Monitoring the one year postoperative infection rate after primary total hip replacement

Abstract

Purpose

Infection of a total hip replacement is potentially a devastating complication. Statistical process control methods have been generating interest as a means of improving the quality of healthcare, and we report our experience with the implementation of such a method to monitor the one year infection rate after primary total hip replacement.

Method

Infection was defined as the growth of the same organism in cultures of at least two aspirates or intra-operative specimens, or growth of one pathogen in a patient with local signs of infection such as erythema, abscess or draining sinus tract. The cumulative summation test (CUSUM test) was used to continuously monitor the one year postoperative infection rate. The target performance was 0.5% and the test was set to detect twice that rate.

Results

Over the three year study period, 2006 primary total hip replacements were performed. Infection developed within one year after surgery in eight (0.4%) hips. The CUSUM test generated no alarms during the study period, indicating that there was no evidence that the process was out of control.

Conclusion

The one year infection rate after primary total hip replacement was in control. The CUSUM test is a useful method to continuously ensure that performance is maintained at an adequate level.

Appendix

The CUSUM test¹ (cumulative summation test) was used to monitor the infection rate after primary total hip replacement (THR). The CUSUM sequentially tests after each observation X _t (t > 0) the following hypothesis H₀: λ = λ₀, i.e. the process is in control, versus H₁: λ≠ λ₀, i.e. the process is out of control. The value λ₀ is referred to as the target infection rate in this report. The test is based on the statistic S _t computed after each observation X _t as:

$$ {S_t} = { \max }(0,{S_{{t - {1}}}} + {W_t}),{S_0} = 0, $$

(1)

where the sample weight W _t depends on the observation X _t , λ₀, and rate ratio (RR) (see Eq. 2). The test statistic S _t is compared with a predefined limit, h. If S _t equals or exceeds h, the null hypothesis is rejected. In quality control wording, the CUSUM test is said to emit an alarm indicating that the process is out of control. As long as S _t remains below h, the null hypothesis cannot be rejected, and monitoring continues under the assumption that the process is in control. In this report, a CUSUM for time to event data based on a Poisson distribution was chosen, with the following sample weight:

$$ {W_j} = {O_j}{ \log }\left( {\text{RR}} \right) - \left( {{\text{RR}} - {1}} \right){E_j}, $$

(2)

where O _j represents the number of THR infection observed on interval j, E _j (see Eq. 3) represents the number of THR infection expected on interval j under the null hypothesis of an infection rate of λ₀, and RR represents the rate ratio defining the smallest unacceptable increase in the infection rate relative to the target that one wants to detect.

E _j is defined as:

$$ Ej = {\lambda_0}\sum\limits_{{i = 0}}^n {{t_i}}, $$

(3)

where t _i is the length of time that a patient i remains infection free during the interval before censoring.

The CUSUM test has a particular feature: it has a holding barrier at zero and can never accept the null hypothesis. Therefore, theoretically, regardless the true performance of the process under observation, type I and type II errors of the test are 100% and 0%, respectively, and performances of CUSUM tests are expressed differently, namely, with the true and false discovery rates (TDR and FDR). These rates correspond to the probability of an alarm to be emitted under the alternative and null hypotheses, respectively, within a defined number of observations². Also, because of that holding barrier at 0, the score S _t cannot deviate too far from the decision limit over long periods without any infection, and it remains responsive at all times to a sudden increase in the infection rate.

In our study, the target infection rate (process in control) chosen was λ₀ = 0.5%, and the RR to detect was  two; the out-of-control infection rate was therefore 1%. A limit, h = 2.5 ,was determined based on computer simulations (10,000 samples) to yield a false discovery rate of 9.9% and a true discovery rate of 75% over five years of monitoring.

References

1. Page ES. Continuous inspection schemes. Biometrika 1954;41: 100–115.

2. Marshall C, Best N, Bottle A, Aylin P. Statistical issues in the prospective monitoring of health outcomes across multiple units. J Roy Stat Soc A 2004;167: 541–559.