Model tumor response as it changes over time, not just a snapshot.
The common analysis of tumor response data based on static percentages of Complete Response (CR) or Partial Response (PR) is inadequate and incomplete. Use Markov chains to analyze tumor response data and obtain a dynamic view of how tumor response states change over time and a complete understanding of patient outcomes.
Tumor Response Markov Chain helps researchers explore transitions among clinically relevant tumor-response states using a Markov-chain framework.
Define response states and transition assumptions to examine projected response patterns over successive assessment periods and support oncology study planning.
Tumor Response Markov Chain
Estimate how response states change over time from patient-level longitudinal assessments. Fit one or more treatment groups. First 5 successful calculations free, without registration.
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Registration alone does not unlock further calculations. The server checks your active Tumor Response trial or subscription.
1. Load assessments
Files are read in your browser. Patient identifiers and individual rows are not uploaded. Fitting sends aggregated state-pair counts by assessment interval and group index (group names stay in your browser) to this website; temporary calculation data expire after 20 minutes of inactivity. Save the fitted results before leaving. Uploaded patient data are not stored in browser storage.
Numeric times use the selected unit and treatment as time zero. Calendar dates use actual elapsed days (month = 365.25/12 days; year = 365.25 days). Treatment groups may have any names, with one fixed group per patient and globally unique patient IDs. Select no treatment groups for an unstratified dataset. Each patient’s likelihood is conditional on their first observed state; no unobserved baseline is imputed. Plot time zero is the selected initial state, not a calendar date.
2. Validate and fit
States: Complete Response (CR), Partial Response (PR), Stable Disease (SD), Progressive Disease (PD), Death. All transitions among living states are allowed, including improvement after progression. Death is absorbing. One completed analysis, including all treatment groups, counts as one calculation. If any group fails to converge, no free calculation is used.
3. Explore the fitted model
Changing treatment group, comparison state, initial state or horizon uses the existing fit and does not consume a calculation. Curves describe a fitted population process, not an individual patient’s clinical prognosis.
Treatment group comparison
All groups use the same selected initial state and horizon. Differences are descriptive model predictions; no treatment-effect test, confidence interval, or adjustment for baseline differences is computed.
State probabilities
Generator Q — transition rates per analysis unit
Transition probabilities P(t) = exp(Qt)
Holding time and cumulative time in each state
Holding time is the mean length of one visit to a state, 1/(-qᵢᵢ). Cumulative time is ∫₀ᵀ P(initial → state, t) dt and can include repeated visits; values sum to the chosen horizon. Death has infinite holding time. Confidence intervals are not computed; displayed precision is for readability, not evidence of accuracy.
Model assumptions, data validation and limitations
The likelihood is the product of exp(Q × interval)[previous state, next state] across observed intervals. State changes between visits are unobserved, and multiple transitions may occur. The model is time-homogeneous and Markov: transition rates depend on the current state, not elapsed time or history. It assumes independent patients, correctly classified states, and noninformative assessment and censoring times.
All observations, including Death, are treated as panel snapshots. Do not use this mode for exact death-time likelihoods. Follow-up ends at each patient’s last observation; no extra survival time is invented. When a treatment column is selected, a separate unrestricted 16-rate model is fitted for each group. Treatment switching is rejected. Other covariates are not modeled. Group comparisons are descriptive and do not establish a causal treatment effect. Missing rows and invalid values are rejected. Identical patient-time duplicates are collapsed; conflicting duplicates and living observations after Death are rejected.
The unrestricted model estimates 16 rates per treatment group. Every group must have at least 20 informative intervals and five outgoing assessment intervals from each living state; validation does not guarantee reliable estimation. Sparse data, infrequent assessments and weakly identified rates can make estimates unreliable even if optimization converges. The tool reports convergence, two-start agreement and likelihood-curvature diagnostics. Nonconverged fits do not consume a free calculation. This version supports 10,000 rows and up to 20 treatment groups and at most 250 distinct assessment intervals per group; do not round times to meet the limit.
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Methods: Jackson, Multi-State Models for Panel Data (2011); panel-observation likelihood; mean sojourn times. Independent statistical review is required before clinical or regulatory use.
Response states, tracked over time — not summarized away.
A Markov chain models the probability that a patient moves between response states from one assessment to the next, so a study team can see the trajectory behind the topline rate.
State definitions
Response states — Complete Response, Partial Response, Stable Disease, Progressive Disease — defined to match your protocol’s endpoints.
Transition probabilities
Assessment-to-assessment transition rates estimated directly from your study’s response data.
Time-dependent outcomes
A dynamic read on how the patient population moves between states across the full follow-up period.
Regulatory-ready output
Analysis and supporting narrative prepared to the standard a submission demands.
Have tumor response data you want a dynamic read on?
Send us your study design and current endpoints, and we’ll walk you through what a Markov chain analysis would look like for your data.
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