Time Without Symptoms of Progression

Time Without Symptoms of Progression in Quality-Adjusted Survival

Time without symptoms of progression, abbreviated TWiST, is the part of a cancer patient's survival lived free of both the treatment side effects an analysis counts and the symptoms of relapse or progressing disease. In oncology health economics it is the time a treatment most hopes to lengthen, and in a Q-TWiST analysis it is the reference state against which the other states of survival are valued. A regimen can lengthen progression-free survival yet add much less TWiST when a large share of the extra time is spent with severe toxicity, so TWiST separates good-quality time from time merely gained. The original expansion is time without symptoms of disease and toxicity of treatment, and the wording with progression matches advanced cancer studies such as Lee and colleagues' renal cell carcinoma analysis, which expands Q-TWiST with symptoms of disease progression and ends the state at progression.

Origin as an endpoint in adjuvant breast cancer trials

TWiST was an endpoint in its own right before it became one state of Q-TWiST. Gelber and Goldhirsch, reporting Ludwig Breast Cancer Study III in 1986, defined it as the time without symptoms of disease and subjective toxic effects of treatment. The trial randomised 463 evaluable postmenopausal women with node-positive operable breast cancer to chemoendocrine therapy, endocrine therapy alone or no adjuvant treatment after mastectomy. Despite a larger initial discount for subjective toxicity with chemoendocrine therapy, by 5 years the net difference in average TWiST against the observation group was positive and approximately equal for both adjuvant programmes.

Gelber, Gelman and Goldhirsch set out the construction formally in 1989, describing TWiST as a single measure of length and quality of survival. For each patient, time with subjective side effects of treatment and time with unpleasant symptoms of disease are subtracted from overall survival time. In the same year Goldhirsch and colleagues made TWiST the reference state of Q-TWiST, weighting the toxicity period (TOX) and the relapse period (REL) relative to it.

Defining TWiST for an individual patient

A TWiST analysis needs two clinical definitions before any data are summarised. The first is the event that ends the state, which is disease progression in advanced cancer and relapse in adjuvant settings, where relapse-free survival or disease-free survival plays the role that progression-free survival plays in advanced disease. The second is the toxicity that counts, which makes TWiST a time-to-event quantity built from two event definitions. Lee and colleagues, analysing lenvatinib plus everolimus in advanced renal cell carcinoma, defined TWiST as time before disease progression and without grade 3 or 4 toxicity, counted any day with several adverse events once, and capped toxicity still ongoing at progression or at the end of follow-up.

$$\text{TWiST}_i = \min(P_i, L) - \text{TOX}_i$$

where $\text{TWiST}_i$ is patient $i$'s time without symptoms of progression, $P_i$ is the time to progression or death measured from randomisation, $L$ is the analysis horizon, and $\text{TOX}_i$ is the time before progression and before $L$ that patient $i$ spends with a qualifying toxicity.

Under this subtraction rule, TWiST is a total of qualifying days, not necessarily one unbroken spell. A patient whose grade 3 toxicity resolves and later returns during treatment accumulates TWiST between the two episodes. The definition also implies that TWiST can never exceed progression-free time, and the two are equal only for a patient with no counted toxicity before progression.

Why observed TWiST cannot simply be averaged

Follow-up often ends before patients progress or die, so individual TWiST is often censored. Gelber, Gelman and Goldhirsch showed by simulation that estimating the distribution of TWiST with actuarial methods is biased, because of induced dependency between TWiST and its censoring distribution. On the TWiST scale a patient's censoring point is the follow-up time minus the toxic time, so patients with more toxicity are censored earlier in TWiST terms, which breaks the independence that standard censoring methods assume and creates dependent censoring. The same paper restricted attention to TWiST accumulated within a specified time $L$ from the start of therapy, which, with estimated TWiST substituted for censored values, reduced the bias and gave a way to judge the payback period for early toxic effects.

Glasziou, Simes and Gelber then proposed partitioning the survival curve instead of analysing each patient's quality-adjusted time. The areas between the partitioned curves represent the mean time in each state and, multiplied by weights, give an unbiased estimate of restricted quality-adjusted survival. The NICE Decision Support Unit's Technical Support Document 19 traces partitioned survival analysis to this work, which avoided the informative censoring that standard methods induced in quality-adjusted survival.

Estimating mean TWiST from partitioned survival curves

In the partitioned approach, mean TWiST in each arm is the difference between two areas under Kaplan-Meier curves, each restricted to the horizon $L$. Lee and colleagues built separate curves for TOX, progression-free survival and overall survival, took the area under each through 24 months, and obtained mean TWiST as the area under the progression-free survival curve minus the area under the TOX curve.

$$\overline{\text{TWiST}}(L) = \int_0^L S_{\text{PFS}}(t)\,dt - \int_0^L S_{\text{TOX}}(t)\,dt$$

where $\overline{\text{TWiST}}(L)$ is the restricted mean TWiST up to horizon $L$, $S_{\text{PFS}}(t)$ is the progression-free survival function at time $t$, and $S_{\text{TOX}}(t)$ is the curve whose area gives the restricted mean time with qualifying toxicity before progression.

Each integral is a restricted mean survival time, so mean TWiST inherits the horizon of the analysis and is not a lifetime quantity. In the lenvatinib study the restricted mean progression-free survival was 12.8 months with the combination and 7.0 months with everolimus alone, a difference of 5.8 months. Mean TOX was 1.9 and 0.7 months, and mean TWiST 10.9 and 6.4 months, a TWiST difference of 4.5 months (95% confidence interval 1.4 to 7.8). The figures are rounded, so 7.0 minus 0.7 gives 6.3, not 6.4. About 1.2 of the 5.8 months of extra progression-free time was spent with grade 3 or 4 toxicity, which matches the gap between the PFS gain and the TWiST gain, 1.3 months on the rounded figures.

A second example comes from a North Central Cancer Treatment Group trial of 204 patients with poor-prognosis resectable rectal cancer. Gelber and colleagues found that over 5 years, adding fluorouracil-based chemotherapy to postoperative radiation therapy gave 3.1 months more time with toxicity, 3.6 months less survival after relapse and 6.1 months more TWiST (95% confidence interval 0.2 to 12.0).

Worked example of the payback period for early toxicity

All figures here are illustrative, in months. An adjuvant regimen, arm A, causes counted toxicity early in treatment, with a restricted mean of 4.5 months of TOX, all within the first year. The comparator, arm B, is observation with no counted toxicity. The table gives the restricted mean relapse-free time in each arm up to three horizons.

1. TWiST in each arm. Arm A's TWiST is its relapse-free time minus its TOX, while arm B's TWiST equals its relapse-free time because it has no counted toxicity.

$$\text{TWiST}_A(60) = 47.0 - 4.5 = 42.5$$

where $\text{TWiST}_A(60)$ is arm A's restricted mean TWiST at 60 months, 47.0 its relapse-free time and 4.5 its TOX. The same subtraction gives 7.0 months at 12 months and 26.5 months at 36 months.

2. The difference over time.

$$\Delta(60) = 42.5 - 41.0 = 1.5$$

where $\Delta(L)$ is the TWiST difference, A minus B, at horizon $L$. The differences are minus 4.0 months at 12 months and minus 1.5 months at 36 months, so early toxicity costs arm A TWiST and its slower rate of relapse earns the time back.

3. Payback horizon. Assuming linear change between 36 and 60 months, the difference rises by 3.0 months over that 24-month span.

$$L^{*} = 36 + 24 \times 0.5 = 48$$

where $L^{*}$ is the payback horizon in months and 0.5 is the 1.5-month shortfall divided by the 3.0-month rise. Before about 48 months the regimen gives less TWiST than observation and after that it gives more, the payback period that Gelber, Gelman and Goldhirsch proposed judging with TWiST restricted to a horizon.

4. Adding weights. Suppose restricted mean overall survival at 60 months is 52.0 months in arm A and 49.0 in arm B, leaving REL of 5.0 and 8.0 months once relapse-free time is taken away. TOX and REL are weighted 0.5 and TWiST 1.

$$\text{Q}_A = 0.5 \times 4.5 + 42.5 + 0.5 \times 5.0 = 47.25$$

where $\text{Q}_A$ is arm A's restricted mean Q-TWiST at 60 months.

$$\text{Q}_B = 41.0 + 0.5 \times 8.0 = 45.0$$

where $\text{Q}_B$ is the same quantity in arm B, which has no TOX. The Q-TWiST gain of 2.25 months exceeds the TWiST gain of 1.5 months because arm A's extra 4.5 months of toxic time, weighted 0.5, adds 2.25 months, more than the 1.5 months arm B gains from its extra 3.0 months after relapse.

A TWiST result therefore needs its horizon stated, since the regimen looks harmful at 12 months and beneficial at 60 months.

TWiST in economic evaluation and partitioned survival models

In the majority of the NICE appraisals reviewed in TSD 19, the modelled survival endpoints were progression-free survival and overall survival, used to split patients into progression-free, progressed and dead states. TWiST is a finer split of the progression-free state of such a partitioned survival model, separating progression-free time with counted toxicity from progression-free time without it. TSD 19 describes Q-TWiST as a variation of partitioned survival analysis that sorts patients by whether they are free of symptoms and toxicity, used in many oncology settings as a trial-based summary of treatment benefit.

The TWiST weight is usually set at 1 as a reference value, not as a measured utility. Lee and colleagues describe health-state utilities on a scale on which 1 represents perfect health, and in one sensitivity scenario they replaced the TWiST weight of 1 with 0.78, a value taken from EQ-5D index data in another renal cell carcinoma trial. A cost-utility analysis would normally attach a preference-based health state utility value to progression-free time instead, so TWiST months weighted at 1 should not be read as QALYs without that change of scale.

Revicki and colleagues proposed that a Q-TWiST difference of 10% of overall survival in a study is clinically important and 15% clearly clinically important. Those benchmarks refer to Q-TWiST relative to overall survival, so they do not transfer directly to a difference in TWiST alone.

TWiST beside nearby survival measures

Progression-free survival includes time with toxicity, so the gap between a PFS gain and a TWiST gain measures how much of the extra progression-free time was lived with counted side effects. Overall survival adds the time after progression, which TWiST excludes. The Time with Symptoms entry describes the complementary phase in which a patient has symptoms of progression or toxicity, and Q-TWiST analyses usually split that phase into the separate TOX and REL states with separate weights.

Common misreadings of TWiST

A TWiST gain is not a survival gain, since the two can move by different amounts, as in the rectal cancer trial, where the combined therapy added 6.1 months of TWiST alongside 3.6 months less time after relapse. Averaging each patient's observed TWiST ignores the induced censoring problem and biases the estimate. Comparing TWiST across trials is unsafe when the toxicity grades, the counting of overlapping events or the horizon differ, since each changes the boundary between TOX and TWiST. Carrying TWiST months weighted at 1 into a cost per QALY calculation treats them as perfect health and overstates quality-adjusted time.

Sources

• Gelber RD, Goldhirsch A. A new endpoint for the assessment of adjuvant therapy in postmenopausal women with operable breast cancer. Journal of Clinical Oncology. 1986;4(12):1772-1779. https://doi.org/10.1200/JCO.1986.4.12.1772
• Gelber RD, Gelman RS, Goldhirsch A. A quality-of-life-oriented endpoint for comparing therapies. Biometrics. 1989;45(3):781-795. https://doi.org/10.2307/2531683
• Gelber RD, Goldhirsch A, Cole BF, Wieand HS, Schroeder G, Krook JE. A quality-adjusted time without symptoms or toxicity (Q-TWiST) analysis of adjuvant radiation therapy and chemotherapy for resectable rectal cancer. Journal of the National Cancer Institute. 1996;88(15):1039-1045. https://doi.org/10.1093/jnci/88.15.1039
• 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
• Revicki DA, Feeny D, Hunt TL, Cole BF. Analyzing oncology clinical trial data using the Q-TWiST method: clinical importance and sources for health state preference data. Quality of Life Research. 2006;15(3):411-423. https://doi.org/10.1007/s11136-005-1579-7
• Woods B, Sideris E, Palmer S, Latimer N, Soares M. NICE DSU Technical Support Document 19: Partitioned survival analysis for decision modelling in health care: a critical review. Decision Support Unit; 2 June 2017. https://sheffield.ac.uk/nice-dsu/tsds/partitioned-survival-analysis