Total Shoulder Replacement Failure Calculator

1. Evidence Base and Model Rationale

• aTSA baseline (any reoperation): the anatomic branch uses year by year conditional reoperation probabilities from Schoch et al. (2017), a large single institution series of 2,786 anatomic total shoulder replacements with 208 reoperations (7.5 percent) followed through 21 years. After year 2 the average failure rate leading to reoperation runs near 1.1 percent per year. All hazards are scaled uniformly by 1.204 so the curve matches the lower 95 percent confidence bound on 20-year survivorship (76.2 percent, an upper plausible 20-year failure of 23.8 percent).
• rTSA baseline (revision only proxy): the evidence sources contained no long horizon any reoperation baseline specific to reverse replacement. The reverse branch therefore applies a constant annual revision hazard derived from Roche et al. (2023), which reported an 8-year cumulative revision rate of 4.4 percent for primary rTSA across multiple government joint registries. This branch is explicitly a revision only proxy; actual reoperation risk may exceed it.
• Conservative by design: the covariate hazard ratios use the upper bound of their 95 percent confidence intervals, producing an upper plausible estimate. Age is entered as a continuous value and used directly in the recursion.

2. Model Coefficients

The Marigi et al. hazard ratios are univariate and come from a mixed primary shoulder arthroplasty cohort (hemiarthroplasty, aTSA, and rTSA together), not from procedure specific adjusted models. They are the only quantitative long horizon covariate evidence in the source studies. BMI, inflammatory arthritis, and prior surgery are collected for future model versions but currently have no effect on the result.

3. Statistical Method

The model runs a discrete time competing risk recursion in 1-year steps (the Beyersmann et al. formulation) to produce the Cumulative Incidence Function (CIF):

• Reoperation or revision hazard (h_R): for aTSA, each Schoch annual conditional probability p_k becomes a cause specific hazard through h = −ln(1 − p_k), then is scaled by 1.204 and multiplied by the composite covariate HR. For rTSA, a constant hazard h = −ln(1 − 0.044)/8 = 0.00563 is multiplied by the composite HR.
• Death hazard (μ_D): computed from the US Life Tables 2023 as μ = −ln(1 − q_x).
• CIF increment: CIF_R(t+1) = CIF_R(t) + S(t) × [1 − exp(−(h_R + μ_D))] × h_R / (h_R + μ_D).
• Overall survival: S(t+1) = S(t) × exp(−(h_R + μ_D)).
• Age input: a continuous integer used directly as the starting age for the recursion.
• Extrapolation: the aTSA branch holds a constant tail hazard (a 1.3 percent per year conditional failure) beyond year 20, in line with the reported post year 2 average. The rTSA branch keeps its constant hazard throughout, since the sources show no evidence of a declining late hazard.
• Terminal age: the recursion runs to age 100.

4. Plausibility Checks

• aTSA reference (female, age 65, no risk factors): remaining lifetime CIF near 25 percent. The baseline reproduces the conservative 20-year upper failure bound of 23.8 percent by construction; the extra point or so comes from tail hazard beyond year 20.
• rTSA reference (female, age 65, no risk factors): remaining lifetime revision CIF near 9 percent, reflecting the revision only endpoint and the lower constant hazard.
• Younger patients accumulate a higher lifetime CIF because they carry more years at risk.
• Older patients see a lower CIF because competing mortality absorbs at-risk time.

Each figure is a remaining lifetime probability, not a fixed horizon rate.

5. Limitations

• The aTSA and rTSA branches use different endpoints (any reoperation versus revision only), so the two results are not directly comparable.
• Covariate hazard ratios come from univariate analysis of a mixed primary shoulder arthroplasty cohort, not procedure specific adjusted models.
• BMI, inflammatory arthritis, and prior shoulder surgery lack quantitative long horizon effect estimates and are held neutral (HR = 1.0).
• Extrapolation beyond the observed follow up assumes a constant tail hazard with no decay.
• The output is a population level statistical estimate, not an individualized surgical prediction.

6. Bibliography

1. Schoch B, Werthel JD, Schleck CD, Harmsen WS, Sperling JW, Sanchez-Sotelo J, Cofield RH. Optimizing follow-up after anatomic total shoulder arthroplasty. J Shoulder Elbow Surg. 2017;26:997-1002.
2. Marigi EM, Alder KD, Yu KE, et al. Patient race and ethnicity are associated with higher unplanned 90-day ED visits and readmissions but not 10-year all-cause complications or reoperations. JSES Reviews, Reports, and Techniques. 2025;5:146-153.
3. Roche CP, Flurin PH, Wright TW, Zuckerman JD. Comparison of survivorship and failure modes between anatomic and reverse total shoulder arthroplasty across multiple government joint registries for a single platform shoulder system. Bull Hosp Jt Dis. 2023;81(2):141-150.
4. Floyd SB, Chapman CG, Thigpen CA, Brooks JM, Hawkins RJ, Tokish JM. Shoulder arthroplasty in the US Medicare population: 1-year evaluation of surgical complications, hospital admissions, and revision surgery. JSES Open Access. 2018;2:40-47.
5. National Center for Health Statistics. United States Life Tables, 2023. National Vital Statistics Reports.
6. Beyersmann J, et al. Competing Risks and Multistate Models with R. Springer, 2012.