Toxicity Period (TOX)

Toxicity Period (TOX) in Q-TWiST Analysis

The toxicity period is the part of a Q-TWiST analysis that holds the harms of treatment, measured as time lived with the side effects the analysts have chosen to count. Its mean length in each trial arm is multiplied by a weight, $u_{TOX}$, so a month with those side effects counts for less than a month free of both symptoms and toxicity. For a health economist this is where toxicity is traded against benefit, because a regimen that keeps patients alive longer but with months of severe side effects can gain less quality-adjusted time than its survival curve suggests. Which side effects count is a choice made in each study, and in an illustrative case a wider definition of toxicity halves the Q-TWiST gain with survival unchanged.

Where the toxicity period sits among the Q-TWiST states

The label TOX comes from adjuvant breast cancer research. Goldhirsch and colleagues, reanalysing Ludwig Trial III in 463 evaluable postmenopausal women with node-positive breast cancer, divided overall survival into time with toxicity (TOX), time without symptoms and toxicity (TWiST) and time after systemic relapse (REL). They weighted TOX and REL by utility coefficients relative to TWiST and summed the weighted times to give Q-TWiST. In a Biometrics paper published later the same year, Gelber, Gelman and Goldhirsch defined TWiST itself by subtracting time with subjective side effects of treatment and time with unpleasant symptoms of disease from each patient's overall survival.

Glasziou, Simes and Gelber gave the approach its statistical form, estimating the mean time in each state from the areas between partitioned survival curves up to a chosen limit. The toxicity period contributes $u_{TOX}$ multiplied by its restricted mean duration to the Q-TWiST total. The state after relapse or progression, with its own weight, is the relapse period.

How the toxicity period shares time before relapse or progression

In most applications the toxicity period lies before relapse or progression. Lee and colleagues, analysing lenvatinib plus everolimus in advanced renal cell carcinoma, defined three mutually exclusive states, with TOX as time with grade 3 or 4 toxicity, TWiST as time before progression without grade 3 or 4 toxicity and REL as time after progression. Toxicity that occurs after progression therefore falls in REL.

$$\text{PFS}_L = \text{TOX} + \text{TWiST}$$

where $\text{PFS}_L$ is mean progression-free survival restricted to the analysis limit $L$ and measured from randomisation, and TOX and TWiST are the restricted mean times in the two states before progression. In adjuvant analyses relapse-free time, also measured from randomisation, takes the place of progression-free survival. The identity shows that extra time before progression can come mostly as TOX, in which case the treatment adds little TWiST.

When toxicity is defined by adverse event grade, a patient with no qualifying event before progression has a toxicity period of zero, and the arm's mean TOX averages these zeros with the toxic time of other patients. Beaumont and colleagues, analysing the COMPARZ trial of pazopanib against sunitinib in renal cell carcinoma, found mean toxicity time 31 days longer with sunitinib (95% confidence interval 13 to 48 days).

Definitions of toxicity across studies

The published definitions of toxicity differ. The early breast cancer work spoke of subjective side effects, and Cole, Gelber and Goldhirsch, in an IBCSG meta-analysis of eight randomised trials with 1,229 patients aged 49 years or younger, defined the first state as the period with subjective toxic effects of chemotherapy.

Later analyses in advanced cancer tied TOX to adverse event grades. Lee and colleagues used grade 3 or 4 toxicity. Beaumont and colleagues based their main analysis on grade 3 or 4 toxicities and also reported a threshold analysis with TOX defined as grade 2 or higher. In the NICE appraisal of pegylated liposomal irinotecan (TA440), the company's Q-TWiST analysis of the NAPOLI-1 trial counted time with grade 3 or higher toxicity.

A wider definition, such as grade 2 or higher, transfers progression-free time from TWiST into TOX, and a narrower one moves that time back. Because TOX is weighted below TWiST, the wider definition lowers Q-TWiST in every arm and lowers it most in the arm with more low-grade side effects. Results that use different toxicity definitions are therefore not directly comparable, even for the same drug.

The toxicity weight in threshold utility analysis

The weight $u_{TOX}$ runs from 0, where a month with toxicity is worth no more than death, to 1, where it is as good as a month without symptoms or toxicity. Goldhirsch and colleagues, and Lee and colleagues in their base case, set it at 0.5. A value assigned in this way is a utility-like coefficient and need not come from a valuation study.

Glasziou and colleagues proposed that, when the weights are uncertain, results should be shown as a threshold analysis across them, read from a simple graph with confidence bands around the threshold line. Gelber and colleagues later described threshold utility analysis as the emphasis of the method, showing trade-offs between health-state durations without aiming at one combined result.

$$\Delta\text{Q} = u_{TOX} \times \Delta\text{TOX} + \Delta\text{TWiST} + u_{REL} \times \Delta\text{REL}$$

where $\Delta\text{Q}$ is the Q-TWiST difference between two arms, $\Delta\text{TOX}$, $\Delta\text{TWiST}$ and $\Delta\text{REL}$ are the differences in restricted mean time in each state, and the TWiST weight is 1. The arm with more toxic time gains from it whenever $u_{TOX}$ is above zero, since that time is still time alive, so a low toxicity weight is what turns extra toxic time against an arm. This is a two-weight form of threshold analysis.

Worked example with two arms and a change of toxicity definition (illustrative)

All figures are illustrative, in months, restricted to 48 months of follow-up. Arm A is a combination with more toxicity and longer survival, and arm B is the standard regimen. With toxicity defined as grade 3 or higher, arm A spends 5 months in TOX, 18 in TWiST and 8 in REL, and arm B spends 1, 17 and 10 months.

1. Q-TWiST with weights of 0.5 for TOX and REL.

$$\text{Q-TWiST}_A = 0.5 \times 5 + 18 + 0.5 \times 8 = 24.5$$

where 5, 18 and 8 are arm A's mean months in TOX, TWiST and REL and 0.5 is the weight on TOX and on REL.

$$\text{Q-TWiST}_B = 0.5 \times 1 + 17 + 0.5 \times 10 = 22.5$$

where 1, 17 and 10 are arm B's mean months in the three states. Arm A gains 2 months of quality-adjusted time.

2. Threshold line. The differences are 4 months of TOX, 1 month of TWiST and minus 2 months of REL.

$$\Delta\text{Q} = 4u_{TOX}+1-2u_{REL}$$

where $u_{TOX}$ and $u_{REL}$ are the weights for toxicity and relapse. The two arms are equal when $u_{REL} = 0.5 + 2u_{TOX}$. If toxicity is judged as bad as death, with $u_{TOX}$ at 0, arm A is preferred only when $u_{REL}$ is below 0.5. Once $u_{TOX}$ exceeds 0.25, arm A is preferred whatever relapse weight between 0 and 1 is chosen.

3. A wider toxicity definition. Suppose grade 2 events are also counted. Arm A now has 9 months of TOX and 14 of TWiST, and arm B has 3 months of TOX and 15 of TWiST, with REL unchanged.

$$\text{Q-TWiST}_A = 0.5 \times 9 + 14 + 0.5 \times 8 = 22.5$$

where 9, 14 and 8 are arm A's months in TOX, TWiST and REL under the wider definition.

$$\text{Q-TWiST}_B = 0.5 \times 3 + 15 + 0.5 \times 10 = 21.5$$

where 3, 15 and 10 are arm B's months under the same definition. The gain for arm A halves to 1 month. Survival is unchanged and only the boundary between TOX and TWiST has moved, which is why the toxicity definition belongs among the reported assumptions of any Q-TWiST result.

A published result that turns on toxicity time

Beaumont and colleagues compared pazopanib and sunitinib in COMPARZ, a trial in which pazopanib had been found non-inferior to sunitinib for progression-free survival. They reported slightly longer Q-TWiST with pazopanib, mainly because patients spent less time with grade 3 or 4 toxicities. Across the utility weights tested, the Q-TWiST difference lay between minus 11 and 43 days, favouring pazopanib for most combinations, and the difference was statistically significant in fewer than half of the weight combinations. The authors described the benefit as statistically significant but small.

Toxicity time in cost-utility analysis and NICE appraisal

A toxicity period and a QALY calculation share the logic of weighting time by quality, but they differ in where the weights come from. The NICE technology appraisal and highly specialised technologies manual (PMG36) asks for health effects to be expressed in QALYs, with changes in health-related quality of life reported directly by patients and their utility based on public preferences using a choice-based method, and EQ-5D is the preferred measure in adults. For new topics starting after its publication on 27 August 2026, the interim methods statement (PMG51) takes precedence over PMG36 and makes the UK EQ-5D-5L value set the source of adult reference-case utilities. A weight of 0.5 assigned by analysts is not a utility of either kind.

In TA440 the committee papers describe the company's Q-TWiST method, with grade 3 or higher toxicity and weights of 0.5 for toxicity, 0.5 for relapse and 1.0 for TWiST, and report that TWiST favoured pegylated liposomal irinotecan with 5-fluorouracil and leucovorin by 1.0 month. In a cost-utility analysis the same toxicity is commonly handled by applying an adverse event disutility for its duration within a model such as a partitioned survival model, which needs preference-based values for each event.

Boundaries with nearby states and measures

The Time with Symptoms entry defines a single phase with symptoms of progression or treatment toxicity, so the toxicity period is one part of that phase. In the Q-TWiST analyses of Goldhirsch, Cole and their colleagues, toxicity and relapse are separate states with separate weights.

TOX also differs from an adverse event rate. A rate counts how many patients have an event, while TOX measures how long they live with qualifying events, so a short severe event and a long moderate one can give the same rate and very different toxicity periods. Disutility is a per-unit loss of quality, and inside Q-TWiST one minus $u_{TOX}$ plays that role without being a measured preference.

Common misreadings of the toxicity period

Reading a large TOX difference as harm alone overlooks that toxicity time is time alive, as step 2 of the illustrative example shows. Comparing TOX across trials without checking the grade threshold, the counting window and the handling of toxicity after progression can mislead, because each changes the mean duration. The toxicity weight is also often taken for a measured utility, when in many analyses the weight is an assumed value tested in a threshold analysis.

Sources

• Beaumont JL, Salsman JM, Diaz J, Deen KC, McCann L, Powles T, Hackshaw MD, Motzer RJ, Cella D. Quality-adjusted time without symptoms or toxicity analysis of pazopanib versus sunitinib in patients with renal cell carcinoma. Cancer. 2016;122(7):1108-1115. https://doi.org/10.1002/cncr.29888
• Cole BF, Gelber RD, Goldhirsch A. A quality-adjusted survival meta-analysis of adjuvant chemotherapy for premenopausal breast cancer. Statistics in Medicine. 1995;14(16):1771-1784. https://doi.org/10.1002/sim.4780141606
• Gelber RD, Cole BF, Gelber S, Goldhirsch A. Comparing treatments using quality-adjusted survival: the Q-TWiST method. The American Statistician. 1995;49(2):161-169. https://doi.org/10.1080/00031305.1995.10476135
• Gelber RD, Gelman RS, Goldhirsch A. A quality-of-life-oriented endpoint for comparing therapies. Biometrics. 1989;45(3):781-795. https://pubmed.ncbi.nlm.nih.gov/2790121/
• Glasziou PP, Simes RJ, Gelber RD. Quality adjusted survival analysis. Statistics in Medicine. 1990;9(11):1259-1276. https://doi.org/10.1002/sim.4780091106
• Goldhirsch A, Gelber RD, Simes RJ, Glasziou P, Coates AS. Costs and benefits of adjuvant therapy in breast cancer: a quality-adjusted survival analysis. Journal of Clinical Oncology. 1989;7(1):36-44. https://doi.org/10.1200/JCO.1989.7.1.36
• Lee CH, Wan Y, Smith A, Xie R, Motzer RJ. Quality-adjusted time without symptoms or toxicity (Q-TWiST) for lenvatinib plus everolimus versus everolimus monotherapy in patients with advanced renal cell carcinoma. European Urology Open Science. 2021;31:1-9. https://pmc.ncbi.nlm.nih.gov/articles/PMC8385286
• National Institute for Health and Care Excellence. Pegylated liposomal irinotecan for treating pancreatic cancer after gemcitabine (TA440), committee papers, 2016. https://www.nice.org.uk/guidance/ta440/documents/committee-papers-2
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36), section 4.3. Published 2022, updated 2026. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• National Institute for Health and Care Excellence. Interim methods statement: implementing the EQ-5D-5L value set (PMG51). Published 27 August 2026. https://www.nice.org.uk/process/pmg51