Survival Analysis (Kaplan-Meier, Cox Regression, Implant Survivorship)

Why follow-up data need their own method. Ordinary statistics struggle with follow-up data because not everyone is followed for the same time and not everyone has the event. Survival analysis solves this with censoring.

Censoring. A patient who is lost to follow-up, dies, or reaches the end of the study without the event is censored at their last known follow-up. They still contribute the information that they were event-free up to that point.

The Kaplan-Meier curve. The Kaplan-Meier estimator uses this to build a step survival curve. Cumulative survival starts at 100% and steps down at each event, with censored patients marked by ticks. From the curve you read survivorship at a time point, for example a 10-year implant survivorship, with a confidence interval.

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The number at risk. The number at risk is tabulated beneath the curve and falls over time, so the late part of the curve is based on few patients and is uncertain. The curve is drawn to the last event, not to the last reliable estimate, so its right-hand end always looks more confident than it is. Each step is calculated from whoever is still under observation at that moment, and by twenty years that may be a handful of patients, typically the youngest, who were operated on earliest. That is not a random remnant of the original cohort.

Reading a late survivorship figure. "95% survivorship at 20 years" means nothing until you know how many were still at risk at 20 years. If the answer is eight, the figure is an anecdote with a percentage sign. Read the number-at-risk table first: a curve without one is not interpretable, and its absence is itself a reason to distrust the paper.

The widening band. Widening confidence intervals are the same warning drawn graphically. If the band at the far end spans a range that would change your advice, the curve has stopped being useful there. Quote survivorship at a time point where the denominator is still substantial, and say what it was.

The log-rank test. A non-parametric hypothesis test comparing two or more Kaplan-Meier curves, for example two implants or two patient groups, for a significant difference in survival over the whole follow-up.

Cox proportional-hazards regression. The multivariable model of survival analysis. It estimates a hazard ratio (HR) for each predictor, such as implant design, age, BMI or sex, while adjusting for the others. An HR above 1 means increased hazard, below 1 means protective, and 1 means no effect. The model rests on the proportional-hazards assumption, that the hazard ratio is roughly constant over time.

In registries. Registries use these methods to compare implants and identify risk factors for failure. Their figures need careful interpretation, because the endpoint definition, the follow-up and competing risks all change what they mean.

Define the endpoint. Revision for any cause gives a lower survivorship than revision for a specific cause such as aseptic loosening. Always check which is reported.

The competing risk of death. Kaplan-Meier treats death as censoring, but a patient who dies can never be revised. In older patients, Kaplan-Meier therefore overestimates the cumulative revision risk, and a competing-risks (cumulative incidence) analysis is more truthful about absolute risk.

Implant camouflage. In registry averages, a poorly performing component combination can be hidden within an overall well-performing brand portfolio. A brand-level Kaplan-Meier curve can therefore mask a bad combination.

Selection and ascertainment. Revision as an endpoint underestimates failure, since some failing implants are not revised (in unfit patients, for example). It also depends on complete registry capture.

What it assumes. The Cox HR is a single number summarising the whole follow-up. It is valid only if the ratio of hazards between the groups is roughly constant over time.

How to check it. Visually, the two survival curves should not cross and should stay roughly parallel on a log-minus-log plot. Formally, test the Schoenfeld residuals: a significant test means the effect changes over time and the assumption is violated.

Crossing curves. Curves that cross, one implant better early and the other better late, are the red flag, and they defeat the log-rank test as well as the HR. A single HR is then meaningless. The log-rank test loses power because the early and late differences cancel out, so it can read "non-significant" despite a real time-varying difference.

When the assumption is violated. The remedies are:

• A stratified Cox model, stratifying on the offending variable
• A time-varying (time-dependent) covariate
• Piecewise HRs, reported separately for early and late periods
• Abandoning the single HR for the restricted mean survival time or the survival difference at fixed time points

What the hazard is. The hazard is the instantaneous event rate among those still at risk (still event-free) at that instant. The HR compares that rate between groups, so an HR of 2.7 means 2.7 times the instantaneous hazard.

Why the HR alone is not enough. It is relative, and conveys neither the absolute magnitude nor the timing. A large HR can be a tiny absolute difference when the event is rare, and a modest HR a large absolute difference when it is common. Nor does the HR tell you when the events occur.

Pair it with an absolute, time-anchored measure. Quote the HR with one or more of these:

• The survival difference at a clinically relevant time point, such as the gap between the curves at 10 years
• The median survival, the time at which survival falls to 50%, often not reached for a good implant
• The restricted mean survival time (RMST), the event-free time gained up to a horizon

For absolute revision risk in the elderly, the cumulative incidence is the measure (see the competing risk of death, above). The relative measures (relative risk, odds ratio, number needed to treat) are developed in our Measures of Effect topic.