Cox Regression Assumptions: Formula, Verified Results, Python, R, SPSS and Excel

Method target

Cox Regression Assumptions is selected to audit proportionality, functional form, independence, censoring, collinearity, ties, and influence before reporting Cox results. 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.

All calculations use the same 649-row CSV, but the analytical role of the prepared fields is specific: cox regression assumptions is selected to audit proportionality, functional form, independence, censoring, collinearity, ties, and influence before reporting cox results. The post therefore separates computational verification from claims about real longitudinal follow-up.

What it does not establish

Interpretation stops at the calculated estimand. The result does not prove a universal population law, and the most important boundary is this: A statistically strong coefficient does not rescue a model whose proportional-hazards or functional-form assumptions are materially wrong.

A statistically strong coefficient does not rescue a model whose proportional-hazards or functional-form assumptions are materially wrong.

Appropriate use

The strongest use case is one in which the analyst needs to audit proportionality, functional form, independence, censoring, collinearity, ties, and influence before reporting Cox results. A nearby method should replace it when the desired estimand, weighting, or distributional shape differs.

Cox Regression Assumptions 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

The procedure is not a rescue for an arbitrary duration, inadequate event information, or unsupported endpoint. If assumptions fail, report the failure and use one of the method-specific alternatives instead of forcing a preferred result.

Do not publish Cox Regression Assumptions output when the matching charts, PDFs, workbook, and dataset describe different definitions or model specifications.

Proportional Hazards

Cox Regression Assumptions requires proportional hazards. 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.

Linearity On The Log-Hazard Scale

Cox Regression Assumptions requires linearity on the log-hazard scale. 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

Cox Regression Assumptions 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.

Absence Of Severe Influence Or Separation

Cox Regression Assumptions requires absence of severe influence or separation. 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.

Adequate Events Per Effective Parameter

Cox Regression Assumptions requires adequate events per effective parameter. 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.

Correct Status, Time, Strata, And Reference Coding

Cox Regression Assumptions requires correct status, time, strata, and reference 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.

Calculation sequence

1. Sort positive durations and verify event/censor coding.
2. Construct the exact risk set immediately before each event time.
3. Calculate the Cox Regression Assumptions contribution defined by the formula.
4. Accumulate products, sums, likelihood terms, or weighted contrasts as required.
5. Attach uncertainty, diagnostics, and a conclusion that matches the estimand.

Formula interpretation

For Formula interpretation, the Cox Regression Assumptions review must connect every symbol to a risk set, event count, likelihood term, or model parameter. This method tests time stability, functional form, influence, independence, and coding conditions required for defensible Cox inference; therefore the editor should combine Schoenfeld trends, time interactions, martingale plots, dfbeta values, and sensitivity refits. The bundled example supplies the following numerical anchor: A rank-time check of Schoenfeld residuals flagged 3 terms at p < .05: studytime, school_MS, gender_M. Checkpoint 1 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

Native MathML preserves fractions, subscripts, superscripts, Greek symbols, and products without an external library. The article then translates the formula into the exact computational steps used for this dataset.

Interpretation order

Data diagnostics

Sensitivity analysis should compare the primary specification with Schoenfeld-residual checks, time-by-covariate interactions, stratified Cox models. A changed conclusion must be explained by the altered estimand, weighting, or model form rather than hidden.

Method diagnostics

Evaluate the assumptions specific to Cox Regression Assumptions: proportional hazards, linearity on the log-hazard scale, independent censoring, absence of severe influence or separation, adequate events per effective parameter, correct status, time, strata, and reference coding. Retain a pass, warning, or fail decision for each.

Sensitivity diagnostics

Compare Cox Regression Assumptions with Schoenfeld-residual checks, time-by-covariate interactions, stratified Cox models, parametric or time-varying alternatives. Explain whether the substantive conclusion changes and why.

1. Research estimand

The publication test at research estimand is practical: could another analyst rebuild the same result from dataset.csv? Translate the research question into the specific survival, hazard, incidence, or test quantity being estimated. That standard matters because this approach tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable.

The stored proportionality check for studytime has rho 0.3461 and p 0.00042, providing a clear warning against an unqualified constant effect. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Directional language must remain consistent with the rule that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

2. Time origin

Time origin can invalidate an otherwise polished article. Identify the starting event and verify that all durations use the same origin. The reason is specific to this procedure: it tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable. The final wording should state any unresolved limitation rather than hide it behind a p-value.

The school_MS and gender_M checks also require graphical review rather than relying only on the global model fit. This is the concrete evidence used for the checkpoint. The sensitivity plan is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the narrative must not forget that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

3. Event and status coding

Use event and status coding to challenge the draft rather than merely document it. Print the status mapping and reconcile each event total with the CSV. The relevant technical fact is that the estimator tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, which determines what must be checked in the stored output.

Integer follow-up produces tied event times, so the declared Efron rule must match across Python and R output. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the reader should be told that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

4. Censoring definition

Censoring definition receives an explicit pass, warning, or fail assessment. Verify that censoring is represented as status information rather than discarded rows. This is necessary because the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, and a different construction would answer a different survival question.

Martingale residuals are the relevant starting point for challenging linear functional forms of continuous predictors. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, because a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

5. Duration scale

The publication test at duration scale is practical: could another analyst rebuild the same result from dataset.csv? Check positivity, units, transformations, and the observed follow-up range. That standard matters because this approach tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable.

Dfbeta and score residuals should be inspected because 100 events support only limited coefficient complexity. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Directional language must remain consistent with the rule that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

6. Risk-set or likelihood construction

At risk-set or likelihood construction, the article must move from terminology to evidence. Show which records enter each denominator or censored likelihood term. Its defining computation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, and the audit should show where the required quantities appear in the CSV or derived table.

Passing a convergence check does not establish proportional hazards, linearity, independence, or absence of influential observations. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the reader should be told that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

7. Ties and discretization

Ties and discretization defines the checkpoint for this article. Check that discretized follow-up does not silently invoke different tie algorithms. Because the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.

The stored proportionality check for studytime has rho 0.3461 and p 0.00042, providing a clear warning against an unqualified constant effect. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, because a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

8. Reference coding

Before interpreting the principal estimate, resolve reference coding. Print factor levels and define the numerator and denominator of every contrast. The calculation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.

The school_MS and gender_M checks also require graphical review rather than relying only on the global model fit. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, while the substantive statement recognizes that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

9. Missing-data handling

Missing-data handling can invalidate an otherwise polished article. Make missing-value handling visible instead of allowing silent listwise deletion. The reason is specific to this procedure: it tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable. The final wording should state any unresolved limitation rather than hide it behind a p-value.

Integer follow-up produces tied event times, so the declared Efron rule must match across Python and R output. This is the concrete evidence used for the checkpoint. The sensitivity plan is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the narrative must not forget that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

10. Dependence and clustering

The reviewer should pause at dependence and clustering and reproduce the relevant step. Document the independence assumption and any clustering correction. In this analysis the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; that mechanism sets the boundary for correct interpretation.

Martingale residuals are the relevant starting point for challenging linear functional forms of continuous predictors. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; when stating direction, note that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

11. Information and event adequacy

The reviewer should pause at information and event adequacy and reproduce the relevant step. Recalculate event categories and counts directly from the source columns. In this analysis the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; that mechanism sets the boundary for correct interpretation.

Dfbeta and score residuals should be inspected because 100 events support only limited coefficient complexity. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, and it will state clearly that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

12. Tail support

Treat tail support as an analytical decision. Check whether sparse risk sets support the requested estimate or coefficient complexity. Here the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

Passing a convergence check does not establish proportional hazards, linearity, independence, or absence of influential observations. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; when stating direction, note that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

13. Uncertainty interval

Uncertainty interval can invalidate an otherwise polished article. Verify the variance formula and avoid intervals based on a neighboring method. The reason is specific to this procedure: it tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable. The final wording should state any unresolved limitation rather than hide it behind a p-value.

The stored proportionality check for studytime has rho 0.3461 and p 0.00042, providing a clear warning against an unqualified constant effect. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, and the final interpretation should remember that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

14. Null hypothesis and p-value

A strong account of null hypothesis and p-value names the decision and shows its consequence. Write the exact null hypothesis and keep practical importance separate from significance. Since the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, hidden defaults at this point would propagate into every later value.

The school_MS and gender_M checks also require graphical review rather than relying only on the global model fit. It provides an audit anchor, not an automatic scientific conclusion. The method-specific safeguard is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Interpret the displayed effect under the constraint that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

15. Effect magnitude

Treat effect magnitude as an analytical decision. Show the size of the modeled difference rather than reporting significance alone. Here the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

Integer follow-up produces tied event times, so the declared Efron rule must match across Python and R output. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, and it will state clearly that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

16. Software defaults

Treat software defaults as an analytical decision. Save the executable command and all defaults needed for an independent rerun. Here the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

Martingale residuals are the relevant starting point for challenging linear functional forms of continuous predictors. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, while the substantive statement recognizes that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

17. Cross-software reconciliation

Cross-software reconciliation receives an explicit pass, warning, or fail assessment. Record package versions, defaults, factor coding, convergence, and tie settings. This is necessary because the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, and a different construction would answer a different survival question.

Dfbeta and score residuals should be inspected because 100 events support only limited coefficient complexity. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, because a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

18. Chart-to-table audit

Chart-to-table audit is reviewed separately from statistical significance. Verify that the figure, caption, data table, and method result describe the same run. For this hazard regression method, the core operation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; the prose, formula, table, and chart must all describe that same operation.

Passing a convergence check does not establish proportional hazards, linearity, independence, or absence of influential observations. It provides an audit anchor, not an automatic scientific conclusion. The method-specific safeguard is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Interpret the displayed effect under the constraint that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

19. Sensitivity specification

Sensitivity specification defines the checkpoint for this article. Document whether the conclusion survives a method-specific sensitivity analysis. Because the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.

The stored proportionality check for studytime has rho 0.3461 and p 0.00042, providing a clear warning against an unqualified constant effect. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, then frame direction according to the principle that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

20. Scientific limitation

The publication test at scientific limitation is practical: could another analyst rebuild the same result from dataset.csv? State what the constructed teaching endpoint cannot establish about a real population. That standard matters because this approach tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable.

The school_MS and gender_M checks also require graphical review rather than relying only on the global model fit. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the directional explanation follows the fact that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

21. Generalizability boundary

This checkpoint asks whether generalizability boundary has been translated into executable analysis. Keep inference inside the observed design, coding, and follow-up window. The method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; therefore a generic survival-analysis explanation is not enough for this post.

Integer follow-up produces tied event times, so the declared Efron rule must match across Python and R output. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Directional language must remain consistent with the rule that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

22. Reproducible record

This checkpoint asks whether reproducible record has been translated into executable analysis. Audit focus-keyword use, content specificity, and asset ownership before import. The method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; therefore a generic survival-analysis explanation is not enough for this post.

Martingale residuals are the relevant starting point for challenging linear functional forms of continuous predictors. That checkpoint is considered complete only when the same value appears in code, table, and interpretation. The robustness review should combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the direction statement remains governed by the fact that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

23. Publication language

Use publication language to challenge the draft rather than merely document it. Preserve the CSV, transformation rules, code, output, metadata, and matched URLs. The relevant technical fact is that the estimator tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, which determines what must be checked in the stored output.

Dfbeta and score residuals should be inspected because 100 events support only limited coefficient complexity. It provides an audit anchor, not an automatic scientific conclusion. The method-specific safeguard is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Interpret the displayed effect under the constraint that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

24. SEO and asset consistency

SEO and asset consistency is reviewed separately from statistical significance. Verify that the figure, caption, data table, and method result describe the same run. For this hazard regression method, the core operation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; the prose, formula, table, and chart must all describe that same operation.

For 24. SEO and asset consistency, the Cox Regression Assumptions review must record a method-specific publication checkpoint and the evidence required to pass it. This method tests time stability, functional form, influence, independence, and coding conditions required for defensible Cox inference; therefore the editor should combine Schoenfeld trends, time interactions, martingale plots, dfbeta values, and sensitivity refits. The bundled example supplies the following numerical anchor: A rank-time check of Schoenfeld residuals flagged 3 terms at p < .05: studytime, school_MS, gender_M. Checkpoint 5 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

25. Proportional hazards

At proportional hazards, the article must move from terminology to evidence. Document the evidence and the consequence of a warning or failure. Its defining computation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, and the audit should show where the required quantities appear in the CSV or derived table.

The stored proportionality check for studytime has rho 0.3461 and p 0.00042, providing a clear warning against an unqualified constant effect. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; when stating direction, note that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

26. Schoenfeld residual pattern

Schoenfeld residual pattern defines the checkpoint for this article. Define the decision operationally and show how it was checked. Because the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.

The school_MS and gender_M checks also require graphical review rather than relying only on the global model fit. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits. Directional language must remain consistent with the rule that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

27. Continuous-variable functional form

Treat continuous-variable functional form as an analytical decision. Connect this checkpoint to a saved calculation rather than a generic claim. Here the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.

Integer follow-up produces tied event times, so the declared Efron rule must match across Python and R output. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, because a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

28. Influence and separation

Influence and separation defines the checkpoint for this article. Document the evidence and the consequence of a warning or failure. Because the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.

Martingale residuals are the relevant starting point for challenging linear functional forms of continuous predictors. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the directional explanation follows the fact that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

29. Collinearity and redundancy

Collinearity and redundancy defines the checkpoint for this article. Define the decision operationally and show how it was checked. Because the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.

For 29. Collinearity and redundancy, the Cox Regression Assumptions review must record a method-specific publication checkpoint and the evidence required to pass it. This method tests time stability, functional form, influence, independence, and coding conditions required for defensible Cox inference; therefore the editor should combine Schoenfeld trends, time interactions, martingale plots, dfbeta values, and sensitivity refits. The bundled example supplies the following numerical anchor: A rank-time check of Schoenfeld residuals flagged 3 terms at p < .05: studytime, school_MS, gender_M. Checkpoint 6 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

30. Baseline hazard and absolute risk

The reviewer should pause at baseline hazard and absolute risk and reproduce the relevant step. Connect this checkpoint to a saved calculation rather than a generic claim. In this analysis the procedure tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; that mechanism sets the boundary for correct interpretation.

Passing a convergence check does not establish proportional hazards, linearity, independence, or absence of influential observations. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, while the substantive statement recognizes that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

31. Partial likelihood and tied events

At partial likelihood and tied events, the article must move from terminology to evidence. Describe every status value in words and verify its frequency before fitting. Its defining computation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, and the audit should show where the required quantities appear in the CSV or derived table.

For 31. Partial likelihood and tied events, the Cox Regression Assumptions review must record a method-specific publication checkpoint and the evidence required to pass it. This method tests time stability, functional form, influence, independence, and coding conditions required for defensible Cox inference; therefore the editor should combine Schoenfeld trends, time interactions, martingale plots, dfbeta values, and sensitivity refits. The bundled example supplies the following numerical anchor: A rank-time check of Schoenfeld residuals flagged 3 terms at p < .05: studytime, school_MS, gender_M. Checkpoint 7 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

32. Interactions, strata, and time-varying effects

Interactions, strata, and time-varying effects is reviewed separately from statistical significance. Add an interpretable probability, ratio, parameter, or time contrast to the test result. For this hazard regression method, the core operation tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; the prose, formula, table, and chart must all describe that same operation.

The school_MS and gender_M checks also require graphical review rather than relying only on the global model fit. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits, and it will state clearly that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

33. Events per effective parameter

Events per effective parameter receives an explicit pass, warning, or fail assessment. Print the status mapping and reconcile each event total with the CSV. This is necessary because the method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable, and a different construction would answer a different survival question.

Integer follow-up produces tied event times, so the declared Efron rule must match across Python and R output. That checkpoint is considered complete only when the same value appears in code, table, and interpretation. The robustness review should combine Schoenfeld residual trends, time interactions, martingale plots, dfbeta values, and stratified refits; the direction statement remains governed by the fact that a significant residual-time association identifies instability; it does not directly estimate a clinically meaningful effect.

34. Adjusted interpretation

This checkpoint asks whether adjusted interpretation has been translated into executable analysis. Document the evidence and the consequence of a warning or failure. The method tests whether the fitted Cox linear predictor behaves consistently over time and whether covariate forms and influential records are acceptable; therefore a generic survival-analysis explanation is not enough for this post.

For 34. Adjusted interpretation, the Cox Regression Assumptions review must record a method-specific publication checkpoint and the evidence required to pass it. This method tests time stability, functional form, influence, independence, and coding conditions required for defensible Cox inference; therefore the editor should combine Schoenfeld trends, time interactions, martingale plots, dfbeta values, and sensitivity refits. The bundled example supplies the following numerical anchor: A rank-time check of Schoenfeld residuals flagged 3 terms at p < .05: studytime, school_MS, gender_M. Checkpoint 8 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.

Include

Reporting should lead with the method’s natural-scale quantity and then add uncertainty and limitations. The wording must preserve the boundary that a statistically strong coefficient does not rescue a model whose proportional-hazards or functional-form assumptions are materially wrong.

Avoid

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.