^{1}

^{2}

^{2}

^{2}

^{2}

If a surgeon performs 200 procedures per year, he/she will have to see 800 patients for follow-up by year 5 and 1300 patients per year by year 10. Normal time constraints make this implausible. When do total hip arthroplasty (THA) patients have the greatest need for follow-up? We reviewed 8331 primary THAs to determine the greatest risk of failure across time. Patients failed with the greatest ratio at 1 year or earlier, followed by 10 and 12 years postoperatively. The median time to failure for all hips was 8.8 years, the average time to failure was 9.2 years, and 75% of failures occurred by 13.0 years. The most common failure mechanisms were due to the cup (5.0%), dislocation (3.2%), cup and stem (1.7%), infection (0.4%), and the stem (0.4%). Based on the most common failure mechanisms, it is recommended to evaluate patients at the 6 months, 1 year, 3 years, 7 years, 10 years, 12 years, 18 years, and 25 years postoperatively.

The Number of total hip arthroplasty (THA) is expected to rise dramatically and, in fact, is already beginning to do so, as a greater portion of the patient population ages [

One method of alleviating this impending strain on clinical practice is to limit follow-up to time periods when THAs are experientially most likely to fail. Development of such a schedule requires an analysis of the time patients are most at risk for failure for various modalities, including polyethylene wear and osteolysis, infection, instability, pain, fracture, loosening, collapse, and dislocation. The optimal follow-up interval after total knee arthroplasty was determined previously after the review of knee records [

Between January 15, 1973 through May 9, 2012, 11,336 THAs were performed at our center. Of these, 9939 (87.7%) were primary operations. 1131 hips were completely lost to follow-up, leaving 8331 primary total hip arthroplasties (THAs) performed on 6769 patients with postoperative follow-up.

There were 3725 females (55.0%) in this patient population, the average age was 66.2 years (S.D. 12.0, range 17 - 96 years), and the average preoperative body mass index was 30.1 kg/m^{2} (S.D. 5.8, range 16.5 - 60.3 kg/m^{2}). Osteoarthritis was the diagnosis in 5.910 patients (87.3%), osteonecrosis in 417 patients (6.2%), rheumatoid arthritis in 183 patients (2.7%), osteoporosis in two patients (0.03%), and other diagnoses in 257 patients (3.8%). Patients were followed for an average of 7.9 years (S.D. 4.8, range 0.1 - 37.3 years). There were 1826 staged bilateral (21.9%), 1298 simultaneous bilateral (15.6%), and 5207 unilateral (62.5%) THAs in this population.

The authors began their analysis with determining the Kaplan-Meier survivorship results for the entire patient population and for each possible failure mechanism or endpoint (infection, fracture, dislocation, radiolucency, stem failure, cup failure, overall aseptic loosening, polyethylene wear, and death). For each group, the authors also examined the average, median, and interquartile ranges of the time to failure. Results of these analyses appear in

Based on the data above, the authors endeavored to identify when patients are most at risk for failure by quantifying the conditional probability of failure at each one-year interval (

Failure Mechanism | n count | mean (yrs) | min. | Q1 (25%) | median (50%) | Q3 (75%) | max. (100%) | Percent |
---|---|---|---|---|---|---|---|---|

Revision Cup & Stem | 145 | 11.9 | 0.0 | 7.7 | 11.1 | 15.3 | 27.7 | 1.7% |

Dislocation (revised or not) | 270 | 1.9 | 3.2% | |||||

Infection | 30 | 2.8 | 0.0 | 0.2 | 1.1 | 3.3 | 18.4 | 0.4% |

Revision Cup | 412 | 9.4 | 0.0 | 5.1 | 9.2 | 13.2 | 27.9 | 4.9% |

Revision Stem | 29 | 5.3 | 0.0 | 2.6 | 4.9 | 6.8 | 11.0 | 0.3% |

Revision Poly Wear | 4 | 11.7 | 10.8 | 10.9 | 11.4 | 12.4 | 13.0 | 0.0% |

Fracture | 6 | 7.6 | 14.4 | 0.1% | ||||

Death | 2786 | 10.0 | 0.0 | 5.1 | 9.0 | 13.8 | 37.3 | 33.4% |

Any revision | 694 | 9.2 | 6.1 | 4.7 | 8.8 | 13.0 | 27.9 | 8.3% |

Non-fail | 7637 | 7.0 | 0.0 | 2.1 | 5.5 | 10.2 | 37.3 | 91.7% |

Equation (1). Kaplan-Meier procedure. Here:

_{i}

i = time in integer years

j = an event occurring at integer or decimal years

d_{j} = hips failed during event j

n_{j} = hips present just prior to event j

Equation (2). Actuarial or life table procedure. Here:

t_{i} = time interval just prior to current time t

n_{i} = hips present at beginning of t_{i}

d_{i} = hips failed or in patients who die within t_{i}

From the actuarial equation (Equation (2)), the authors could determine_{i} (Equation (3)).

Equation (3). Conditional probability of failure. Here:

_{i}

d_{i} = hips failed or deceased within t_{i}

n_{i} = hips present at beginning of t_{i}

When the q_{i} values for each endpoint at each time interval are examined, it is possible to determine when most endpoint events will occur, as represented by a peak or peaks (also known as local maxima) of

Equation (4). Follow-up load per time period. Here:

_{i }

t = time interval just prior to the current time interval t_{i} (at the authors’ center, either 6 months or 1, 3, 5, 7, 10, 12, 15, 17, 20, 22, or 25 years)

N_{t} = new THAs performed during t_{i} requiring post-op follow-up

D_{t} = hips in patients who die during t_{i}

F_{t} = aseptic failures during t_{i}

I_{t} = infections during t_{i}

… = other failure mechanisms

The peaks in conditional probability can be mathematically derived by taking the first derivative of the best fit curve of these possibilities over time. This best fit curve can provide the closest approximation with a balance of simplicity by using a cubic polynomial equation (a function with a polynomial of degree three). In the authors’ analysis, this best-fit curve is expressed in Equation (5):

Equation (5). Cubic polynomial equation of the best-fit curve for conditional probabilities. Here, a, b, c, and d can be determined by common graphics or spreadsheet software; the authors used matrix algebra similar to that used in linear regression.

The first derivation of Equation (5) results in Equation (6):

Equation (6). Quadratic polynomial equation, the first derivative of Equation (5).

Setting this equation equal to zero, it is possible to determine the local maxima and minima of the original conditional probability equation (Equation (5)), and thus the time intervals that exhibit the highest and lowest probabilities of failure. The zeros of this equation can be determined through the quadratic formula, Equation (7):

Equation (7). Quadratic formula for determining maximum conditional probabilities of reaching an endpoint, whether failure or death. Here, a, b, and c are found in Equation (6).

The most common failure mechanisms in group of 8331 THAs were acetabular cup failure only (5.0% of total population), dislocation (3.2%), cup and stem failure (1.7%), infection (0.4%), and femoral stem failure only (0.4%).

As a population, the proportion of hip failures peaked at 10 years and at the subsequent two follow-up periods (

As can be seen in

Time Interval | Failures | n remaining | Failure rate from actual count | Conditional probability of failure | Failure rate out of max. possible | Maximum number of THAs remaining |
---|---|---|---|---|---|---|

6 months | 57 | 8299 | 0.7% | - | 0.6% | 9943 |

1 year | 9 | 7921 | 0.1% | 0.9% | 0.1% | 9943 |

3 years | 58 | 7129 | 0.8% | 0.5% | 0.7% | 8847 |

5 years | 64 | 5900 | 1.1% | 0.7% | 0.8% | 8068 |

7 years | 82 | 4753 | 1.7% | 0.8% | 1.1% | 7305 |

10 years | 129 | 3650 | 3.5% | 1.6% | 2.1% | 6166 |

12 years | 94 | 2348 | ^{* } | 2.5% | 1.7% | 5439 |

15 years | 78 | 1652 | ^{* } | ^{* } | 1.7% | 4537 |

17 years | 42 | 948 | ^{* } | ^{* } | 1.1% | 3903 |

20 years | 41 | 604 | ^{* } | ^{* } | 1.4% | 3016 |

22 years | 17 | 299 | ^{* } | ^{* } | 0.8% | 2035 |

25 years | 17 | 175 | ^{* } | ^{* } | 0.9% | 1823 |

25^{+} years | 6 | 94 | ^{* } | ^{* } | 0.4% | 1652 |

^{*}Omitted since failure is overestimated due to follow-up rate, we referred to determine max possible failure rate to peak rate. -: conditional probability of failure was annual for this comparison.

mean of 5.3 years, and 75% of failures occurred by 6.8 years; acetabular cup failures occurred at a median of 9.2 years and an average of 9.4 years, and 75% of failures occurred by 13.2 years; polyethylene wear failures occurred at a median of 11.4 years and a mean of 11.7 years, and 75% of failures occurred at 12.4 years; and infection occurred at a median of 1.1 years and a mean of 2.8 years, and 75% of failures occurred by 3.3 years.

Based on the most common failure mechanisms, the data suggest that the overall THA patient population should be seen at 6 months, 1 year, 3 years, 7 years, 10 years, 12 years, 18 years, and 25 years after the index surgery. This schedule would cut nearly in half the follow-up schedule used currently by the authors at their center while still allowing for sufficient opportunity to monitor for expected failures.

The number of primary and revision total hip and knee arthroplasties is expected to rise dramatically as more patients wish to remain active [

The authors found data that support a revised schedule of follow-up for total hip arthroplasty that maximizes the gathering of relevant patient data while minimizing the number of follow-up appointments required of the typical THA patient. The data apply to the patient population as a whole; while further research may support the need for specific schedules for certain patients, the data here do not confer a predictive power on early (6 months to 1 year) increased pain or higher BMI (>41 kg/m^{2}).

Of concern for clinical research is the loss of potentially valuable follow-up data if the contracted observation schedule proposed above is adopted. Total hip arthroplasty has enjoyed highly satisfactory rates of success since their establishment and throughout their development [hip survivorship papers], but specific issues such as the most advantageous surgical approach remain unresolved due to a lack of solid data favoring one option over the others [

This trove of clinical information, however, must be balanced with the demands of data gathering on large surgery centers. The proposed schedules are an attempt to balance between monitoring changes and differences in large patient populations and allowing surgeons to continue to meet the surgical demands of their patients without an inhibitively large follow-up caseload. These findings aim to assist the clinician in using follow-up resources at the most relevant points, allowing for a full, yet efficient, postoperative analysis of the patient.

This follow-up schedule is unique to THA and should not be applied to practice in total knee arthroplasty (TKA). A study at the authors’ center, concurrent with the present analysis, of optimal follow-up intervals following total knee arthroplasty found predictive value in the 6-month pain subscore and in preoperative BMI reported as previously [^{2}, contrary to the predictive value that may be found in TKA. Early follow-up, however, should by no means be sacrificed to aid in decreased workload. These data points can help the evaluating surgeon anticipate future actions; these periods are also known intuitively to assist in monitoring for deep periprosthetic joint infection [

The proposed decrease in frequency of follow-up in clinic after total hip arthroplasty may, if the operating surgeon desires, be supplemented with questionnaires given over the phone. The Oxford, WOMAC, and SF-36 forms have been validated for such use [

This study is, to the authors’ knowledge, the first to propose efficient schedules of follow-up based on data from such a large sample of total hip arthroplasties. The findings here are valuable for both small community hospitals and large joint specialty centers, as both will find increasing populations of patients requiring hip replacement and will need to manage finite resources of personnel and time.

There are some limitations in the current study. First, it was not a prospective study and there were wide ranges of prosthesis including different sizes of cups, femoral stems and liners. Second, the committed surgeons were similar and rarely changed but were not exactly the same. This study was performed at one large surgery center with a relatively stable patient population, so its proposals may need to be adapted for tertiary care centers whose patients do not reside in the surrounding area and for whom attendance at follow-up is more difficult than it is for our population. This limitation mostly applies to the necessity of early follow-up, however, as the longer intervals between later follow-up periods would allow for greater flexibility for those patients who require follow-up but reside far from the clinic.

These findings, while important to the study of effective follow-up for patient populations, should be verified by clinicians in other practice settings. In addition, studies involving further variables, such as age at time of surgery, extent of arthritic damage, gender, and diagnosis, may determine other schedules that the current study did not elucidate. The results and conclusions made here provide a stable foundation for future work that may provide even more personalized schedules of follow-up so that clinical resources are expended with greater efficiency and greater benefit to the patient.

John B.Meding,Merrill A.Ritter,Kenneth E.Davis,AlexFarris,TatsuyaSueyoshi, (2015) Meeting Increased Demand for THA and Follow-Up: An Actuarial Method to Determine Optimal Follow-Up Schedules. Open Journal of Orthopedics,05,245-252. doi: 10.4236/ojo.2015.58033