Multiple mutually exclusive event types

Competing Risks Analysis: Formula, Verified Results, Python, R, SPSS and Excel

Competing Risks Analysis is presented as a complete, dataset-grounded survival analysis guide. It explains estimate the probability of each event type without treating competing failures as ordinary censoring, 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.

649 records100 events549 censoredNative MathMLDraft-only importer

Primary metricCIF₁ 0.576

Duration1–33

GroupsGP 423 / MS 226

ConclusionBoth event types materially contribute

Quick answer

Both event types materially contribute

At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded.

Interpretation boundary: A competing event changes the probability structure; it is not equivalent to a record that simply disappears from observation.

What does Competing Risks Analysis measure?

cause-specific cumulative incidence for the primary and competing event types

Competing Risks Analysis focuses on cause-specific cumulative incidence for the primary and competing event types. The estimand must remain separate from related quantities such as ordinary probability, crude event proportion, mean duration, or an unrelated regression coefficient.

Method target

Competing Risks Analysis is selected to estimate the probability of each event type without treating competing failures as ordinary censoring. 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.

This article derives a positive duration from absences + 1 and marks G3 < 10 as the event. That transparent construction lets readers reproduce F k ( t ) = ∫ 0 t S ( u − ) d Λ k ( u ), while the educational origin of the endpoint remains visible throughout the interpretation.

What it does not establish

A correct numerical result is conditional on the time origin, event rule, censoring interpretation, and risk-set construction. The article does not convert the prepared endpoint into clinical risk; it uses the data to audit how Competing Risks Analysis behaves.

A competing event changes the probability structure; it is not equivalent to a record that simply disappears from observation.

Supporting concepts: Review P Value Confidence Interval Statistical Power Parametric vs Nonparametric Tests when interpreting uncertainty, evidence, design, and method choice for Competing Risks Analysis.

When should Competing Risks Analysis 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 Competing Risks Analysis to the estimand.

Assumptions?

Audit censoring, risk sets, ties, and model form.

Reportable?

Retain numerical evidence and limitations.

Appropriate use

Use the procedure only after confirming that competing risks analysis is selected to estimate the probability of each event type without treating competing failures as ordinary censoring. The design must supply an interpretable origin, a clearly coded event, and enough event-time information for the method’s specific calculation.

Competing Risks Analysis 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

Avoid the analysis when censoring is treated as deletion, event codes are reversed, or the interpretation substitutes probability language for cause-specific cumulative incidence for the primary and competing event types. Those errors change the scientific question rather than merely changing presentation.

Do not publish Competing Risks Analysis output when the matching charts, PDFs, workbook, and dataset describe different definitions or model specifications.

Competing Risks Analysis dataset and variable construction

The exact 649-row teaching structure

The bundled 649-row dataset is used specifically for Aalen–Johansen allocation of event-free probability across two causes. Status is coded as 100 primary events, 51 competing events, and 498 records censored from both causes so the two cumulative-incidence functions remain distinct. 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

Mean duration4.659Prepared time scale

Median duration3Ordinary raw median

GP events32of 423 records

MS events68of 226 records

Substantive limitation: absences plus one is a prepared positive duration and G3 below 10 is a prepared event. The Competing Risks Analysis article demonstrates computation and interpretation discipline; it must not be presented as naturally observed time to disease, machine failure, churn, or death.

Competing Risks Analysis assumptions

Conditions required for a defensible result

Mutually Exclusive Event Types

Competing Risks Analysis 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

Competing Risks Analysis 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

Competing Risks Analysis 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

Competing Risks Analysis 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 Competing Risks Analysis converts each condition into a check against the prepared records rather than declaring the method assumption-free. At time 10, cumulative incidence is 0.2567 for cause 1 and 0.1216 for cause 2. A warning remains visible whenever the event process, censoring, support, weighting, or model form cannot be justified.

Adequate Events For Each Cause

Competing Risks Analysis 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.

Critical condition: A competing event changes the probability structure; it is not equivalent to a record that simply disappears from observation.

Competing Risks Analysis formula and mechanics

Native browser MathML and a plain-language audit trail

F_{k} (t) = \int_{0}^{t} S (u -) d Λ_{k} (u)

Competing Risks Analysis uses this expression to estimate or test cause-specific cumulative incidence for the primary and competing event types. 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 Competing Risks Analysis 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 Competing Risks Analysis review must connect every symbol to a risk set, event count, likelihood term, or model parameter. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 1 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

Equation rendering is local to WordPress and the browser. More importantly, the notation is operational: each symbol in F k ( t ) = ∫ 0 t S ( u − ) d Λ k ( u ) is connected to a column or intermediate table that can be checked against the included files.

Competing Risks Analysis verified results

Values calculated from the included dataset

Result item	Verified value
Primary events	100
Competing events	51
Censored	498
Primary CIF at 10	0.257
Competing CIF at 10	0.122
Final primary CIF	0.576

Verified result: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded.

How to interpret Competing Risks Analysis

From statistical output to a restrained conclusion

Primary conclusion

CIF₁ 0.576

Both event types materially contribute

For Primary conclusion, the Competing Risks Analysis review must translate the numerical result without overstating causality, equivalence, or natural follow-up. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 2 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

Interpretation order

Restate the event, censor, time, group, and reference coding.

Name the exact estimand or null hypothesis for Competing Risks Analysis.

Report the estimate, test statistic, interval, or p-value with units.

Read direction and practical magnitude from curves or coefficients.

Add assumption, tail-support, and educational-data limitations.

Do not overclaim: Competing Risks Analysis is evidence about the prepared event process. It does not prove causal effects, equivalence, or natural real-world survival behavior.

Competing Risks Analysis in Python

Transparent data preparation and reproducible calculations

This Python section reconstructs cause-specific cumulative incidence for the primary and competing event types from explicit arrays and auditable intermediate tables. Updates overall event-free survival and allocates each decrement to its observed cause through the aalen–johansen recursion, so the code below exposes the quantities that determine the final result.

Python — reproducible calculation

import numpy as np

import pandas as pd
df = pd.read_csv("dataset.csv")

time = pd.to_numeric(df["absences"]).to_numpy(float) + 1

status = np.zeros(len(df), dtype=int)

status[pd.to_numeric(df["G3"]).to_numpy() < 10] = 1

status[(status == 0) & (pd.to_numeric(df["failures"]).to_numpy() > 0)] = 2

S, cif1, cif2 = 1.0, 0.0, 0.0 rows = [] for tj in np.sort(np.unique(time[status > 0])): n = (time >= tj).sum() d1 = ((time == tj) & (status == 1)).sum() d2 = ((time == tj) & (status == 2)).sum() cif1 += S * d1 / n cif2 += S * d2 / n S *= 1.0 - (d1 + d2) / n rows.append((tj, n, d1, d2, S, cif1, cif2)) print(pd.DataFrame(rows, columns=["time","risk","d1","d2","S","CIF1","CIF2"]).tail())

Python verification checklist

In the Competing Risks Analysis Python section, the source CSV is read directly and the method-specific equation is reproduced before interpretation. Final cumulative incidences are about 0.5759 and 0.3700, so their sum remains below one after accounting for the no-event state. Package output is accepted only after its coding and defaults agree with the manual trail.

The source register controls every embedded image and download. Filename, extension, software label, and topic stem are reconciled before the URL is assigned to Competing Risks Analysis.

Competing Risks Analysis in R

Independent survival-analysis validation

R provides an independent implementation of the same cause-specific cumulative incidence for the primary and competing event types. The script states status coding, factor references, and the function or manual calculation needed for this method instead of relying on defaults.

R — independent validation

library(survival)

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

# Aalen–Johansen multi-state estimate with survival::survfit.

ms <- survfit(Surv(time, factor(status)) ~ 1, data=df)

print(ms)

R validation checklist

The R validation for Competing Risks Analysis prints the survival object or derived table, factor levels, tie or weighting settings, and the final result. Ordinary one-minus-Kaplan–Meier calculations would not estimate the same absolute cause probability. Differences from Python are investigated through definitions and defaults because the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion.

Competing Risks Analysis 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.

SPSS — saved syntax

COMPUTE surv_time=absences+1.

COMPUTE cause=0.

IF (G3<10) cause=1.

IF (cause=0 AND failures>0) cause=2.

FREQUENCIES VARIABLES=cause.

* Use validated extension code or R/Python integration for Aalen–Johansen cumulative incidence.

SPSS control: Verify that /STATUS identifies the intended event value. Compare the case-processing summary, event/censor counts, and group references with the included dataset before interpreting any chart or Exp(B).

Competing Risks Analysis in Excel

A visible calculation and reconciliation workbook

The Excel workbook exposes the arithmetic behind F_k(t) = ∫₀ᵗ S(u−) dΛ_k(u) 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 Competing Risks Analysis review must make the spreadsheet an auditable calculation rather than a decorative download. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 3 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

Competing Risks Analysis charts and chart-specific interpretation

First chart full-width; remaining charts arranged in pairs

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.

Competing Risks Analysis Python chart — Python chart 1 — Competing Risks Analysis
Python chart 1: shows the prepared 1–33 duration distribution, event/censor pattern, and where the competing-risk method obtains most of its information. For this topic, the display should be read with the event definition and the fact that the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion.

Competing Risks Analysis R chart — R chart 1 — Competing Risks Analysis
R chart 1 independently reproduces the prepared duration, event, and censoring structure for Competing Risks Analysis. Read it with the declared event definition before comparing groups or fitted quantities.

Competing Risks Analysis diagnostics and sensitivity analysis

Evidence required beyond the primary number

Data diagnostics

Diagnostics begin with data integrity and continue with the assumptions listed above. For this topic, the central interpretive rule is that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

Method diagnostics

The Competing Risks Analysis sensitivity analysis asks whether its substantive conclusion survives a defensible neighboring specification. Cause coding gives priority to the primary G3 event before assigning the failures-based competing event. Chart behavior, tail support, coding, and the method-specific plan to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities are documented together.

Sensitivity diagnostics

Compare Competing Risks Analysis 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.

Tail warning: survival estimates and hazard increments after time 20 rely on small risk sets. Late values can change sharply after a single event and should not dominate the conclusion without adequate support.

Full Competing Risks Analysis publication audit

Method-specific checkpoints for content, data, formulas, results, and assets

1. Research estimand

A strong account of research estimand names the decision and shows its consequence. State the exact population quantity and contrast before examining results. Since the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, hidden defaults at this point would propagate into every later value.

The constructed outcome has 100 primary events, 51 competing events, and 498 records censored from both causes. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities. Directional language must remain consistent with the rule that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

2. Time origin

At time origin, the article must move from terminology to evidence. Document what time zero represents and reject records measured from a different baseline. Its defining computation updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, and the audit should show where the required quantities appear in the CSV or derived table.

At time 10, cumulative incidence is 0.2567 for cause 1 and 0.1216 for cause 2. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, and it will state clearly that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

3. Event and status coding

Event and status coding 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 updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, and a different construction would answer a different survival question.

Final cumulative incidences are about 0.5759 and 0.3700, so their sum remains below one after accounting for the no-event state. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; when stating direction, note that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

4. Censoring definition

Before interpreting the principal estimate, resolve censoring definition. Explain why a censored observation contributes to earlier risk sets and not later events. The calculation updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.

Ordinary one-minus-Kaplan–Meier calculations would not estimate the same absolute cause probability. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, then frame direction according to the principle that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

5. Duration scale

This checkpoint asks whether duration scale has been translated into executable analysis. Audit the numerical time scale and any recoding used to obtain it. The method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; therefore a generic survival-analysis explanation is not enough for this post.

Cause coding gives priority to the primary G3 event before assigning the failures-based competing event. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities. Directional language must remain consistent with the rule that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

6. Risk-set or likelihood construction

The reviewer should pause at risk-set or likelihood construction and reproduce the relevant step. Trace the core estimating equation to observable rows and event times. In this analysis the procedure updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; that mechanism sets the boundary for correct interpretation.

Every interpretation must identify the cause number because a generic event label would merge different terminal states. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, while the substantive statement recognizes that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

7. Ties and discretization

A strong account of ties and discretization names the decision and shows its consequence. Declare how simultaneous event times are aggregated or approximated. Since the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, hidden defaults at this point would propagate into every later value.

The constructed outcome has 100 primary events, 51 competing events, and 498 records censored from both causes. It provides an audit anchor, not an automatic scientific conclusion. The method-specific safeguard is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities. Interpret the displayed effect under the constraint that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

8. Reference coding

Reference coding is reviewed separately from statistical significance. Establish reference coding before assigning better or worse direction. For this competing-risk method, the core operation updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; the prose, formula, table, and chart must all describe that same operation.

At time 10, cumulative incidence is 0.2567 for cause 1 and 0.1216 for cause 2. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the reader should be told that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

9. Missing-data handling

Missing-data handling defines the checkpoint for this article. Reconcile every omitted row and confirm that exclusions do not change status coding. Because the procedure updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.

Final cumulative incidences are about 0.5759 and 0.3700, so their sum remains below one after accounting for the no-event state. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, and it will state clearly that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

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 updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, which determines what must be checked in the stored output.

Ordinary one-minus-Kaplan–Meier calculations would not estimate the same absolute cause probability. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, and it will state clearly that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

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 updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, and the audit should show where the required quantities appear in the CSV or derived table.

Cause coding gives priority to the primary G3 event before assigning the failures-based competing event. This is the concrete evidence used for the checkpoint. The sensitivity plan is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the narrative must not forget that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

12. Tail support

Tail support can invalidate an otherwise polished article. Separate stable follow-up from the thin tail before generalizing results. The reason is specific to this procedure: it updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion. The final wording should state any unresolved limitation rather than hide it behind a p-value.

Every interpretation must identify the cause number because a generic event label would merge different terminal states. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, then frame direction according to the principle that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

13. Uncertainty interval

Use uncertainty interval to challenge the draft rather than merely document it. Report sampling uncertainty on the natural scale and reproduce its calculation. The relevant technical fact is that the estimator updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, which determines what must be checked in the stored output.

The constructed outcome has 100 primary events, 51 competing events, and 498 records censored from both causes. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the directional explanation follows the fact that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

14. Null hypothesis and p-value

Treat null hypothesis and p-value as an analytical decision. Explain what the p-value conditions on and what it cannot establish. Here the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

At time 10, cumulative incidence is 0.2567 for cause 1 and 0.1216 for cause 2. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, while the substantive statement recognizes that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

15. Effect magnitude

Before interpreting the principal estimate, resolve effect magnitude. Translate the numerical output into the method’s own effect scale. The calculation updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.

Final cumulative incidences are about 0.5759 and 0.3700, so their sum remains below one after accounting for the no-event state. This is the concrete evidence used for the checkpoint. The sensitivity plan is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the narrative must not forget that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

16. Software defaults

Treat software defaults as an analytical decision. Record package versions, defaults, factor coding, convergence, and tie settings. Here the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

Ordinary one-minus-Kaplan–Meier calculations would not estimate the same absolute cause probability. This is the concrete evidence used for the checkpoint. The sensitivity plan is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the narrative must not forget that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

17. Cross-software reconciliation

The publication test at cross-software reconciliation is practical: could another analyst rebuild the same result from dataset.csv? Reconcile output differences by checking definitions before blaming numerical software. That standard matters because this approach updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion.

Cause coding gives priority to the primary G3 event before assigning the failures-based competing event. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the directional explanation follows the fact that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

18. Chart-to-table audit

The reviewer should pause at chart-to-table audit and reproduce the relevant step. Reject any image or download whose filename, values, or method label belongs to another post. In this analysis the procedure updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; that mechanism sets the boundary for correct interpretation.

Every interpretation must identify the cause number because a generic event label would merge different terminal states. This is the concrete evidence used for the checkpoint. The sensitivity plan is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the narrative must not forget that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

19. Sensitivity specification

This checkpoint asks whether sensitivity specification has been translated into executable analysis. Repeat the analysis under a defensible neighboring specification and explain the comparison. The method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; therefore a generic survival-analysis explanation is not enough for this post.

The constructed outcome has 100 primary events, 51 competing events, and 498 records censored from both causes. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, then frame direction according to the principle that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

20. Scientific limitation

The publication test at scientific limitation is practical: could another analyst rebuild the same result from dataset.csv? Keep inference inside the observed design, coding, and follow-up window. That standard matters because this approach updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion.

At time 10, cumulative incidence is 0.2567 for cause 1 and 0.1216 for cause 2. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, then frame direction according to the principle that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

21. Generalizability boundary

Generalizability boundary receives an explicit pass, warning, or fail assessment. Separate computational correctness from scientific validity and causal interpretation. This is necessary because the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, and a different construction would answer a different survival question.

For 21. Generalizability boundary, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 4 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

22. Reproducible record

Reproducible record receives an explicit pass, warning, or fail assessment. Preserve the CSV, transformation rules, code, output, metadata, and matched URLs. This is necessary because the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, and a different construction would answer a different survival question.

For 22. Reproducible record, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 5 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

23. Publication language

This checkpoint asks whether publication language has been translated into executable analysis. Make the published record independently reproducible and free of unsupported wording. The method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; therefore a generic survival-analysis explanation is not enough for this post.

Cause coding gives priority to the primary G3 event before assigning the failures-based competing event. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, and the final interpretation should remember that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

24. SEO and asset consistency

The publication test at seo and asset consistency is practical: could another analyst rebuild the same result from dataset.csv? Reject any image or download whose filename, values, or method label belongs to another post. That standard matters because this approach updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion.

Every interpretation must identify the cause number because a generic event label would merge different terminal states. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; when stating direction, note that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

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 updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; therefore a generic survival-analysis explanation is not enough for this post.

For 25. Mutually exclusive causes, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 6 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

This checkpoint asks whether cumulative incidence versus one minus km has been translated into executable analysis. Connect this checkpoint to a saved calculation rather than a generic claim. The method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; therefore a generic survival-analysis explanation is not enough for this post.

At time 10, cumulative incidence is 0.2567 for cause 1 and 0.1216 for cause 2. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; when stating direction, note that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

27. Aalen–Johansen recursion

Use aalen–johansen recursion to challenge the draft rather than merely document it. Document the evidence and the consequence of a warning or failure. The relevant technical fact is that the estimator updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, which determines what must be checked in the stored output.

Final cumulative incidences are about 0.5759 and 0.3700, so their sum remains below one after accounting for the no-event state. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities, while the substantive statement recognizes that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

28. Cause-specific hazard

Treat cause-specific hazard as an analytical decision. Define the decision operationally and show how it was checked. Here the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

Ordinary one-minus-Kaplan–Meier calculations would not estimate the same absolute cause probability. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; when stating direction, note that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

29. Subdistribution hazard

A strong account of subdistribution hazard names the decision and shows its consequence. Connect this checkpoint to a saved calculation rather than a generic claim. Since the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, hidden defaults at this point would propagate into every later value.

For 29. Subdistribution hazard, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 7 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

30. Cause-specific group comparison

Cause-specific group comparison can invalidate an otherwise polished article. Document the evidence and the consequence of a warning or failure. The reason is specific to this procedure: it updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion. The final wording should state any unresolved limitation rather than hide it behind a p-value.

For 30. Cause-specific group comparison, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 8 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

31. Censoring weights

A strong account of censoring weights names the decision and shows its consequence. Explain why a censored observation contributes to earlier risk sets and not later events. Since the method updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, hidden defaults at this point would propagate into every later value.

For 31. Censoring weights, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 9 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

Use multi-state probability accounting 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 updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion, which determines what must be checked in the stored output.

For 32. Multi-state probability accounting, the Competing Risks Analysis review must record a method-specific publication checkpoint and the evidence required to pass it. This method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; therefore the editor should reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum. The bundled example supplies the following numerical anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. Checkpoint 10 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

33. Event-specific validation

The reviewer should pause at event-specific validation and reproduce the relevant step. Describe every status value in words and verify its frequency before fitting. In this analysis the procedure updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; that mechanism sets the boundary for correct interpretation.

Final cumulative incidences are about 0.5759 and 0.3700, so their sum remains below one after accounting for the no-event state. That checkpoint is considered complete only when the same value appears in code, table, and interpretation. The robustness review should compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the direction statement remains governed by the fact that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

34. Cause-based decision target

Cause-based decision target is reviewed separately from statistical significance. Define the decision operationally and show how it was checked. For this competing-risk method, the core operation updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion; the prose, formula, table, and chart must all describe that same operation.

Ordinary one-minus-Kaplan–Meier calculations would not estimate the same absolute cause probability. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities; the directional explanation follows the fact that interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve.

Final Competing Risks Analysis 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 updates overall event-free survival and allocates each decrement to its observed cause through the Aalen–Johansen recursion. 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 compare cause-specific event counts, cumulative incidence curves, and the sum of all state probabilities. The directional interpretation remains: interpret each cumulative incidence as an absolute probability for that cause, not as one minus a cause-censored Kaplan–Meier curve. 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.

Competing Risks Analysis 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 Competing Risks Analysis only when cause-specific cumulative incidence for the primary and competing event types 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 Competing Risks Analysis only when cause-specific cumulative incidence for the primary and competing event types 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 Competing Risks Analysis only when cause-specific cumulative incidence for the primary and competing event types 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 Competing Risks Analysis only when cause-specific cumulative incidence for the primary and competing event types is the actual target.

Selection rule: keep Competing Risks Analysis primary only when its estimand and assumptions match the research question more closely than the alternatives above.

How to report Competing Risks Analysis

A complete, restrained result statement

Reporting template

“A Competing Risks Analysis 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. At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. 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

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: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded.

Avoid

Reporting should lead with the method’s natural-scale quantity and then add uncertainty and limitations. The wording must preserve the boundary that a competing event changes the probability structure; it is not equivalent to a record that simply disappears from observation.

Competing Risks Analysis downloads

Only assets assigned to this topic after filename and extension audit

PYPython PDFPython output assigned to this survival topicOpen matching file →RR PDFR output assigned to this survival topicOpen matching file →SSPSS PDF 1SPSS output assigned to this survival topicOpen matching file →SSPSS PDF 2SPSS output assigned to this survival topicOpen matching file →XLSXExcel workbookWorked Excel analysis assigned to this topicOpen matching file →

Each PDF and workbook is a supporting audit artifact, not the sole evidence for a claim. Numerical statements in the article must also be recoverable from dataset.csv and the visible calculation steps.

Competing Risks Analysis frequently asked questions

Method-specific answers for draft review

What does Competing Risks Analysis measure?

Competing Risks Analysis is used for the estimand defined in this article. It updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion. 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 Competing Risks Analysis be used?

Use Competing Risks Analysis when the research objective requires Aalen–Johansen allocation of event-free probability across two causes 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 Competing Risks Analysis example?

Status is coded as 100 primary events, 51 competing events, and 498 records censored from both causes so the two cumulative-incidence functions remain distinct. All values come from the uploaded 649-row file and the disclosed absences-plus-one/G3 event construction.

What is the main Competing Risks Analysis result?

The result is summarized by this verified anchor: At the end of observed follow-up, the Aalen–Johansen cumulative incidence was 0.576 for the primary event and 0.370 for the competing event; 100 primary and 51 competing events were coded. 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 Competing Risks Analysis?

Censored records contribute to risk sets or likelihood survival terms until their observed duration. Their handling matters because the method updates event-free survival and allocates each decrement to its observed cause through cumulative-incidence recursion; treating censoring as an event or deleting censored rows would change the estimate and usually bias the analysis.

How are ties handled in Competing Risks Analysis?

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 Competing Risks Analysis, and software results should be reconciled only after those defaults match.

Can Competing Risks Analysis be completed in Python?

Yes. The Python section reconstructs the data fields and exposes the intermediate quantities required for Competing Risks Analysis. It prints the benchmark result and supports the diagnostic task to reconcile cause counts, cumulative-incidence increments, event-free probability, and their probability sum.

Can Competing Risks Analysis 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 Competing Risks Analysis.

Can Competing Risks Analysis be completed in SPSS?

SPSS is used only where a native procedure matches Competing Risks Analysis. 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 Competing Risks Analysis?

Excel supports Competing Risks Analysis by displaying the cause-specific Aalen–Johansen increments S(t−)d_k/n 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 Competing Risks Analysis?

The largest Competing Risks Analysis reporting error is treating competing events as ordinary censoring and reporting one minus Kaplan–Meier as cause-specific incidence. 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 Competing Risks Analysis?

Start with Fine Gray Model because it provides the nearest check on Aalen–Johansen allocation of event-free probability across two causes. Use Cumulative Hazard Function, Survival Function, Cox Proportional Hazards Regression to compare weighting, probability scale, model assumptions, or software implementation; each link has a specific methodological role rather than serving as generic navigation.

Both event types materially contribute

What does Competing Risks Analysis measure?

Method target

What it does not establish

When should Competing Risks Analysis be used?

Time outcome?

Event defined?

Method target?

Assumptions?

Reportable?

Appropriate use

Inappropriate use

Competing Risks Analysis dataset and variable construction

Competing Risks Analysis assumptions

Mutually Exclusive Event Types

Complete Event-Type Coding

Independent Censoring

A Defensible Time Origin

Appropriate Interpretation Of Cause-Specific Versus Subdistribution Effects

Adequate Events For Each Cause

Competing Risks Analysis formula and mechanics

Calculation sequence

Formula interpretation

Competing Risks Analysis verified results

How to interpret Competing Risks Analysis

Primary conclusion

Interpretation order

Competing Risks Analysis in Python

Python verification checklist

Competing Risks Analysis in R

R validation checklist

Competing Risks Analysis in SPSS

Competing Risks Analysis in Excel

Excel step 1

Excel step 2

Excel step 3

Excel step 4

Excel step 5

Excel controls

Competing Risks Analysis charts and chart-specific interpretation

Python chart 1 — Competing Risks Analysis

Python chart 2 — Competing Risks Analysis

Python chart 3 — Competing Risks Analysis

Python chart 4 — Competing Risks Analysis

Python chart 5 — Competing Risks Analysis

R chart 1 — Competing Risks Analysis

R chart 2 — Competing Risks Analysis

R chart 3 — Competing Risks Analysis

R chart 4 — Competing Risks Analysis

R chart 5 — Competing Risks Analysis

Competing Risks Analysis diagnostics and sensitivity analysis

Data diagnostics

Method diagnostics

Sensitivity diagnostics

Full Competing Risks Analysis publication audit

1. Research estimand

2. Time origin

3. Event and status coding

4. Censoring definition

5. Duration scale

6. Risk-set or likelihood construction

7. Ties and discretization

8. Reference coding

9. Missing-data handling

10. Dependence and clustering

11. Information and event adequacy

12. Tail support

13. Uncertainty interval

14. Null hypothesis and p-value

15. Effect magnitude

16. Software defaults

17. Cross-software reconciliation

18. Chart-to-table audit

19. Sensitivity specification

20. Scientific limitation

21. Generalizability boundary

22. Reproducible record

23. Publication language

24. SEO and asset consistency

25. Mutually exclusive causes