Fine Gray Model: Formula, Verified Results, Python, R, SPSS and Excel
Fine Gray Model is presented as a complete, dataset-grounded survival analysis guide. It explains model the subdistribution hazard while retaining competing-event records in the modified risk set, the exact formula, assumptions, verified calculations, interpretation, software workflows, matched charts, reports, workbook, internal links, and publication checks. The verified example uses an explicitly prepared teaching endpoint from the uploaded 649-row dataset.
Subdistribution hazard differs by school
For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event.
What does Fine Gray Model measure?
covariate effects on the cumulative incidence of one event type in the presence of competing events
Fine Gray Model focuses on covariate effects on the cumulative incidence of one event type in the presence of competing events. The estimand must remain separate from related quantities such as ordinary probability, crude event proportion, mean duration, or an unrelated regression coefficient.
Method target
Fine Gray Model is selected to model the subdistribution hazard while retaining competing-event records in the modified risk set. The method is applied to ordered follow-up times and event indicators, not to a standalone numeric outcome with censoring ignored. The analysis therefore starts from risk sets and event times.
The worked example defines time as absences plus one and the primary event as G3 below 10. For Fine Gray Model, these variables are used only to demonstrate covariate effects on the cumulative incidence of one event type in the presence of competing events; they are not presented as naturally observed medical survival times.
What it does not establish
The procedure cannot create causality or a real-world failure process from cross-sectional student records. Its defensible output is the method-specific estimate or test under the stated coding, and a Fine–Gray subdistribution hazard ratio describes cumulative-incidence ordering; it is not interchangeable with a cause-specific Cox hazard ratio.
A Fine–Gray subdistribution hazard ratio describes cumulative-incidence ordering; it is not interchangeable with a cause-specific Cox hazard ratio.
When should Fine Gray Model be used?
Decision logic before software
Time outcome?
Confirm a meaningful duration from a common origin.
Event defined?
State event=1 and censor=0 unambiguously.
Method target?
Match Fine Gray Model to the estimand.
Assumptions?
Audit censoring, risk sets, ties, and model form.
Reportable?
Retain numerical evidence and limitations.
Appropriate use
Choose this method when the research question is genuinely about covariate effects on the cumulative incidence of one event type in the presence of competing events and the required assumptions can be defended. It is preferable to a simple mean or binary comparison because it retains event timing and censoring information relevant to models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
Fine Gray Model is especially useful when its specific estimand is more informative than an ordinary mean comparison or binary event analysis that discards follow-up time.
Inappropriate use
Do not force the data into Fine Gray Model by merely renaming columns. It is unsuitable when causes are not mutually exclusive, event types are incomplete, or a competing event is incorrectly treated as ordinary censoring. A valid application must reproduce the method’s own inputs and assumptions. The verified school_MS subdistribution coefficient is 1.7304, giving SHR 5.6431.
Do not publish Fine Gray Model output when the matching charts, PDFs, workbook, and dataset describe different definitions or model specifications.
Fine Gray Model dataset and variable construction
The exact 649-row teaching structure
The bundled 649-row dataset is used specifically for subdistribution-hazard regression that retains competing-event records in a weighted risk set. The primary cause, competing cause, and censored state are kept separate, and school is the modeled contrast for the stored subdistribution hazard ratio. The prepared endpoint remains a transparent teaching construction rather than natural clinical, mortality, or equipment-failure follow-up.
| Variable | Role | Coding | Audit note |
|---|---|---|---|
| surv_time | Duration | absences + 1 | Positive values from 1 to 33 |
| surv_event | Primary event | 1 when G3 < 10; 0 otherwise | 100 events and 549 censorings |
| school | Group | GP reference; MS comparison | 423 GP and 226 MS records |
| competing cause | Secondary event | failures > 0 among records without the primary event | 51 competing events |
| predictors | Cox covariates | age, parental education, travel/study time, failures, family relationship, free time, school, gender | Ten-term model |
Fine Gray Model assumptions
Conditions required for a defensible result
Mutually Exclusive Event Types
Fine Gray Model requires mutually exclusive event types. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Complete Event-Type Coding
Fine Gray Model requires complete event-type coding. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Independent Censoring
Fine Gray Model requires independent censoring. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
A Defensible Time Origin
Fine Gray Model requires a defensible time origin. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Appropriate Interpretation Of Cause-Specific Versus Subdistribution Effects
The assumption review for Fine Gray Model converts each condition into a check against the prepared records rather than declaring the method assumption-free. The 95% interval for the subdistribution hazard ratio is 3.6767 to 8.6611, with p about 2.44×10^-15. A warning remains visible whenever the event process, censoring, support, weighting, or model form cannot be justified.
Adequate Events For Each Cause
Fine Gray Model requires adequate events for each cause. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Fine Gray Model formula and mechanics
Native browser MathML and a plain-language audit trail
Fine Gray Model uses this expression to estimate or test covariate effects on the cumulative incidence of one event type in the presence of competing events. Every symbol should be linked to a risk set, event count, survival estimate, covariate, distribution parameter, or weight defined in the surrounding text.
Calculation sequence
- Sort positive durations and verify event/censor coding.
- Construct the exact risk set immediately before each event time.
- Calculate the Fine Gray Model contribution defined by the formula.
- Accumulate products, sums, likelihood terms, or weighted contrasts as required.
- Attach uncertainty, diagnostics, and a conclusion that matches the estimand.
Formula interpretation
For Formula interpretation, the Fine Gray Model review must connect every symbol to a risk set, event count, likelihood term, or model parameter. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 1 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
The displayed expression uses browser-native MathML and ordinary semantic HTML. Its symbols correspond to the risk sets, event counts, weights, coefficients, or distribution parameters defined in this section; no remote rendering script or equation image is required.
Fine Gray Model verified results
Values calculated from the included dataset
| Result item | Verified value |
|---|---|
| Subdistribution beta | 1.730 |
| SE | 0.219 |
| SHR | 5.643 |
| 95% CI | 3.677 to 8.661 |
| p-value | < .001 |
| Primary events | 100 |
How to interpret Fine Gray Model
From statistical output to a restrained conclusion
Primary conclusion
Subdistribution hazard differs by school
For Primary conclusion, the Fine Gray Model review must translate the numerical result without overstating causality, equivalence, or natural follow-up. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 2 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
Interpretation order
Fine Gray Model in Python
Transparent data preparation and reproducible calculations
This Python section reconstructs covariate effects on the cumulative incidence of one event type in the presence of competing events from explicit arrays and auditable intermediate tables. Models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, so the code below exposes the quantities that determine the final result.
import pandas as pddf = pd.read_csv("dataset.csv")
df["time"] = pd.to_numeric(df["absences"]) + 1
df["status"] = 0
df.loc[pd.to_numeric(df["G3"]) < 10, "status"] = 1
df.loc[(df["status"] == 0) & (pd.to_numeric(df["failures"]) > 0), "status"] = 2
df["school_MS"] = df["school"].eq("MS").astype(int)
print(df["status"].value_counts().sort_index())
# Python core libraries do not expose one universal Fine–Gray regression API.
# Use a validated Fine–Gray implementation and pass: time, status, event_of_interest=1,
# censor_code=0, and school_MS. Record the library version, censoring-weight method,
# coefficient, standard error, exp(coefficient), confidence interval, and convergence status.
# The R cmprsk::crr result below is the independent reference used for this post.
Python verification checklist
In the Fine Gray Model Python section, the source CSV is read directly and the method-specific equation is reproduced before interpretation. The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. Package output is accepted only after its coding and defaults agree with the manual trail.
Only topic-matching URLs from the uploaded register are embedded. When a Python, R, SPSS, or Excel file is absent, the article states that limitation rather than fabricating a filename or borrowing another post’s asset.
Fine Gray Model in R
Independent survival-analysis validation
R provides an independent implementation of the same covariate effects on the cumulative incidence of one event type in the presence of competing events. The script states status coding, factor references, and the function or manual calculation needed for this method instead of relying on defaults.
library(cmprsk)
df <- read.csv("dataset.csv")
df$time <- as.numeric(df$absences)+1
df$status <- 0
df$status[as.numeric(df$G3)<10] <- 1
df$status[df$status==0 & as.numeric(df$failures)>0] <- 2
X <- model.matrix(~ relevel(factor(school), ref="GP"), data=df)[,-1,drop=FALSE]
fit <- crr(ftime=df$time, fstatus=df$status, cov1=X, failcode=1, cencode=0)
print(summary(fit))R validation checklist
R provides an independent route for Fine Gray Model with explicit formulas and saved output rather than a second decorative code block. The SHR concerns the cumulative incidence of cause 1 and is not interchangeable with a cause-specific Cox hazard ratio. The audit records package versions and uses the plan to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models.
Fine Gray Model in SPSS
Syntax-first setup and output audit
The SPSS workflow separates native procedures from extensions and preserves the event value in saved syntax. It is reviewed against the same dataset counts and interpretation used by the other software sections.
COMPUTE surv_time=absences+1.
COMPUTE cause=0.
IF (G3<10) cause=1.
IF (cause=0 AND failures>0) cause=2.
FREQUENCIES VARIABLES=cause BY school.
* Native COXREG is cause-specific, not Fine–Gray; use a validated extension or R integration for subdistribution regression.Fine Gray Model in Excel
A visible calculation and reconciliation workbook
The Excel workbook exposes the arithmetic behind h̃_k(t|x) = h̃_k0(t) exp(βᵀx) and reconciles selected rows with the programmatic output. It is an auditable calculation, not a black-box result.
Excel step 1
Code 0=censored, 1=primary event, 2=competing event.
Excel step 2
At each event time compute all-cause survival just before the time.
Excel step 3
Add S(t-)×d1/n to CIF1 and S(t-)×d2/n to CIF2.
Excel step 4
Do not use 1-KM as the primary-event CIF when competing events exist.
Excel step 5
Label every cause and group reference explicitly.
Excel controls
For Excel controls, the Fine Gray Model review must make the spreadsheet an auditable calculation rather than a decorative download. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 3 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
Fine Gray Model charts and chart-specific interpretation
First chart full-width; remaining charts arranged in pairs
For Fine Gray Model charts and chart-specific interpretation, the Fine Gray Model review must tie each chart caption to the displayed quantity and its numerical source. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 4 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
Python chart 1 — Fine Gray Model
Python chart 1: summarizes the principal Fine Gray Model output and the numerical components behind the reported conclusion. For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event.
Python chart 2 — Fine Gray Model
Python chart 2: places uncertainty, residuals, weighted contributions, or fitted discrepancies on a distributional scale. It supports the model or test audit but does not replace the natural-scale result or its confidence interval.
Python chart 3 — Fine Gray Model
Python chart 3: collects the key verified metrics used in the article, including sample information and the method-specific estimate. Every displayed value must reconcile with dataset.csv and the downloadable Python output.
R chart 1 — Fine Gray Model
R chart 1 independently reproduces the prepared duration, event, and censoring structure for Fine Gray Model. Read it with the declared event definition before comparing groups or fitted quantities.
R chart 2 — Fine Gray Model
R chart 2 presents the benchmark output using R conventions. Its values should agree with the Python calculation after reference levels, tie handling, weighting, and status coding are aligned.
R chart 3 — Fine Gray Model
R chart 3 focuses on the diagnostic evidence for Fine Gray Model. Visible departures or sparse-tail behavior should trigger a sensitivity analysis rather than a cosmetic interpretation.
R chart 4 — Fine Gray Model
R chart 4 displays uncertainty or residual structure on the scale used by the R workflow. It supports the numerical audit but does not replace the natural-scale estimate and its limitation.
R chart 5 — Fine Gray Model
R chart 5 consolidates the principal metrics used in the R output. Every annotation must reconcile with dataset.csv, the printed result, and the matched downloadable file.
Fine Gray Model diagnostics and sensitivity analysis
Evidence required beyond the primary number
Data diagnostics
Before interpreting the primary result, verify the 649-row count, 100 events, 549 censorings, 1–33 duration range, GP/MS composition, tied times, and missing values. The method-specific review then asks analysts to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models.
Method diagnostics
The Fine Gray Model sensitivity analysis asks whether its substantive conclusion survives a defensible neighboring specification. The model is fitted to 100 primary events, 51 competing events, and 498 censored records. Chart behavior, tail support, coding, and the method-specific plan to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models are documented together.
Sensitivity diagnostics
Compare Fine Gray Model with cause-specific Cox regression, Fine–Gray subdistribution regression, Aalen–Johansen cumulative incidence, naive Kaplan–Meier that incorrectly censors competing events. Explain whether the substantive conclusion changes and why.
Full Fine Gray Model publication audit
Method-specific checkpoints for content, data, formulas, results, and assets
1. Research estimand
Research estimand is reviewed separately from statistical significance. State the exact population quantity and contrast before examining results. For this competing-risk method, the core operation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; the prose, formula, table, and chart must all describe that same operation.
The verified school_MS subdistribution coefficient is 1.7304, giving SHR 5.6431. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, while the substantive statement recognizes that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
2. Time origin
The publication test at time origin is practical: could another analyst rebuild the same result from dataset.csv? Document what time zero represents and reject records measured from a different baseline. That standard matters because this approach models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
The 95% interval for the subdistribution hazard ratio is 3.6767 to 8.6611, with p about 2.44×10^-15. This is the concrete evidence used for the checkpoint. The sensitivity plan is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the narrative must not forget that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
3. Event and status coding
The publication test at event and status coding is practical: could another analyst rebuild the same result from dataset.csv? Describe every status value in words and verify its frequency before fitting. That standard matters because this approach models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, while the substantive statement recognizes that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
4. Censoring definition
This checkpoint asks whether censoring definition has been translated into executable analysis. Explain why a censored observation contributes to earlier risk sets and not later events. The method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; therefore a generic survival-analysis explanation is not enough for this post.
The SHR concerns the cumulative incidence of cause 1 and is not interchangeable with a cause-specific Cox hazard ratio. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, and the final interpretation should remember that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
5. Duration scale
Duration scale is reviewed separately from statistical significance. Audit the numerical time scale and any recoding used to obtain it. For this competing-risk method, the core operation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; the prose, formula, table, and chart must all describe that same operation.
The model is fitted to 100 primary events, 51 competing events, and 498 censored records. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the reader should be told that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
6. Risk-set or likelihood construction
Before interpreting the principal estimate, resolve risk-set or likelihood construction. Trace the core estimating equation to observable rows and event times. The calculation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.
The supplied Python section validates coding while the independent R cmprsk calculation supplies the regression reference. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, then frame direction according to the principle that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
7. Ties and discretization
Ties and discretization is reviewed separately from statistical significance. Declare how simultaneous event times are aggregated or approximated. For this competing-risk method, the core operation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; the prose, formula, table, and chart must all describe that same operation.
The verified school_MS subdistribution coefficient is 1.7304, giving SHR 5.6431. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, and the final interpretation should remember that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
8. Reference coding
Reference coding can invalidate an otherwise polished article. Establish reference coding before assigning better or worse direction. The reason is specific to this procedure: it models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights. The final wording should state any unresolved limitation rather than hide it behind a p-value.
The 95% interval for the subdistribution hazard ratio is 3.6767 to 8.6611, with p about 2.44×10^-15. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the reader should be told that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
9. Missing-data handling
Missing-data handling can invalidate an otherwise polished article. Reconcile every omitted row and confirm that exclusions do not change status coding. The reason is specific to this procedure: it models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights. The final wording should state any unresolved limitation rather than hide it behind a p-value.
The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the reader should be told that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
10. Dependence and clustering
Use dependence and clustering to challenge the draft rather than merely document it. Assess whether repeated, matched, or nested records require robust or multilevel treatment. The relevant technical fact is that the estimator models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, which determines what must be checked in the stored output.
The SHR concerns the cumulative incidence of cause 1 and is not interchangeable with a cause-specific Cox hazard ratio. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, while the substantive statement recognizes that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
11. Information and event adequacy
At information and event adequacy, the article must move from terminology to evidence. Print the status mapping and reconcile each event total with the CSV. Its defining computation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, and the audit should show where the required quantities appear in the CSV or derived table.
The model is fitted to 100 primary events, 51 competing events, and 498 censored records. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, and it will state clearly that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
12. Tail support
Treat tail support as an analytical decision. Separate stable follow-up from the thin tail before generalizing results. Here the method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.
For 12. Tail support, the Fine Gray Model review must record a method-specific publication checkpoint and the evidence required to pass it. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 5 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
13. Uncertainty interval
This checkpoint asks whether uncertainty interval has been translated into executable analysis. Report sampling uncertainty on the natural scale and reproduce its calculation. The method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; therefore a generic survival-analysis explanation is not enough for this post.
The verified school_MS subdistribution coefficient is 1.7304, giving SHR 5.6431. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, then frame direction according to the principle that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
14. Null hypothesis and p-value
This checkpoint asks whether null hypothesis and p-value has been translated into executable analysis. Explain what the p-value conditions on and what it cannot establish. The method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; therefore a generic survival-analysis explanation is not enough for this post.
The 95% interval for the subdistribution hazard ratio is 3.6767 to 8.6611, with p about 2.44×10^-15. It provides an audit anchor, not an automatic scientific conclusion. The method-specific safeguard is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models. Interpret the displayed effect under the constraint that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
15. Effect magnitude
Effect magnitude receives an explicit pass, warning, or fail assessment. Translate the numerical output into the method’s own effect scale. This is necessary because the method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, and a different construction would answer a different survival question.
The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, and the final interpretation should remember that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
16. Software defaults
The publication test at software defaults is practical: could another analyst rebuild the same result from dataset.csv? Record package versions, defaults, factor coding, convergence, and tie settings. That standard matters because this approach models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
The SHR concerns the cumulative incidence of cause 1 and is not interchangeable with a cause-specific Cox hazard ratio. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; when stating direction, note that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
17. Cross-software reconciliation
Use cross-software reconciliation to challenge the draft rather than merely document it. Reconcile output differences by checking definitions before blaming numerical software. The relevant technical fact is that the estimator models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, which determines what must be checked in the stored output.
The model is fitted to 100 primary events, 51 competing events, and 498 censored records. This is the concrete evidence used for the checkpoint. The sensitivity plan is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the narrative must not forget that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
18. Chart-to-table audit
Before interpreting the principal estimate, resolve chart-to-table audit. Reject any image or download whose filename, values, or method label belongs to another post. The calculation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.
The supplied Python section validates coding while the independent R cmprsk calculation supplies the regression reference. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the reader should be told that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
19. Sensitivity specification
Use sensitivity specification to challenge the draft rather than merely document it. Repeat the analysis under a defensible neighboring specification and explain the comparison. The relevant technical fact is that the estimator models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, which determines what must be checked in the stored output.
The verified school_MS subdistribution coefficient is 1.7304, giving SHR 5.6431. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, because exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
20. Scientific limitation
Treat scientific limitation as an analytical decision. Keep inference inside the observed design, coding, and follow-up window. Here the method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.
The 95% interval for the subdistribution hazard ratio is 3.6767 to 8.6611, with p about 2.44×10^-15. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the directional explanation follows the fact that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
21. Generalizability boundary
The publication test at generalizability boundary is practical: could another analyst rebuild the same result from dataset.csv? Separate computational correctness from scientific validity and causal interpretation. That standard matters because this approach models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. That checkpoint is considered complete only when the same value appears in code, table, and interpretation. The robustness review should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the direction statement remains governed by the fact that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
22. Reproducible record
A strong account of reproducible record names the decision and shows its consequence. Preserve the CSV, transformation rules, code, output, metadata, and matched URLs. Since the method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, hidden defaults at this point would propagate into every later value.
The SHR concerns the cumulative incidence of cause 1 and is not interchangeable with a cause-specific Cox hazard ratio. This is the concrete evidence used for the checkpoint. The sensitivity plan is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the narrative must not forget that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
23. Publication language
A strong account of publication language names the decision and shows its consequence. Make the published record independently reproducible and free of unsupported wording. Since the method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, hidden defaults at this point would propagate into every later value.
For 23. Publication language, the Fine Gray Model review must record a method-specific publication checkpoint and the evidence required to pass it. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 6 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
24. SEO and asset consistency
SEO and asset consistency can invalidate an otherwise polished article. Reject any image or download whose filename, values, or method label belongs to another post. The reason is specific to this procedure: it models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights. The final wording should state any unresolved limitation rather than hide it behind a p-value.
The supplied Python section validates coding while the independent R cmprsk calculation supplies the regression reference. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, and it will state clearly that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
25. Mutually exclusive causes
This checkpoint asks whether mutually exclusive causes has been translated into executable analysis. Define the decision operationally and show how it was checked. The method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; therefore a generic survival-analysis explanation is not enough for this post.
For 25. Mutually exclusive causes, the Fine Gray Model review must record a method-specific publication checkpoint and the evidence required to pass it. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 7 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
26. Cumulative incidence versus one minus KM
Use cumulative incidence versus one minus km to challenge the draft rather than merely document it. Connect this checkpoint to a saved calculation rather than a generic claim. The relevant technical fact is that the estimator models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, which determines what must be checked in the stored output.
The 95% interval for the subdistribution hazard ratio is 3.6767 to 8.6611, with p about 2.44×10^-15. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, because exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
27. Aalen–Johansen recursion
The publication test at aalen–johansen recursion is practical: could another analyst rebuild the same result from dataset.csv? Document the evidence and the consequence of a warning or failure. That standard matters because this approach models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, and it will state clearly that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
28. Cause-specific hazard
Use cause-specific hazard to challenge the draft rather than merely document it. Define the decision operationally and show how it was checked. The relevant technical fact is that the estimator models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, which determines what must be checked in the stored output.
The SHR concerns the cumulative incidence of cause 1 and is not interchangeable with a cause-specific Cox hazard ratio. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models; the directional explanation follows the fact that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
29. Subdistribution hazard
At subdistribution hazard, the article must move from terminology to evidence. Connect this checkpoint to a saved calculation rather than a generic claim. Its defining computation models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, and the audit should show where the required quantities appear in the CSV or derived table.
The model is fitted to 100 primary events, 51 competing events, and 498 censored records. It provides an audit anchor, not an automatic scientific conclusion. The method-specific safeguard is to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models. Interpret the displayed effect under the constraint that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
30. Cause-specific group comparison
The publication test at cause-specific group comparison is practical: could another analyst rebuild the same result from dataset.csv? Document the evidence and the consequence of a warning or failure. That standard matters because this approach models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights.
The supplied Python section validates coding while the independent R cmprsk calculation supplies the regression reference. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, while the substantive statement recognizes that exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
31. Censoring weights
This checkpoint asks whether censoring weights has been translated into executable analysis. Explain why a censored observation contributes to earlier risk sets and not later events. The method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; therefore a generic survival-analysis explanation is not enough for this post.
For 31. Censoring weights, the Fine Gray Model review must record a method-specific publication checkpoint and the evidence required to pass it. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 8 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
32. Multi-state probability accounting
The reviewer should pause at multi-state probability accounting and reproduce the relevant step. Connect this checkpoint to a saved calculation rather than a generic claim. In this analysis the procedure models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; that mechanism sets the boundary for correct interpretation.
For 32. Multi-state probability accounting, the Fine Gray Model review must record a method-specific publication checkpoint and the evidence required to pass it. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 9 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
33. Event-specific validation
Event-specific validation receives an explicit pass, warning, or fail assessment. Describe every status value in words and verify its frequency before fitting. This is necessary because the method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights, and a different construction would answer a different survival question.
The modified risk set keeps individuals who experienced the competing cause through weighting rather than ordinary censoring. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models, because exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard.
34. Cause-based decision target
This checkpoint asks whether cause-based decision target has been translated into executable analysis. Define the decision operationally and show how it was checked. The method models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights; therefore a generic survival-analysis explanation is not enough for this post.
For 34. Cause-based decision target, the Fine Gray Model review must record a method-specific publication checkpoint and the evidence required to pass it. This method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; therefore the editor should check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models. The bundled example supplies the following numerical anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. Checkpoint 10 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
Final Fine Gray Model release decision
This draft is released only when its exact formula, event definition, software settings, numerical result, chart captions, download files, and contextual links agree. The central computational mechanism is that it models the subdistribution risk set for the primary cause while retaining people who experienced a competing event through censoring weights. That statement differentiates the article from the other twenty survival posts and prevents a shared template from substituting for method-specific explanation.
The final robustness record directs the editor to check cause coding, censoring weights, proportional subdistribution hazards, cumulative-incidence fit, and cause-specific sensitivity models. The directional interpretation remains: exp(beta) describes relative subdistribution hazard and therefore the ordering of cumulative incidence, not the instantaneous cause-specific hazard. Because the example is built from absences and G3 in a student-performance dataset, publication must keep the teaching-purpose limitation visible and must not recast the endpoint as clinical survival, mortality, equipment failure, or causal evidence.
Fine Gray Model compared with related methods
Choose the method by estimand, not menu proximity
| Related method | Comparison question |
|---|---|
| cause-specific Cox regression | Cause-specific cox regression models the instantaneous hazard among people currently free of all competing events. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Fine Gray Model only when covariate effects on the cumulative incidence of one event type in the presence of competing events is the actual target. |
| Fine–Gray subdistribution regression | Fine–gray subdistribution regression models a modified hazard linked to cumulative incidence for one cause. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Fine Gray Model only when covariate effects on the cumulative incidence of one event type in the presence of competing events is the actual target. |
| Aalen–Johansen cumulative incidence | Aalen–johansen cumulative incidence estimates absolute cause probability nonparametrically across event times. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Fine Gray Model only when covariate effects on the cumulative incidence of one event type in the presence of competing events is the actual target. |
| naive Kaplan–Meier that incorrectly censors competing events | Naive kaplan–meier that incorrectly censors competing events overstates cause probability because a competing event is not ordinary independent censoring. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Fine Gray Model only when covariate effects on the cumulative incidence of one event type in the presence of competing events is the actual target. |
How to report Fine Gray Model
A complete, restrained result statement
Reporting template
“A Fine Gray Model analysis used 649 records from dataset(100).csv. Duration was defined as absences plus one, and the event indicator equaled one when G3 was below 10; 100 events and 549 right-censored observations were available. For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. The analysis documented event coding, reference groups, risk sets, ties, assumptions, software settings, diagnostics, matching files, and the educational nature of the prepared survival endpoint.”
Include
Avoid calling hazard a probability, treating censoring as missingness, or converting a nonsignificant result into proof of equality. The final sentence should answer the stated estimand and no broader question.
Avoid
A complete report states the prepared time origin, event and censor codes, sample and event counts, group or predictor reference, exact method, formula, estimate or statistic, uncertainty, and the relevant diagnostics. It then gives this result: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event.
Fine Gray Model downloads
Only assets assigned to this topic after filename and extension audit
The download panel contains only URLs whose filenames and extensions match this topic in the source register. The plugin does not infer a missing asset from another post or alter the registered media path.
Fine Gray Model frequently asked questions
Method-specific answers for draft review
What does Fine Gray Model measure?
Fine Gray Model is used for the estimand defined in this article. It models a primary cause through the subdistribution risk set while retaining competing-event records with weighting. The interpretation remains conditional on the stated time origin, event code, censoring rule, group or predictor coding, and any distributional or proportionality assumptions.
When should Fine Gray Model be used?
Use Fine Gray Model when the research objective requires subdistribution-hazard regression that retains competing-event records in a weighted risk set and the assumptions listed in the article are defensible. The method is inappropriate when a different event type, time emphasis, adjustment strategy, or hazard shape is the scientific target.
What data are used in this Fine Gray Model example?
The primary cause, competing cause, and censored state are kept separate, and school is the modeled contrast for the stored subdistribution hazard ratio. All values come from the uploaded 649-row file and the disclosed absences-plus-one/G3 event construction.
What is the main Fine Gray Model result?
The result is summarized by this verified anchor: For the MS versus GP contrast, the fitted subdistribution hazard ratio was 5.643, 95% CI [3.677, 8.661], p < .001, for the primary event in the presence of the competing event. It should be read together with the method-specific assumptions, uncertainty, and the teaching-endpoint limitation rather than as a stand-alone causal conclusion.
How does censoring affect Fine Gray Model?
Censored records contribute to risk sets or likelihood survival terms until their observed duration. Their handling matters because the method models a primary cause through the subdistribution risk set while retaining competing-event records with weighting; treating censoring as an event or deleting censored rows would change the estimate and usually bias the analysis.
How are ties handled in Fine Gray Model?
The prepared durations are integer-valued, so tied times are common. The article states the exact pooled-event rule, weight, or Efron/Breslow approximation used for Fine Gray Model, and software results should be reconciled only after those defaults match.
Can Fine Gray Model be completed in Python?
Yes. The Python section reconstructs the data fields and exposes the intermediate quantities required for Fine Gray Model. It prints the benchmark result and supports the diagnostic task to check cause coding, censoring weights, proportional subdistribution hazards, and cause-specific sensitivity models.
Can Fine Gray Model be completed in R?
Yes. The R section uses a method-appropriate survival or competing-risk routine, declares factor references and tie or weighting settings, and provides an independent check of the benchmark result for Fine Gray Model.
Can Fine Gray Model be completed in SPSS?
SPSS is used only where a native procedure matches Fine Gray Model. When no exact native command exists, the post describes SPSS as a data-management, charting, or integration route and does not rename a different test or model.
How does Excel support Fine Gray Model?
Excel supports Fine Gray Model by displaying cause coding, subdistribution risk-set weights, coefficient, SHR, interval, and p-value in visible cells. The matching workbook must reproduce selected Python and R benchmark values and retain the exact event, censoring, group, tie, and interval definitions.
What is the largest reporting mistake for Fine Gray Model?
The largest Fine Gray Model reporting error is calling a cause-specific Cox hazard ratio a Fine–Gray subdistribution hazard ratio. The article also keeps the teaching-endpoint limitation visible so the worked result is not presented as causal or naturally observed survival evidence.
Which internal guides support Fine Gray Model?
Start with Competing Risks Analysis because it provides the nearest check on subdistribution-hazard regression that retains competing-event records in a weighted risk set. Use Cox Proportional Hazards Regression, Cumulative Hazard Function, Survival Function to compare weighting, probability scale, model assumptions, or software implementation; each link has a specific methodological role rather than serving as generic navigation.