What a Tumor Growth Inhibition Metric Summarizes
Serial tumor measurements describe a trajectory, not just an endpoint. A treatment group can have a larger tumor volume at the final visit yet have grown less during the study, for example, if its tumors were larger at baseline. Conversely, a small endpoint difference does not by itself show that treatment inhibited growth. A useful summary therefore specifies the starting measurement, the follow-up time and the comparator.
The metrics in this tutorial summarize observed tumor volume. They do not, by themselves, identify the biological process that produced the trajectory or establish why groups differ. For a treatment-control comparison, the basic design assumption is that groups are measured on the same schedule and that the control group provides a meaningful estimate of growth without active treatment. Interpretation also depends on consistent measurement methods and sufficiently reliable baseline and follow-up measurements.
Absolute change is expressed in the volume unit used for measurement, such as mm3. Percentage change is dimensionless. Both require an explicit baseline: in a longitudinal treatment study, this is commonly the measurement immediately before treatment begins. If a different measurement is used, the resulting change answers a different question.
Absolute-Increment Tumor Growth Inhibition
A common group-level measure compares the change in mean tumor volume in a treated group with the change in mean tumor volume in a control group over the same interval. Let \(\bar V_{T,0}\) and \(\bar V_{T,t}\) denote the treated-group mean volumes at baseline and follow-up, and let \(\bar V_{C,0}\) and \(\bar V_{C,t}\) denote the corresponding control-group means. When control tumors grow over the interval, absolute-increment tumor growth inhibition (TGI) is:
The numerator and denominator are the mean absolute changes in the treated and control groups. The denominator must be nonzero; in practice, a small or negative control-group change makes this measure unstable or difficult to interpret as inhibition of growth. The expression is time-specific: the treated and control changes must cover the same baseline-to-follow-up interval.
The calculation compares changes, not endpoint volumes. It should be reported with its interval and units for the underlying volumes. TGI is a descriptive contrast of group mean changes; it is not a probability, and it does not alone show whether the observed difference is statistically distinguishable from measurement or sampling variation.
Worked Example: Calculating Change and TGI With Matched Baselines
In a hypothetical study, three control animals have baseline tumor volumes of 100, 110 and 90 mm3, and their day-14 volumes are 180, 198 and 162 mm3. Three treated animals have baseline volumes of 100, 110 and 90 mm3, and their day-14 volumes are 110, 121 and 99 mm3. Calculate the group mean changes and absolute-increment TGI.
The control baseline mean is \((100+110+90)/3=100\) mm3; its day-14 mean is \((180+198+162)/3=180\) mm3. Thus the mean control change is \(180-100=80\) mm3, an 80% increase from baseline.
The treated baseline mean is also \((100+110+90)/3=100\) mm3; its day-14 mean is \((110+121+99)/3=110\) mm3. The mean treated change is \(110-100=10\) mm3, a 10% increase from baseline. Substituting the changes:
Over the baseline-to-day-14 interval, the treated group had 87.5% less absolute mean growth than the control group. Its mean tumor volume still increased by 10 mm3; 87.5% TGI does not mean that tumors shrank by 87.5%.
Baseline-Normalized Growth and Endpoint Ratios
Absolute-increment TGI is sensitive to baseline differences because it compares volume changes in the measurement unit. When baseline volumes differ materially, a complementary calculation compares each group’s change relative to its own baseline. Define the group-level relative changes as \(R_T=(\bar V_{T,t}-\bar V_{T,0})/\bar V_{T,0}\) and \(R_C=(\bar V_{C,t}-\bar V_{C,0})/\bar V_{C,0}\). If \(R_C\ne0\), relative-growth TGI is:
This is a ratio of group-level relative changes, not necessarily the average of individual percentage changes. The two summaries can differ when baseline volumes vary among subjects. Analysts should state which calculation they use and should not silently substitute one for the other. As with absolute-increment TGI, the relative version is unstable when control relative change is close to zero and is not a useful inhibition ratio if control tumors shrink.
An endpoint treated-to-control ratio, often written as \(100\bar V_{T,t}/\bar V_{C,t}\), compares final mean volumes. It does not subtract baseline volumes or adjust for baseline imbalance. It therefore answers a different question from either TGI measure. Reporting an endpoint ratio as though it were baseline-adjusted growth inhibition can give a misleading interpretation.
Worked Example: Baseline Imbalance Changes the Comparison
In a hypothetical study, the control mean volume increases from 100 to 200 mm3, while the treated mean increases from 150 to 225 mm3 over the same period. Calculate the endpoint T/C ratio, absolute-increment TGI and relative-growth TGI.
The endpoint ratio is \(100(225/200)=112.5\%\). The treated endpoint mean is 12.5% higher than the control endpoint mean. But this comparison does not account for the treated group’s higher baseline.
The control change is \(200-100=100\) mm3, and the treated change is \(225-150=75\) mm3. Thus:
The relative control change is \(100/100=1.00\), or 100%; the relative treated change is \(75/150=0.50\), or 50%. Therefore:
The three results are not contradictory: the endpoint ratio describes final group means, absolute-increment TGI compares growth in mm3, and relative-growth TGI compares proportional growth from each group’s baseline. The baseline imbalance makes the choice consequential. Each should be labeled by its definition rather than presented as an interchangeable “TGI.”
Why Assessment Time Matters
A TGI value summarizes growth only up to the chosen follow-up. If the response changes over time, different assessment times can produce different values even when the same animals and baseline are used. An early assessment may precede a measurable treatment-associated change; a later one may capture a larger separation, or may include regrowth. The value is not a time-independent property of a treatment.
Worked Example: TGI at Two Follow-Up Times
In a hypothetical study, the control and treated group means are both 100 mm3 at baseline. At day 7, their means are 140 and 130 mm3, respectively. At day 21, their means are 220 and 150 mm3. Calculate absolute-increment TGI at each time.
At day 7, control growth is \(140-100=40\) mm3 and treated growth is \(130-100=30\) mm3:
At day 21, control growth is \(220-100=120\) mm3 and treated growth is \(150-100=50\) mm3:
The treated group had less absolute mean growth than control at both assessments, but the estimated inhibition differed by time. These calculations alone do not establish why the difference changed. They do establish that reporting “58.3% TGI” without naming day 21 and the baseline-to-day-21 interval omits essential context.
Calculation Checks, Comparisons, and Limitations
A short justification clarifies the scale of absolute-increment TGI. Let \(G_T=\bar V_{T,t}-\bar V_{T,0}\) and \(G_C=\bar V_{C,t}-\bar V_{C,0}\), with \(G_C>0\). Then \(\mathrm{TGI}_{\Delta}=100(1-G_T/G_C)\%\). If \(G_T=G_C\), the ratio is 1 and TGI is 0%; if \(G_T=0\), the ratio is 0 and TGI is 100%. If \(G_T<0\), then \(G_T/G_C<0\), so TGI exceeds 100%. If \(G_T>G_C\), the ratio exceeds 1, so TGI is negative. These cases explain why values outside 0% to 100% are possible rather than automatically being calculation errors.
Use the following checks before interpreting a result:
- Verify the baseline and interval. Confirm that baseline is defined consistently, and that treatment and control measurements span the same elapsed time. If visits differ, identify the actual times rather than treating them as equivalent.
- Inspect control growth. A zero control change makes absolute-increment TGI undefined. A very small control change makes the ratio highly sensitive to small measurement differences. A shrinking control group does not provide the usual positive-growth reference.
- Compare baseline distributions. A difference in baseline group means can affect absolute-increment TGI and endpoint ratios. Show baseline and follow-up summaries, and consider a baseline-normalized measure where appropriate.
- Check the trajectories and data quality. Look for isolated measurements that dominate a group mean, inconsistent measurement procedures, missing follow-up data, and changes in the number of animals observed. A group mean can conceal substantial variation or divergent individual trajectories.
The metrics have distinct uses and limitations:
| Summary | What it compares | Main caution |
|---|---|---|
| Absolute change, \(\Delta V\) | Follow-up minus baseline volume, in volume units | Does not adjust for starting size when comparing subjects or groups |
| Percentage change from baseline | Change relative to the same subject’s or group’s baseline | Can be unstable for very small baselines; individual and group-level calculations differ |
| Absolute-increment TGI | Treated versus control absolute mean growth | Requires meaningful positive control growth; sensitive to baseline imbalance |
| Relative-growth TGI | Treated versus control proportional mean growth | Requires nonzero control relative growth; is not generally the mean of individual ratios |
| Endpoint T/C ratio | Treated versus control follow-up mean volume | Does not account for baseline volume or change from baseline |
None of these summaries replaces inspection of serial measurements. A single endpoint can miss the shape of the trajectory, and a single percentage can hide between-subject variability. These descriptive metrics also do not supply uncertainty intervals or a formal statistical comparison. Their interpretation should remain tied to the observed data, the selected baseline, the assessment time and the calculation used.
Common Mistakes
- Calling a percentage change “TGI.” A treated group’s change from its own baseline is not a treatment-control inhibition measure. TGI requires a specified comparator and formula.
- Using endpoint T/C as baseline-adjusted TGI. The endpoint ratio ignores starting volumes. State it as an endpoint ratio unless a baseline-adjusted calculation was actually performed.
- Assuming TGI must lie between 0% and 100%. Negative values or values above 100% can follow directly from the formula. Check the group changes and denominator before deciding whether a value is erroneous.
- Comparing different time intervals without qualification. TGI depends on assessment time. Report the baseline and follow-up days and compare like intervals.
- Interpreting reduced growth as tumor shrinkage. Positive TGI can coexist with positive treated-group growth, as in the first worked example. Use the treated group’s actual change to determine whether mean volume increased or decreased.
Check Your Understanding
Answer each question, then compare with the worked solutions below.
- A hypothetical control mean rises from 80 to 140 mm3, while a treated mean rises from 80 to 110 mm3. Calculate absolute-increment TGI and the treated percentage change from baseline.
- Control mean volume rises from 100 to 160 mm3, while treated mean volume falls from 120 to 100 mm3. Calculate absolute-increment TGI. What does the treated change say about volume?
- Why can endpoint T/C be above 100% while absolute-increment TGI is positive?
- What happens to absolute-increment TGI if the control mean has no change over the assessment interval?
Solutions. (1) Control growth is \(140-80=60\) mm3; treated growth is \(110-80=30\) mm3. TGI is \(100(1-30/60)=50.0\%\). Treated percentage change is \(100(30/80)=37.5\%\). (2) Control growth is 60 mm3; treated change is \(100-120=-20\) mm3. TGI is \(100[1-(-20/60)]=133.3\%\). The treated mean volume decreased by 20 mm3 over the interval. (3) The treated group may start at a larger baseline, so its final mean can exceed control even while its change is smaller. Endpoint T/C and baseline-to-follow-up growth compare different quantities. (4) The denominator is zero, so absolute-increment TGI is undefined; a ratio near zero in the denominator would also make it unstable.