Progression-Free Survival

What progression-free survival measures

Participants without an observed event are censored according to the trial's prespecified rules.

The abbreviation is PFS. The exact time origin, progression criteria, death handling, assessment method, and censoring rules are part of the endpoint definition and must be reported rather than inferred from the label alone.

The composite event behind PFS

PFS combines progression and death into one time-to-event endpoint. This avoids treating death before documented progression as though the patient remained progression-free, but it also means the endpoint mixes two clinically different event types.

For patient $i$, let $T_{Pi}$ denote time to progression and $T_{Di}$ denote time to death. The latent PFS event time is

$$T_i^{PFS}=\min(T_{Pi},T_{Di}).$$

With censoring time $C_i$, the observed time and event indicator are

$$X_i=\min(T_i^{PFS},C_i)$$

and

$$\delta_i=\mathbf{1}\!\left(T_i^{PFS}\le C_i\right).$$

The protocol and statistical analysis plan determine how events after missed assessments, new anticancer therapy, withdrawal, or loss to follow-up are handled. Different rules can produce different PFS results from the same underlying patient history.

How progression is defined and assessed

Progression is not a generic clinical impression; it must follow a prespecified rule appropriate to the disease and trial. In solid tumours this commonly uses radiographic response criteria, while haematological malignancies and other conditions may require different clinical, laboratory, or composite definitions.

The assessment process should specify:

• The progression criteria should define the lesions, measurements, clinical findings, or biomarkers that constitute an event.
• The assessment schedule should state the planned timing and any visit windows.
• The assessor should be identified as the treating investigator, a blinded independent central review, or another defined process.
• The confirmation rule should state whether progression requires a subsequent assessment.
• The death window should state whether deaths after prolonged missing assessment are counted as PFS events.
• The analysis should prespecify handling of new therapy, missed visits, withdrawal, and incomplete imaging.

Blinded review may reduce assessment bias when knowledge of treatment could influence progression timing. It does not remove bias created by differential visit schedules, missing scans, or informative dropout.

Why assessment timing matters

Progression is often detected at a scheduled visit rather than at the biological moment it begins. The true event time is then known only to lie between the last non-progressive assessment and the first progressive assessment, creating interval censoring.

If the last negative scan occurs at $L_i$ and the first progressive scan at $R_i$, then

$$L_i<T_{Pi}\le R_i.$$

Conventional analyses often use the detection date $R_i$ as the event time. Unequal assessment frequency between groups can therefore create apparent PFS differences even when biological progression is similar, so schedules and adherence should be compared by treatment arm.

Estimating the PFS curve

The Kaplan–Meier estimator is commonly used to estimate the probability of remaining alive and progression-free beyond time $t$. It updates the survival probability at each observed event time and accounts for right-censored observations under the assumption that censoring is non-informative conditional on the analysis design.

$$\widehat S_{PFS}(t)=\prod_{t_j\le t}\left(1-\frac{d_j}{n_j}\right),$$

where $d_j$ is the number of PFS events at time $t_j$ and $n_j$ is the number at risk immediately before that time. A PFS rate at a landmark such as 12 months is $\widehat S_{PFS}(12)$, not the proportion of all randomised patients whose last recorded status happens to be progression-free at that date.

Median PFS and restricted mean PFS

Median PFS is the earliest time at which the estimated PFS curve reaches or falls below $0.5$. It is easy to communicate but uses only one point on the curve and may be unreached or unstable when follow-up is immature.

$$\widehat m_{PFS}=\inf\left\{t:\widehat S_{PFS}(t)\le0.5\right\}.$$

Restricted mean PFS up to horizon $\tau$ summarises the area under the full PFS curve:

$$RM_{PFS}(\tau)=\int_0^{\tau}S_{PFS}(t)\,dt.$$

Its unit is time, such as progression-free months or years, and its interpretation depends on the prespecified horizon. Unlike a hazard ratio, the restricted mean difference is an absolute measure on the time scale.

Hazard ratios and proportional hazards

A Cox model often compares treatment groups using a hazard ratio for progression or death. The hazard ratio is a relative comparison of instantaneous event rates among participants still at risk, not a ratio of median PFS values or a direct statement about the probability of remaining progression-free.

$$HR=\frac{h_1(t)}{h_0(t)}$$

under the proportional-hazards assumption that this ratio is constant over time. When hazards are non-proportional, a single hazard ratio can obscure delayed effects, waning effects, or crossing curves; time-specific PFS, restricted mean PFS, or flexible survival models may then be more informative.

PFS is not the same as overall survival

Overall survival counts death from any cause and does not depend on tumour-assessment rules. PFS may be observed earlier and can be less affected by subsequent therapies, but it is more vulnerable to assessment timing, progression definitions, missing scans, and reviewer disagreement.

Names are not sufficient to establish comparability across studies. Analysts should compare the full endpoint definitions and estimands before pooling or indirectly comparing results.

PFS and clinical benefit

Delaying progression can matter to patients when it delays symptoms, functional decline, burdensome treatment changes, or resource use. A PFS improvement does not automatically establish improved quality of life or overall survival, because progression definitions may be radiographic and post-progression outcomes may offset earlier gains.

The clinical meaning should be assessed using the size and duration of the PFS effect, toxicity, patient-reported outcomes, subsequent treatment, overall-survival evidence, and the disease context. PFS should not be labelled a validated surrogate for overall survival without endpoint-, disease-, treatment-, and context-specific evidence.

Sources of bias

PFS can be biased when event detection or censoring differs between treatment groups. The direction and size of bias depend on the assessment schedule, missingness mechanism, treatment discontinuation, subsequent therapy, and analysis rules.

• Differential assessment frequency can detect progression earlier in the more frequently assessed group.
• Informative censoring can occur when withdrawal or missed assessments are related to prognosis.
• Open-label assessment can introduce bias when treatment knowledge affects interpretation or visit timing.
• Backdating or using inconsistent progression dates can alter risk sets and event ordering.
• Censoring at new therapy can favour a group if treatment changes are related to impending progression.
• Imbalanced deaths after missed assessments can make death-window rules influential.
• Immature follow-up can make medians and tail behaviour unstable.

Sensitivity analyses should test alternative defensible censoring and event-date rules. They should be specified before unblinded results are examined whenever possible.

A worked partitioned-survival example

Health-economic oncology models often use PFS together with overall survival to allocate a cohort among progression-free, progressed-disease, and dead states. This is an accounting construction based on the two survival curves and requires the modelled overall-survival probability to remain at least as large as the PFS probability.

At time $t$, state membership is calculated as

$$p_{PF}(t)=S_{PFS}(t),$$ $$p_{PD}(t)=S_{OS}(t)-S_{PFS}(t),$$

and

$$p_D(t)=1-S_{OS}(t).$$

Suppose that at month 24 the model estimates $S_{PFS}(24)=0.55$ and $S_{OS}(24)=0.75$. The cohort is therefore $55\%$ progression-free, $20\%$ alive with progressed disease, and $25\%$ dead.

If progression-free utility is $u_{PF}=0.80$, progressed-disease utility is $u_{PD}=0.60$, and the cycle length is $0.25$ years, the undiscounted quality-adjusted life-years accrued during that cycle under a cycle-start approximation are

$$QALY_{24}=0.25\left[(0.55\times0.80)+(0.20\times0.60)\right]=0.14.$$

This value is illustrative and depends on the occupancy convention, cycle correction, utility evidence, and timing of transitions. Using only the PFS curve would omit health accrued after progression.

Extrapolating PFS beyond trial follow-up

Economic models often require a longer horizon than the trial provides. Extrapolation therefore combines observed PFS data with assumptions about the survival function after follow-up becomes sparse.

Candidate distributions may include exponential, Weibull, Gompertz, log-logistic, lognormal, generalized gamma, splines, or other justified models. Selection should consider clinical plausibility, visual and statistical fit, proportional-hazards assumptions, external evidence, treatment-effect waning, and consistency with overall survival.

The extrapolated curves must satisfy coherent state relationships. In a partitioned-survival model, $S_{PFS}(t)>S_{OS}(t)$ is impossible and signals incompatible fits, numerical problems, or a need for a constrained modelling approach.

Treatment switching and subsequent therapy

PFS is measured before or at progression, so it is generally less affected than overall survival by treatments received after progression. It can still be affected by treatment discontinuation, new therapy before documented progression, and censoring rules tied to those events.

Economic models must not assume that a PFS effect automatically determines the post-progression survival effect. Post-progression hazards, treatment sequences, subsequent costs, and utilities need separate evidence or explicit assumptions.

A reproducible analysis workflow

PFS analysis should begin with a precise estimand and an auditable patient-level event derivation. The workflow should make every censoring and event decision traceable to dated assessments and prespecified rules.

1. Define the population, treatment condition, variable, intercurrent-event strategy, and population-level summary.
2. Specify the time origin and the exact progression and death events.
3. Define the assessment schedule, visit windows, review process, and confirmation rules.
4. Prespecify handling of missed assessments, withdrawal, new therapy, and deaths after missing visits.
5. Derive each participant's event or censoring date with a reproducible algorithm.
6. Reconcile deaths, progression dates, assessment dates, and treatment records.
7. Estimate and plot PFS with numbers at risk, confidence intervals, events, and censoring marks.
8. Test proportional hazards and report complementary absolute measures where needed.
9. Perform sensitivity analyses using alternative defensible event and censoring rules.
10. Validate economic-model curves against trial estimates and maintain $S_{PFS}(t)\le S_{OS}(t)$.
11. Document data cut-off, follow-up maturity, software, model version, and unresolved limitations.

Independent programming or a trace review should reproduce a sample of patient-level derivations. Small changes to event rules can materially alter the tail of the curve and subsequent economic extrapolation.

Validation checks

Validation should cover the clinical endpoint and its economic-model use. Reproducing a published median is not enough if event counts, censoring, curve shape, or state occupancy are inconsistent.

• Every randomised participant should have a traceable time origin and event or censoring rule.
• Event counts should reconcile with the analysis dataset and Kaplan–Meier output.
• Numbers at risk should decline consistently with events and censoring.
• PFS probabilities should remain between zero and one and should not increase over time.
• Treatment groups should use comparable assessment schedules and progression rules.
• Alternative censoring rules should be examined when missing assessments or new therapy are material.
• Extrapolated PFS should be clinically plausible and should not exceed overall survival.
• Partitioned-survival state proportions should sum to one at every time point.
• QALY and cost calculations should use consistent cycle lengths, time units, and discounting.

Discrepancies should be resolved or carried into scenario and sensitivity analysis. Validation should state which curve version, data cut-off, and endpoint definition were tested.

How PFS should be reported

Transparent reporting includes the full endpoint definition, time origin, data cut-off, assessment criteria and frequency, review method, death handling, censoring rules, event count, follow-up, numbers at risk, and analysis method. Results should include uncertainty and should not rely only on a median or hazard ratio.

For economic models, report the source and data cut-off for each PFS curve, extrapolation method, fit and plausibility checks, relationship with overall survival, treatment-effect assumptions, state-occupancy calculation, and sensitivity analyses. Interpretation should distinguish delayed progression from demonstrated gains in survival or quality of life.