Total Shoulder Replacement Failure Calculator

1. Evidence Extraction & Model Rationale

• aTSA baseline (any reoperation): annual conditional reoperation probabilities from Schoch et al. (2017), a large single-institution aTSA series (2,786 cases; 208 reoperations; 7.5 %) with year-by-year conditional failure probabilities through 21 years. After year 2, the average failure rate leading to reoperation is ~1.1 %/year. Hazards are uniformly scaled by a factor of 1.204 to match the lower 95 % CI survivorship at year 20 (S₂₀ = 76.2 %; upper-plausible 20-year failure = 23.8 %).
• rTSA baseline (revision-only proxy): no rTSA-specific “any reoperation” long-horizon baseline was identified in the evidence sources. The rTSA branch therefore uses a constant annual revision hazard derived from Roche et al. (2023): 8-year cumulative revision rate of 4.4 % for primary rTSA across multiple government joint registries. This is explicitly labeled as a revision-only proxy; actual reoperation risk may exceed this estimate.
• Conservative design: covariate HRs use the upper 95 % CI for a conservative upper-plausible estimate. Age is entered as a continuous value (slider or number input) and used directly in the model.

2. Model Coefficients

Marigi et al. HRs are univariate and from a mixed primary shoulder arthroplasty cohort (hemi, aTSA, rTSA), not procedure-specific adjusted models. They are the only quantitative long-horizon covariate evidence available from the source studies. BMI, inflammatory arthritis, and prior surgery inputs are collected for future model versions but currently have no effect.

3. Statistical Method

A discrete-time competing-risk recursion (1-year steps, Beyersmann et al. formulation) calculates the Cumulative Incidence Function (CIF):

• Reoperation/revision hazard (h_R): for aTSA, the Schoch annual conditional probability p_k is converted to a cause-specific hazard via h = −ln(1 − p_k), then 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 used, multiplied by the composite HR.
• Death hazard (μ_D): derived from US Life Tables 2023 via μ = −ln(1 − q_x), providing the proper cause-specific mortality hazard.
• 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: age is entered as a continuous integer and used directly as the starting age for the recursion.
• Extrapolation: aTSA uses a constant tail hazard (1.3 %/year conditional failure) beyond year 20, consistent with the reported post-2-year average. rTSA uses constant hazard throughout (no evidence of declining late hazard).
• Terminal age: recursion runs to age 100.

4. Plausibility Checks

• aTSA reference (Female, age 65, no risk factors): remaining-lifetime CIF ≈ 25 %. The aTSA baseline reproduces the conservative 20-year upper failure bound of 23.8 % by construction; the additional ~1 % comes from tail hazard beyond year 20.
• rTSA reference (Female, age 65, no risk factors): remaining-lifetime revision CIF ≈ 9 %, reflecting the revision-only endpoint and lower constant hazard.
• Younger patients accumulate higher lifetime CIF due to more years at risk.
• Older patients have lower CIF due to competing mortality.

These figures represent the remaining-lifetime probability, not a fixed-horizon rate.

5. Limitations

• The aTSA and rTSA endpoints differ (any reoperation vs. revision-only), limiting direct comparison between branches.
• Covariate HRs are from univariate analysis on 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 set to neutral (HR = 1.0).
• Extrapolation beyond observed follow-up assumes constant tail hazard (no decay).
• The model produces 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.