Comparing Dose Size and Dosing Interval

Why Compare Dose Size and Dosing Interval Together?

A regimen is defined by both the amount given at each administration and the time between administrations. Comparing only the dose size can therefore be misleading: a larger dose given less often may deliver the same amount per day as smaller, more frequent doses. Even when the average exposure is the same, the concentration-time profiles need not be. The less frequent regimen may produce higher peaks and lower troughs.

A fair comparison starts by stating which exposure metric is being matched. AUC over a dosing interval, average concentration, peak concentration, trough concentration, and time within an exposure range answer different questions. In simulation for dose justification, a regimen should be evaluated using the metrics that correspond to the intended efficacy and safety targets, rather than assuming that one matching metric makes the regimens interchangeable.

Thus, for regimens with the same \(F\), \(CL\), and dose rate \(D/\tau\), the average concentration is the same, even if their doses and intervals differ. AUC per interval itself is not generally the same: if the interval doubles while dose rate stays constant, both the dose and interval AUC double. When regimen intervals differ, compare either average concentration or AUC normalized to a common duration, such as a day, as well as the profile metrics relevant to the decision.

Steady-State Profile Under a Simple Model

The following derivation uses a one-compartment model with intravenous bolus doses, first-order elimination, and linear, time-invariant pharmacokinetics. The dose is instantaneously available, \(V\) is the apparent volume of distribution, \(k\) is the elimination rate constant, and \(CL=kV\). There is no absorption phase. The derivation assumes repeated equal doses at interval \(\tau\) have continued long enough for steady state to be reached.

At steady state, the concentration immediately after a dose is the residual concentration from earlier doses plus the concentration increment \(D/V\) from the new dose. Each earlier dose's contribution is reduced by a factor \(e^{-k\tau}\) for every additional dosing interval. Summing these contributions gives a geometric series:

Immediately before the next dose, the peak has declined for \(\tau\) hours. Therefore \(C_{\min,ss}=C_{\max,ss}e^{-k\tau}\). Integrating the declining concentration over the interval also gives a useful result:

The cancellation shows why interval AUC does not depend on the interval in this model when dose is held fixed. Changing the interval while also changing the dose changes interval AUC according to the dose given. The result depends on linear elimination and constant clearance; it should not be treated as a general result for nonlinear pharmacokinetics or changing clearance.

Use the Metrics That Match the Decision

AUC and average concentration summarize total exposure over time. They do not describe how that exposure is distributed within the interval. Peak and trough can matter when efficacy or toxicity is related to concentrations at particular times, and time above or below a threshold can matter when the target is duration-based. The appropriate comparison depends on the prespecified target and the clinical question.

When using a population simulation, calculate each metric for each simulated individual under each candidate regimen. Keep the parameters, covariates, and random-effect realization paired across regimens when the purpose is to isolate the effect of the regimen schedule. Then summarize the resulting distributions or calculate the relevant probability of target attainment. Averaging individual parameters first can conceal variation and does not generally reproduce the distribution of individual exposures.

For an oral regimen, a dose may not enter the systemic circulation instantly. The simple bolus formulas above then do not provide the full peak and trough profile. A consistent comparison can still use interval AUC and average concentration under the appropriate model, but peak, trough, and time-above-target values should come from concentration-time profiles that include the modeled absorption process. The same principle applies when the model has multiple compartments or other features that affect profile shape.

Diagnostics, Alternatives, and Limitations

A useful comparison first verifies the regimen inputs and the meaning of each metric. Check dose units, interval units, bioavailability assumptions, and the time window used for AUC. Confirm that the simulated profile has reached steady state if steady-state metrics are being reported. For a bolus model, the peak occurs immediately after dosing and the trough immediately before the next dose; a coarse time grid that misses these event times can understate the peak or misplace the trough. Use dose-event-aware calculations or a sufficiently resolved profile.

If two regimens have equal dose rate and the same linear model parameters, their average concentrations should agree, even though their interval AUCs and peak-trough patterns can differ. A mismatch in average concentration can signal inconsistent AUC windows, a coding or unit error, unequal dose rates, or model features that invalidate the simple assumptions. Inspect representative concentration-time profiles and individual-level metrics rather than relying only on a single summary.

The main alternative to matching dose rate is to compare regimens against a common clinical target directly. For example, a decision may prioritize a minimum trough, a maximum peak, time within a range, or a joint criterion. This can be more relevant than matching average concentration, but it requires specifying the target and computing the corresponding metric consistently. AUC-based comparisons remain useful when total exposure is the intended basis for comparison; they are incomplete when profile shape also affects the decision.

These analytic formulas are a transparent benchmark for a simple model, not a substitute for a suitable model of the drug and route. Absorption, multiple compartments, time-varying clearance, nonlinear kinetics, adherence patterns, and uncertainty can alter the profile or the distribution of exposures. In those settings, simulate the candidate schedules with the fitted model and compare the same well-defined metrics for each. Whether dose changes are proportional under the model is a separate question; the equal-average result here relies on linearity and should not be extrapolated when that assumption is unsupported.

Common Pitfalls

• Calling interval AUC the average concentration. AUC is accumulated exposure over a specified time window and has units of concentration multiplied by time. Average concentration is AUC divided by the length of that window.
• Assuming equal average exposure means equal profiles. The calculation above shows equal average concentrations alongside different peaks and troughs. Evaluate the metrics tied to the decision.
• Comparing mismatched windows. A 12-hour AUC and a 24-hour AUC are not directly equal-dose-rate summaries. State the interval and, when appropriate, normalize to a common duration.
• Rounding intermediate values too early. Carry unrounded exponentials and concentrations through calculations, then round the reported results. Small rounding discrepancies can matter when comparing values near a target.
• Reporting a deterministic value as a population probability. A single parameter set gives one predicted profile. A population probability requires evaluating the criterion across the simulated population, with the intended sources of variability represented appropriately.