. 2022 May 28;4(3):100281. doi: 10.1016/j.ocarto.2022.100281

Table 3.

Estimated probability of total knee replacement (TKR) at five years.

Probability of TKR at five years	$= 1 - exp (- exp (X_{J} β) \cdot \int_{0}^{5} {\bar{λ}}_{1,0} (s) d s)$
$X_{J} β$	= 0.51∗Age-0.0039∗Age²+0.41∗Prescribing_OA_medication-0.14∗CCI_condition_count-0.14∗Mental_health_condition+0.97∗Past_knee_replacement+ 0.93∗Other_knee_surgery Where, Age is in years (range between 45 and 113) Prescribing_OA_medication = 1 if prescribed an OA medication in the year prior to baseline and 0 otherwise, CCI_condition_count = count of chronic conditions listed in the Charlson comorbidity index (range between 0 and 8), Mental_health_condition = 1 if recording of a mental health condition and 0 otherwise, Past_knee_replacement = 1 if history of previous TKR and 0 otherwise, Other_knee_surgery = 1 if history of past knee surgery (excluding TKR) and 0 otherwise.
$\int_{0}^{5} {\bar{λ}}_{1,0} (s) d s$	= baseline cumulative subdistribution hazard at five years = 5.6 × 10⁻⁹

Probability of TKR at five years

= 1 - exp (- exp (X_{J} β) \cdot \int_{0}^{5} {\bar{λ}}_{1,0} (s) d s)

X_{J} β

= 0.51∗Age-0.0039∗Age²+0.41∗Prescribing_OA_medication-0.14∗CCI_condition_count-0.14∗Mental_health_condition+0.97∗Past_knee_replacement+
0.93∗Other_knee_surgery
Where,
Age is in years (range between 45 and 113)
Prescribing_OA_medication = 1 if prescribed an OA medication in the year prior to baseline and 0 otherwise,
CCI_condition_count = count of chronic conditions listed in the Charlson comorbidity index (range between 0 and 8),
Mental_health_condition = 1 if recording of a mental health condition and 0 otherwise,
Past_knee_replacement = 1 if history of previous TKR and 0 otherwise,
Other_knee_surgery = 1 if history of past knee surgery (excluding TKR) and 0 otherwise.

\int_{0}^{5} {\bar{λ}}_{1,0} (s) d s

= baseline cumulative subdistribution hazard at five years
= 5.6 × 10⁻⁹

AbbreviationsTKR = total knee replacement; OA = osteoarthritis; CCI = count of conditions from the Charlson Comorbidity Index; and “exp” = exponential function.