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Tail-volume loss and ratio inflation in truncated expiration connects unrecorded late gas to a biased FEV1 to FVC ratio. Suppose a valid first-second volume $A$ is retained, the recorded total is $M$, and additional uncollected volume is $L\ge 0$. The complete ratio is $A/(M+L)$, while using $M$ as FVC gives $A/M$.

If independent information bounds $L\le L_{\max }$, thenFor an original example with $A=2.4$ L, $M=3$ L and $L_{\max }=1$ L, the complete ratio lies between 0.60 and 0.80 under this bound. This is a deterministic interval conditional on the tail bound, not automatically a statistical confidence interval.

Bounding uncollected expiratory volume from terminal flow adds a model. Let volumetric flow rate after the stop time be $Q(T+s)=q_T{e}^{-s/\tau }$. The missing volume isIf $\tau \le {\tau }_{\max }$, this gives $L\le q_T{\tau }_{\max }$. For stipulated terminal volumetric flow rate $q_T=0.050\mathrm{L}{\mathrm{s}}^{-1}$ and ${\tau }_{\max }=4$ s, the bound is 0.20 L. With the same $A$ and $M$, the ratio is then between 0.75 and 0.80.

The bound extends to a positive sum of exponential tails: if each component has terminal volumetric flow rate $q_i$ and time constant at most ${\tau }_{\max }$, then $L={\sum }_i{q}_i{\tau }_i\le {\tau }_{\max }{\sum }_i{q}_i$. Without a justified upper time scale, however, very small terminal volumetric flow rate can coexist with a large slowly emptying volume. A visually flat trace alone does not supply that missing assumption.

The relative inflation from using the truncated ratio is especially simple:for positive $A$. In the bounded 0.20 L example it is at most $0.20/3\approx 6.67\%$. The result assumes termination after a valid first second; an invalid numerator needs another error model.

The primary spirometry standard evaluates end of forced expiration and distinguishes it from the validity of FEV1.^[ref] The calculations explain sensitivity to lost tail volume rather than replace the standard's actual maneuver criteria.