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eduKateSG · Why Mathematics? · Net Reclassification Improvement for Reliability Predictions: Risk Categories, Censoring, Time Horizons and Validation
Start with the question, audit the worked example, or jump to the assumptions and practice. Every chapter stays open for uninterrupted reading.
Understand the question
Define the quantity and follow the mechanism.Route 2 · Chapters 6–10
Reproduce the example
Audit the numbers one step at a time.Route 3 · Chapters 11–15
Check assumptions
See where design and calibration matter.Route 4 · Chapters 16–20
Explore applications
Connect the method to a concrete investigation.Route 5 · Chapters 21–25
Study and verify
Practise, inspect failure cases and read further.
Full chapter index · Practice and checking · Mathematics Learning Hub
The benefits of learning mathematics become practical when an updated reliability model changes predicted risks and a team asks whether those movements are in helpful directions. Net reclassification improvement separates upward and downward risk movement for units that experience the target event and for those that do not by a fixed horizon. For censored time-to-event data, event status and rates must be estimated with survival-aware methods rather than assigned from incomplete follow-up.
This guide develops old and new predictions, justified categories, event and non-event components, category-free variants, a worked NRI calculation, censoring, time horizons, uncertainty and limitations. NRI can describe directional reclassification under a precise definition; it does not by itself prove better calibration, overall prediction, causal value or decision benefit.
Full chapter index
Chapters 1–5 · Understand the question
Chapters 6–10 · Reproduce the example
Chapters 11–15 · Check assumptions
Chapters 16–20 · Explore applications
Chapters 21–25 · Study and verify
CHAPTER 1 OF 25 · Understand the question
1. Why reclassification is a real question
An updated model matters only if changes in predicted risk move relevant units in useful directions for a defined event and horizon. Adding vibration history moves some pumps above a 20 percent 500-hour risk band. This is the central mathematical mechanism in why reclassification is a real question. Write the quantities and assumptions before using software, then reproduce the calculation or geometric argument in a small example. Any movement is not automatically improvement. Define useful direction before comparing models. The useful habit is to keep the physical question, the probability model and the numerical method in separate columns so that a correct computation is not mistaken for complete evidence.
Did You Know? A result can be numerically stable and still answer the wrong question if the failure event, denominator or transformation changes. Test one nearby case and predict the direction of change before recalculating. Save inputs, intermediate values and units so a second reader can audit the path.
For practice, turn the example into a sensitivity check. Change one defensible input while holding the others fixed, compare the new result with the original and explain why it moved. Then construct a counterexample in which the shortcut fails. End with two sentences: what the mathematics supports, and what remains uncertain.
Start with the operational question behind freeze the event and horizon. Classify event status for one target failure by one fixed time because direction depends on that definition. In the illustrative case, The target is bearing failure by 1,000 hours. Draw the relevant graph, density, boundary or timeline before calculating; the picture should use the same variables and sign convention as the equations. Changing horizon can reverse who counts as an event. Put event and horizon in the title of the analysis.
A student should be able to rebuild the result without hidden settings. Record the sampling rule or optimisation criterion, the exact failure definition, and the evidence used for every distribution or parameter. Compare a transparent baseline with the advanced method. If they disagree, investigate the mechanism before deciding which answer is more credible.
This chapter belongs to a larger decision, so translate the number carefully. State one action the evidence permits and one action it does not. A parent or educator can ask which school ideas are doing the work: algebra organises relationships, probability represents uncertainty, calculus describes local change, and computing repeats the documented rules at scale.
Treat old and new risk predictions as a model-checking problem rather than a vocabulary exercise. Each unit needs two probabilities calculated for the same horizon, population and event under frozen models. Old risk is .18 and new risk .24 for one unit. Recompute the example from the raw values and label every unit. Scores on different scales cannot be compared as probabilities. Validate both probability outputs.
The strongest check uses evidence the model did not choose for itself. Hold out later observations, an independent simulation set or a known-answer benchmark. Report errors where decisions are sensitive, especially near the failure boundary, instead of relying on one global accuracy score. A method that performs well on easy safe cases can still fail at the rare cases that motivated the analysis.
Now change one assumption and make a directional prediction before running the calculation. If the result moves the opposite way, inspect the sign convention, transformation, density ratio or constraint. This prediction-first routine develops transferable problem-solving skills because it connects symbolic work to a testable expectation.
The mathematics of upward and downward movement becomes useful only when its mechanism is explicit. Up means the new prediction is higher or enters a higher prespecified category; down means the opposite. Consider the worked illustration: A move from .18 to .24 crosses a .20 boundary upward. Preserve the original inputs, calculate step by step and compare with a second method whenever an analytic or high-budget reference exists. Tiny changes can count in category-free NRI. Report movement magnitudes too.
There are three uncertainties to keep apart. Sampling or numerical uncertainty comes from finite computation. Parameter uncertainty comes from estimating inputs. Model-form uncertainty comes from simplified physics, distributions or dependence. Reducing the first does not automatically reduce the other two. A credible report names all three and shows which one drives the decision.
For a practical investigation, create a small reproducible notebook or spreadsheet with a frozen data sheet, formula sheet, diagnostics sheet and decision note. Another student should be able to change one input and obtain the same update without guessing what the model meant.
Primary source: https://doi.org/10.1002/sim.4085. Read it for the method and its assumptions; do not transfer its performance claims automatically to another model.
Use event component to practise sensitivity analysis. Among event units, upward movement is counted as helpful and downward movement as harmful. Of 40 events, 12 move up and 4 down, giving 12/40-4/40=.20. Before accepting the result, identify the quantity that would change the conclusion most. Censored units cannot be labelled from incomplete raw follow-up. Use a horizon-appropriate estimator.
A simple baseline is essential. It reveals whether the advanced method is improving accuracy or only adding complexity. Compare model calls, wall time, uncertainty and failure-mode coverage under one declared budget. Repeat stochastic calculations with several seeds; a favourable single run is not evidence of dependable efficiency.
Students can extend the example by adding correlation, a second failure mode or a modest measurement error. Explain which part of the formula changes and which remains fixed. This exercise shows how mathematics transfers from a clean textbook case to engineering and computing without pretending that the classroom model is a certified design tool.
Build a small counterexample for non-event component. Among non-event units, downward movement is helpful and upward movement harmful. The initial example is: Of 60 non-events, 15 move down and 9 up, giving 15/60-9/60=.10. Then create a nearby case where the usual shortcut becomes unreliable. A non-event means known event-free through the horizon under the target design. Check follow-up completeness.
Counterexamples are positive learning tools. They reveal the conditions that make a method work and help students recognise when a software output deserves a pause. Keep the counterexample small enough to plot or enumerate. Check sign, support, bounds and conservation of probability before adding complexity.
When writing the conclusion, separate a documented fact from an interpretation and from an illustrative scenario. Cite the primary method paper for the factual mechanism, use the local calculation for the illustration, and label any recommendation as conditional on the stated model. This keeps career and engineering advice age-appropriate and honest.
Connect total category nri to a real decision while protecting the boundary between calculation and judgement. The total NRI is the event component plus the non-event component. The worked components .20 and .10 sum to .30. First verify the arithmetic, then translate it into an allowed action and an action the evidence does not support. A total can hide one negative component. Always report both parts.
The audit should include the original question, input provenance, failure convention, algorithm settings, convergence or stopping rule, and a sensitivity result. For an adaptive method, also preserve the sequence of choices. For an optimisation, preserve every constraint. For Bayesian updating, preserve the prior and observation model. These records turn a result into something another person can challenge and improve.
A final transfer question is useful: where else would the same mathematical idea appear? Density ratios appear in survey correction and machine learning, probabilistic constraints in planning, and conditional probability in medical testing. The context changes, but transparent assumptions and reproducible checks remain valuable.
Cross-tabulate old and new categories separately for event and non-event groups so directions are auditable. Rows are old bands and columns are new bands. This is the central mathematical mechanism in build the reclassification table. Write the quantities and assumptions before using software, then reproduce the calculation or geometric argument in a small example. A total-only table hides the two denominators. Preserve counts and percentages. The useful habit is to keep the physical question, the probability model and the numerical method in separate columns so that a correct computation is not mistaken for complete evidence.
Did You Know? A result can be numerically stable and still answer the wrong question if the failure event, denominator or transformation changes. Test one nearby case and predict the direction of change before recalculating. Save inputs, intermediate values and units so a second reader can audit the path.
For practice, turn the example into a sensitivity check. Change one defensible input while holding the others fixed, compare the new result with the original and explain why it moved. Then construct a counterexample in which the shortcut fails. End with two sentences: what the mathematics supports, and what remains uncertain.
Start with the operational question behind why categories need meaning. Category thresholds should correspond to real actions or accepted risk bands rather than maximise the sample result. In the illustrative case, A .20 boundary triggers enhanced inspection in a declared policy. Draw the relevant graph, density, boundary or timeline before calculating; the picture should use the same variables and sign convention as the equations. Data-chosen cutpoints inflate apparent NRI. Justify boundaries before validation.
A student should be able to rebuild the result without hidden settings. Record the sampling rule or optimisation criterion, the exact failure definition, and the evidence used for every distribution or parameter. Compare a transparent baseline with the advanced method. If they disagree, investigate the mechanism before deciding which answer is more credible.
This chapter belongs to a larger decision, so translate the number carefully. State one action the evidence permits and one action it does not. A parent or educator can ask which school ideas are doing the work: algebra organises relationships, probability represents uncertainty, calculus describes local change, and computing repeats the documented rules at scale.
Treat category-free nri as a model-checking problem rather than a vocabulary exercise. The category-free form counts any increase or decrease and removes dependence on chosen bands. A change from .180 to .181 counts upward. Recompute the example from the raw values and label every unit. It can look large for clinically or operationally trivial movements. Pair direction with calibration and magnitude.
The strongest check uses evidence the model did not choose for itself. Hold out later observations, an independent simulation set or a known-answer benchmark. Report errors where decisions are sensitive, especially near the failure boundary, instead of relying on one global accuracy score. A method that performs well on easy safe cases can still fail at the rare cases that motivated the analysis.
Now change one assumption and make a directional prediction before running the calculation. If the result moves the opposite way, inspect the sign convention, transformation, density ratio or constraint. This prediction-first routine develops transferable problem-solving skills because it connects symbolic work to a testable expectation.
The mathematics of why nri values differ across studies becomes useful only when its mechanism is explicit. Category-based and category-free definitions, event rates, horizons and populations produce different scales and cannot be compared casually. Consider the worked illustration: A .30 NRI with two action bands is not equivalent to .30 with any-change counting. Preserve the original inputs, calculate step by step and compare with a second method whenever an analytic or high-budget reference exists. The same label can conceal different estimands. Report the complete definition.
There are three uncertainties to keep apart. Sampling or numerical uncertainty comes from finite computation. Parameter uncertainty comes from estimating inputs. Model-form uncertainty comes from simplified physics, distributions or dependence. Reducing the first does not automatically reduce the other two. A credible report names all three and shows which one drives the decision.
For a practical investigation, create a small reproducible notebook or spreadsheet with a frozen data sheet, formula sheet, diagnostics sheet and decision note. Another student should be able to change one input and obtain the same update without guessing what the model meant.
Use right censoring to practise sensitivity analysis. For time-to-event data, event probabilities within movement groups can be estimated using Kaplan–Meier or other suitable survival methods. A unit censored at 700 hours has unknown 1,000-hour status. Before accepting the result, identify the quantity that would change the conclusion most. Treating it as a non-event biases the table. Use the prospective survival formulation.
A simple baseline is essential. It reveals whether the advanced method is improving accuracy or only adding complexity. Compare model calls, wall time, uncertainty and failure-mode coverage under one declared budget. Repeat stochastic calculations with several seeds; a favourable single run is not evidence of dependable efficiency.
Students can extend the example by adding correlation, a second failure mode or a modest measurement error. Explain which part of the formula changes and which remains fixed. This exercise shows how mathematics transfers from a clean textbook case to engineering and computing without pretending that the classroom model is a certified design tool.
A second primary source is https://pmc.ncbi.nlm.nih.gov/articles/PMC3341973/. Compare the problem definition, estimator and validation rather than quoting one result in isolation.
Build a small counterexample for prospective survival formulation. The censored-data NRI can use expected event and non-event numbers among upward and downward movers instead of naive complete cases. The initial example is: Kaplan–Meier estimates event risk within pooled up and down groups. Then create a nearby case where the usual shortcut becomes unreliable. Small movement groups produce unstable survival estimates. Report support and uncertainty.
Counterexamples are positive learning tools. They reveal the conditions that make a method work and help students recognise when a software output deserves a pause. Keep the counterexample small enough to plot or enumerate. Check sign, support, bounds and conservation of probability before adding complexity.
When writing the conclusion, separate a documented fact from an interpretation and from an illustrative scenario. Cite the primary method paper for the factual mechanism, use the local calculation for the illustration, and label any recommendation as conditional on the stated model. This keeps career and engineering advice age-appropriate and honest.
Connect competing risks to a real decision while protecting the boundary between calculation and judgement. When another failure prevents the target failure, event probabilities should match the competing-risk estimand. Electronics replacement prevents later observation of bearing failure. First verify the arithmetic, then translate it into an allowed action and an action the evidence does not support. One-minus Kaplan–Meier can overstate cause-specific cumulative incidence. Use cumulative incidence when appropriate.
The audit should include the original question, input provenance, failure convention, algorithm settings, convergence or stopping rule, and a sensitivity result. For an adaptive method, also preserve the sequence of choices. For an optimisation, preserve every constraint. For Bayesian updating, preserve the prior and observation model. These records turn a result into something another person can challenge and improve.
A final transfer question is useful: where else would the same mathematical idea appear? Density ratios appear in survey correction and machine learning, probabilistic constraints in planning, and conditional probability in medical testing. The context changes, but transparent assumptions and reproducible checks remain valuable.
Reclassification of miscalibrated probabilities can reward movement across thresholds that do not represent actual risk. Both old and new models overpredict 1,000-hour failure. This is the central mathematical mechanism in calibration comes first. Write the quantities and assumptions before using software, then reproduce the calculation or geometric argument in a small example. Directional movement does not repair level error. Calibrate and validate both models. The useful habit is to keep the physical question, the probability model and the numerical method in separate columns so that a correct computation is not mistaken for complete evidence.
Did You Know? A result can be numerically stable and still answer the wrong question if the failure event, denominator or transformation changes. Test one nearby case and predict the direction of change before recalculating. Save inputs, intermediate values and units so a second reader can audit the path.
For practice, turn the example into a sensitivity check. Change one defensible input while holding the others fixed, compare the new result with the original and explain why it moved. Then construct a counterexample in which the shortcut fails. End with two sentences: what the mathematics supports, and what remains uncertain.
Start with the operational question behind discrimination is complementary. NRI focuses on changes between two models, while concordance asks about pair ordering within a model. In the illustrative case, The new model improves event movement but barely changes concordance. Draw the relevant graph, density, boundary or timeline before calculating; the picture should use the same variables and sign convention as the equations. Neither result invalidates the other. Report both when relevant.
A student should be able to rebuild the result without hidden settings. Record the sampling rule or optimisation criterion, the exact failure definition, and the evidence used for every distribution or parameter. Compare a transparent baseline with the advanced method. If they disagree, investigate the mechanism before deciding which answer is more credible.
This chapter belongs to a larger decision, so translate the number carefully. State one action the evidence permits and one action it does not. A parent or educator can ask which school ideas are doing the work: algebra organises relationships, probability represents uncertainty, calculus describes local change, and computing repeats the documented rules at scale.
Treat statistical significance is not enough as a model-checking problem rather than a vocabulary exercise. A new predictor's small p-value does not establish useful reclassification or prediction improvement. A large sample detects a tiny coefficient with negligible movement. Recompute the example from the raw values and label every unit. NRI can also be optimistic after selection. Validate the full update process.
The strongest check uses evidence the model did not choose for itself. Hold out later observations, an independent simulation set or a known-answer benchmark. Report errors where decisions are sensitive, especially near the failure boundary, instead of relying on one global accuracy score. A method that performs well on easy safe cases can still fail at the rare cases that motivated the analysis.
Now change one assumption and make a directional prediction before running the calculation. If the result moves the opposite way, inspect the sign convention, transformation, density ratio or constraint. This prediction-first routine develops transferable problem-solving skills because it connects symbolic work to a testable expectation.
The mathematics of uncertainty and confidence intervals becomes useful only when its mechanism is explicit. Movement proportions and survival estimates are sampled quantities, so NRI needs an uncertainty method respecting the model-development process. Consider the worked illustration: A bootstrap refits both models and recalculates NRI. Preserve the original inputs, calculate step by step and compare with a second method whenever an analytic or high-budget reference exists. Bootstrapping fixed predictions understates selection uncertainty. Resample at the independent unit or cluster.
There are three uncertainties to keep apart. Sampling or numerical uncertainty comes from finite computation. Parameter uncertainty comes from estimating inputs. Model-form uncertainty comes from simplified physics, distributions or dependence. Reducing the first does not automatically reduce the other two. A credible report names all three and shows which one drives the decision.
For a practical investigation, create a small reproducible notebook or spreadsheet with a frozen data sheet, formula sheet, diagnostics sheet and decision note. Another student should be able to change one input and obtain the same update without guessing what the model meant.
Use external validation to practise sensitivity analysis. Calculate reclassification using frozen old and new models in a new target fleet. The vibration update is assessed on later production. Before accepting the result, identify the quantity that would change the conclusion most. Different baseline risk and predictor spread can change NRI. Do not transport the number without the context.
A simple baseline is essential. It reveals whether the advanced method is improving accuracy or only adding complexity. Compare model calls, wall time, uncertainty and failure-mode coverage under one declared budget. Repeat stochastic calculations with several seeds; a favourable single run is not evidence of dependable efficiency.
Students can extend the example by adding correlation, a second failure mode or a modest measurement error. Explain which part of the formula changes and which remains fixed. This exercise shows how mathematics transfers from a clean textbook case to engineering and computing without pretending that the classroom model is a certified design tool.
Build a small counterexample for small cells and instability. Sparse event counts near category boundaries make component estimates volatile. The initial example is: Only three events enter the highest band. Then create a nearby case where the usual shortcut becomes unreliable. A single move changes the event component sharply. Show cell counts and sensitivity.
Counterexamples are positive learning tools. They reveal the conditions that make a method work and help students recognise when a software output deserves a pause. Keep the counterexample small enough to plot or enumerate. Check sign, support, bounds and conservation of probability before adding complexity.
When writing the conclusion, separate a documented fact from an interpretation and from an illustrative scenario. Cite the primary method paper for the factual mechanism, use the local calculation for the illustration, and label any recommendation as conditional on the stated model. This keeps career and engineering advice age-appropriate and honest.
Connect decision value is still separate to a real decision while protecting the boundary between calculation and judgement. Helpful reclassification by the metric does not encode costs, capacity or the consequences of an unnecessary action. Moving ten pumps upward may overwhelm the inspection team. First verify the arithmetic, then translate it into an allowed action and an action the evidence does not support. Positive NRI is not net benefit or profit. Use decision-curve or utility analysis.
The audit should include the original question, input provenance, failure convention, algorithm settings, convergence or stopping rule, and a sensitivity result. For an adaptive method, also preserve the sequence of choices. For an optimisation, preserve every constraint. For Bayesian updating, preserve the prior and observation model. These records turn a result into something another person can challenge and improve.
A final transfer question is useful: where else would the same mathematical idea appear? Density ratios appear in survey correction and machine learning, probabilistic constraints in planning, and conditional probability in medical testing. The context changes, but transparent assumptions and reproducible checks remain valuable.
Compute the event, non-event and total NRI from 12 up and 4 down among 40 events and 15 down and 9 up among 60 non-events. The components are .20 and .10, total .30. This is the central mathematical mechanism in practice calculation. Write the quantities and assumptions before using software, then reproduce the calculation or geometric argument in a small example. The toy counts assume complete horizon status. Explain how censoring changes the estimator. The useful habit is to keep the physical question, the probability model and the numerical method in separate columns so that a correct computation is not mistaken for complete evidence.
Did You Know? A result can be numerically stable and still answer the wrong question if the failure event, denominator or transformation changes. Test one nearby case and predict the direction of change before recalculating. Save inputs, intermediate values and units so a second reader can audit the path.
For practice, turn the example into a sensitivity check. Change one defensible input while holding the others fixed, compare the new result with the original and explain why it moved. Then construct a counterexample in which the shortcut fails. End with two sentences: what the mathematics supports, and what remains uncertain.
Start with the operational question behind parent and educator guidance. NRI connects fractions, signed differences, two-way tables, conditional probability and the need for consistent denominators. In the illustrative case, Ask why upward movement is good for events but bad for non-events. Draw the relevant graph, density, boundary or timeline before calculating; the picture should use the same variables and sign convention as the equations. Students may add raw counts with different denominators. Calculate each component separately.
A student should be able to rebuild the result without hidden settings. Record the sampling rule or optimisation criterion, the exact failure definition, and the evidence used for every distribution or parameter. Compare a transparent baseline with the advanced method. If they disagree, investigate the mechanism before deciding which answer is more credible.
This chapter belongs to a larger decision, so translate the number carefully. State one action the evidence permits and one action it does not. A parent or educator can ask which school ideas are doing the work: algebra organises relationships, probability represents uncertainty, calculus describes local change, and computing repeats the documented rules at scale.
Treat common misconceptions as a model-checking problem rather than a vocabulary exercise. NRI is not a universal percentage gain, not comparable across definitions, not immune to censoring and not proof the new model is better overall. A high total can hide a harmful component. Recompute the example from the raw values and label every unit. Category-free movement can be practically tiny. Report components, categories, horizon and validation.
The strongest check uses evidence the model did not choose for itself. Hold out later observations, an independent simulation set or a known-answer benchmark. Report errors where decisions are sensitive, especially near the failure boundary, instead of relying on one global accuracy score. A method that performs well on easy safe cases can still fail at the rare cases that motivated the analysis.
Now change one assumption and make a directional prediction before running the calculation. If the result moves the opposite way, inspect the sign convention, transformation, density ratio or constraint. This prediction-first routine develops transferable problem-solving skills because it connects symbolic work to a testable expectation.
Continue with the Mathematics Learning Hub, the eduKate Mathematics Learning System, the approach to learning mathematics, the Singapore Mathematics curriculum overview, the cross-subject learning approach and the previous reliability article. Each destination has its own role: subject navigation, learning method, school-to-advanced progression, or continuity with the latest reliability mechanism.
The mathematics of research and next reading becomes useful only when its mechanism is explicit. Pencina, D'Agostino and Steyerberg developed a prospective NRI formulation for survival and competing-risk data and stressed clear justification of choices. Consider the worked illustration: Read the primary paper beside the reclassification tables. Preserve the original inputs, calculate step by step and compare with a second method whenever an analytic or high-budget reference exists. The metric remains debated and should be one part of evaluation. Reproduce the .30 example first.
There are three uncertainties to keep apart. Sampling or numerical uncertainty comes from finite computation. Parameter uncertainty comes from estimating inputs. Model-form uncertainty comes from simplified physics, distributions or dependence. Reducing the first does not automatically reduce the other two. A credible report names all three and shows which one drives the decision.
For a practical investigation, create a small reproducible notebook or spreadsheet with a frozen data sheet, formula sheet, diagnostics sheet and decision note. Another student should be able to change one input and obtain the same update without guessing what the model meant.
Quick answers
What should I calculate first? Start with the estimand or failure event, then a simple baseline.
Does the advanced method guarantee accuracy? No. It needs input, numerical and model checks.
Which school mathematics matters? Algebra, graphs, probability, functions and careful units all contribute.
How can a student practise safely? Use fictional or open benchmark data and preserve every intermediate value.
What makes a career claim responsible? Describe how the mathematics is used without promising admission, salary or employment.
Extended practice laboratory
Practice case 1: Why reclassification is a real question
Setup: Use this chapter’s illustrative case: Adding vibration history moves some pumps above a 20 percent 500-hour risk band.
Task: Define useful direction before comparing models.
Checking target: Any movement is not automatically improvement.
Practice case 2: Freeze the event and horizon
Setup: Use this chapter’s illustrative case: The target is bearing failure by 1,000 hours.
Task: Put event and horizon in the title of the analysis.
Checking target: Changing horizon can reverse who counts as an event.
Practice case 3: Old and new risk predictions
Setup: Use this chapter’s illustrative case: Old risk is .18 and new risk .24 for one unit.
Task: Validate both probability outputs.
Checking target: Scores on different scales cannot be compared as probabilities.
Practice case 4: Upward and downward movement
Setup: Use this chapter’s illustrative case: A move from .18 to .24 crosses a .20 boundary upward.
Task: Report movement magnitudes too.
Checking target: Tiny changes can count in category-free NRI.
Practice case 5: Event component
Setup: Use this chapter’s illustrative case: Of 40 events, 12 move up and 4 down, giving 12/40-4/40=.20.
Task: Use a horizon-appropriate estimator.
Checking target: Censored units cannot be labelled from incomplete raw follow-up.
Practice case 6: Non-event component
Setup: Use this chapter’s illustrative case: Of 60 non-events, 15 move down and 9 up, giving 15/60-9/60=.10.
Task: Check follow-up completeness.
Checking target: A non-event means known event-free through the horizon under the target design.
Practice case 7: Total category NRI
Setup: Use this chapter’s illustrative case: The worked components .20 and .10 sum to .30.
Task: Always report both parts.
Checking target: A total can hide one negative component.
Practice case 8: Build the reclassification table
Setup: Use this chapter’s illustrative case: Rows are old bands and columns are new bands.
Task: Preserve counts and percentages.
Checking target: A total-only table hides the two denominators.
Practice case 9: Why categories need meaning
Setup: Use this chapter’s illustrative case: A .20 boundary triggers enhanced inspection in a declared policy.
Task: Justify boundaries before validation.
Checking target: Data-chosen cutpoints inflate apparent NRI.
Practice case 10: Category-free NRI
Setup: Use this chapter’s illustrative case: A change from .180 to .181 counts upward.
Task: Pair direction with calibration and magnitude.
Checking target: It can look large for clinically or operationally trivial movements.