5 mg strength | 10 mg strength | 20 mg strength |
|---|---|---|---|
| Active ingredient | 5 mg | 10 mg | 20 mg |
| Filler | 25 mg | 50 mg | 100 mg |
| Binder | 5 mg | 10 mg | 20 mg |
| Disintegrant | 2.5 mg | 5 mg | 10 mg |
| Lubricant | 2.5 mg | 5 mg | 10 mg |
Check the scaling. Relative to the 5 mg tablet, the strength factors are \(10/5=2\) and \(20/5=4\). Each listed ingredient amount also increases by factors of 2 and 4. For example, filler changes from 25 mg to 50 mg and 100 mg, while binder changes from 5 mg to 10 mg and 20 mg. The ingredient amounts are therefore exactly proportional in this hypothetical formulation.
This supports a formulation bridge, but does not establish waiver eligibility by itself. The manufacturing process, pharmacokinetic behavior across doses, dissolution evidence, and applicable regulatory requirements still need to be addressed.
A less direct composition relationship requires particular care. If the active ingredient scales with strength but some excipients remain fixed, or if the higher strength uses a different excipient amount or manufacturing process, the reviewer must determine whether that difference is allowed and adequately supported. A difference is not automatically disqualifying in every jurisdiction, but it means that simple exact proportionality cannot be claimed.
Worked Example: A Formulation That Is Not Exactly Proportional
Consider a hypothetical 20 mg tablet containing 20 mg active ingredient, 80 mg filler, 10 mg binder, 5 mg disintegrant, and 5 mg lubricant. A 10 mg tablet contains 10 mg active ingredient, 50 mg filler, 10 mg binder, 5 mg disintegrant, and 5 mg lubricant.
Compare the strength factor. The active ingredient changes by \(10/20=0.5\). Exact proportionality would therefore predict 40 mg filler, 5 mg binder, 2.5 mg disintegrant, and 2.5 mg lubricant in the 10 mg tablet.
Compare with the actual composition. The 10 mg tablet contains 50 mg filler, 10 mg binder, 5 mg disintegrant, and 5 mg lubricant. Those amounts are not the values predicted by the 0.5 scaling factor. The two strengths are not exactly quantitatively proportional.
That conclusion does not alone settle the regulatory decision. A regulator might accept a specified alternative composition relationship with adequate justification, or might require a study at the additional strength. The sponsor should describe the differences and their potential effects on product performance rather than labeling the formulations proportional.
Pharmacokinetic Extrapolation and Choice of Strength
The strength used in the in vivo study must provide a sound basis for the proposed extrapolation. One consideration is whether exposure changes predictably with dose over the relevant range. If pharmacokinetics are approximately linear over that range, a dose change is not expected to produce a disproportionate change in exposure. If exposure is nonlinear, evidence at one dose may not adequately predict the relative performance of another strength.
This pharmacokinetic question is distinct from formulation proportionality. A tablet may have quantitatively proportional ingredients even when the drug’s exposure is not dose proportional. Conversely, dose-proportional exposure does not establish that two strengths have comparable formulations or dissolution. Both lines of reasoning must be considered where required.
Regulators often specify which strength should be studied, with the highest strength commonly used when it can be administered safely and is suitable for the comparison. The choice may depend on the drug’s safety, the product’s formulation, dose proportionality, and the applicable guidance. Do not infer a universal rule that the highest strength must always be used or that a study at the highest strength automatically supports every lower strength.
In the study at the selected strength, the relevant bioequivalence endpoints and acceptance criteria still apply. For example, a regulator may require the applicable confidence intervals for the geometric mean ratios of AUC and \(C_{\max}\) to meet the prespecified limits. Passing those criteria supports bioequivalence at the studied strength; it does not remove the need to justify the bridge to each proposed unstudied strength.
Dissolution Similarity as Supporting Evidence
Dissolution testing compares the amount of drug released from the different strengths over time under specified in vitro conditions. Similar profiles support the argument that the strengths release drug comparably. The comparison should use appropriate test conditions and a suitable sampling schedule, with adequate units tested for each strength. A single matching time point or a comparison made under uninformative conditions is not enough to establish similar profiles.
One commonly used summary is the similarity factor \(f_2\), which expresses the average squared difference between the reference and test dissolution percentages at matched time points. In settings where its use is appropriate, \(f_2\) values from 50 to 100 are commonly treated as indicating profile similarity. The precise conditions for using this statistic and the acceptance convention are guidance-dependent, not a universal rule for every product.
The direction of this relationship follows directly from the formula. If the matched profiles are identical, every difference \(R_t-T_t\) is zero, so the sum of squared differences is zero and the term in square brackets equals 1. Thus \(f_2=50\log_{10}(100)=100\). As the squared differences increase, the bracket becomes greater than 1, its negative one-half power decreases, and the resulting \(f_2\) decreases. This makes \(f_2\) a summary of profile distance, not a clinical bioequivalence statistic.
Worked Example: Calculating a Dissolution Similarity Factor
In a hypothetical comparison, the mean percentages dissolved at six matched times are 10, 30, 55, 75, 85, and 90 for the reference strength, and 10, 31, 54, 74, 84, and 89 for the test strength. Assume the testing conditions and sampling design meet the applicable requirements for using \(f_2\).
Calculate the differences and squared differences. The differences \(R_t-T_t\) are \(0,-1,1,1,1,1\), so the squared differences are \(0,1,1,1,1,1\). Their sum is 5 and \(n=6\).
Substitute into the formula.
The calculated value exceeds 50 and, under a convention that applies the 50-to-100 criterion to this comparison, supports dissolution similarity. It does not by itself prove bioequivalence or qualify the strengths for a waiver: the formulation, process, pharmacokinetic, and regulatory conditions also need to be satisfactory.
Before relying on \(f_2\), check that the profiles were measured under comparable conditions and that the time points were selected appropriately. Regulatory guidance commonly specifies additional conditions, such as the number of units, variability, and limits on how many observations occur after a high fraction has dissolved. If those conditions are not met, the calculated value may not be interpretable under the usual convention. A poor or variable profile may require investigation or another justified comparison rather than an unqualified pass/fail reading of \(f_2\).
Assessing a Proposed Waiver
Identify the strength studied in vivo and each strength for which a study is proposed to be waived. Confirm that the products are the same dosage form and that the comparison is within the scope of the applicable guidance.
Document excipients and their amounts, explain any nonproportional differences, and establish whether manufacturing processes and relevant product attributes are sufficiently comparable.
Determine whether exposure is sufficiently predictable over the proposed dose range and whether the studied strength is appropriate under the product-specific requirements. Consider safety and tolerability when selecting the study dose.
Compare suitable profiles for the strengths, apply the relevant conditions for any summary statistic, and check whether the authority’s current guidance requires further evidence or limits the waiver.
This assessment is different from a waiver based on a drug’s biopharmaceutic classification. An additional-strength waiver relies on a bridge from a studied strength of the product to its other strengths. A BCS-based biowaiver uses a separate set of eligibility criteria. The two rationales should not be conflated, even if dissolution evidence is relevant to both.
Diagnostics, Alternatives, and Limitations
Warning signs include a strength with a different excipient, a change in manufacturing process, a nonlinear exposure pattern over the relevant dose range, or dissolution profiles that diverge at times relevant to drug release. Each finding weakens a particular part of the bridge and should prompt a targeted explanation or additional evidence. A high \(f_2\) cannot repair an unsupported formulation relationship; proportional ingredients cannot compensate for clearly dissimilar dissolution.
The main alternative is to conduct an in vivo bioequivalence study at the additional strength rather than extrapolate from another strength. Depending on the product and regulatory pathway, other supporting evidence may also be requested. A waiver can reduce unnecessary duplication, but it cannot resolve uncertainty simply by reducing the amount of evidence collected. Its limitations are important: the conclusion applies only to the strengths and conditions justified in the submission, and a change in formulation, process, or relevant product performance may require reassessment.
A common mistake is to reason, “The 20 mg strength passed bioequivalence, so the 10 mg strength is automatically covered because it contains the same active ingredient.” That conclusion skips the bridge. The correction is to verify the composition and manufacturing relationship, consider whether exposure can be extrapolated across doses, assess suitable dissolution evidence, and apply the authority’s specific conditions. A waiver is justified by the combined evidence, not by strength labels alone.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A product’s 10 mg and 20 mg strengths have excipient amounts that double along with the active ingredient. Does this alone establish eligibility for a strength waiver? State two other issues to assess.
- For a 5 mg tablet with 30 mg filler, exact proportionality predicts how much filler in a 15 mg tablet?
- Two dissolution profiles are identical at all matched time points. What is their \(f_2\), and what does that value establish?
- Why can a formulation with proportional ingredient amounts still fail to support extrapolation across strengths?
- A proposed waiver is based only on the claim that the active ingredient is highly soluble. What is the problem with treating this as sufficient for an additional-strength waiver?
Solutions. (1) No. Proportional composition supports the formulation bridge but is not sufficient alone. Assess, for example, manufacturing comparability, dose-related pharmacokinetics, suitable dissolution similarity, and the specific regulatory requirements. (2) The strength factor is \(15/5=3\), so the predicted filler amount is \(30\times3=90\) mg. (3) The squared differences are all zero, so \(f_2=50\log_{10}(100)=100\), indicating identical measured profiles under the tested conditions. It does not alone establish clinical bioequivalence or waiver eligibility. (4) Exposure may not change predictably across the dose range, or dissolution and manufacturing may not be comparable; ingredient scaling does not settle those questions. (5) Solubility alone is not the rationale for an additional-strength bridge. That waiver requires the relevant cross-strength formulation, pharmacokinetic, dissolution, and regulatory conditions; a BCS-based waiver is a distinct pathway with its own criteria.