M.F. Schinsky, C.J. Della Valle, S.M. Sporer, and W.G. Paprosky reply:
We appreciate the insight shared on our recent article, "Perioperative Testing for Joint Infection in Patients Undergoing Revision Total Hip Arthroplasty." We regret any confusion related to the set of statistical parameters that we presented in Tables IV and V (i.e., sensitivity, specificity, positive predictive value, negative predictive value, and accuracy). In Table IV, the parameters of concern corresponded to the dichotomy of synovial fluid white blood-cell counts at a cut-point of >4200, the value that maximized the magnitudes of statistical parameters when cross-classified erythrocyte sedimentation rate and C-reactive protein information was ignored. Similarly, in Table V, the parameters of concern corresponded to dichotomies of synovial fluid white blood-cell counts at cut-points of >3000 and >9000, values that corresponded to maxima in statistical parameters for the respective groups: (1) all patients (n = 79) who had both an elevated erythrocyte sedimentation rate (>30 mm/hr) and an elevated C-reactive protein level (>10 mg/L) and (2) all patients (n = 60) with an elevated erythrocyte sedimentation rate (>30 mm/hr) who did not have an elevated C-reactive protein level (=10 mg/L) combined with all patients with an elevated C-reactive protein level (>10 mg/L) who did not have an elevated erythrocyte sedimentation rate (=30 mm/hr).
The analysis subgroups that are summarized in Table V are defined on page 1873 of our paper. Results from a third group of patients, those with an erythrocyte sedimentation rate and C-reactive protein levels at or below elevation (=30 mm/hr, =10 mg/L) were excluded as there were no infections in that group.
We reported that a synovial fluid white blood-cell cut-point of >3000 maximized the statistical parameters for the group with elevations in both erythrocyte sedimentation rate and C-reactive protein level. This cut-point was lower than the "marginal" synovial fluid white blood-cell cut-point of >4200. For the group with elevations in erythrocyte sedimentation rate or C-reactive protein level (but not both), we reported that a synovial fluid white blood-cell cut-point of >9000 maximized the statistical parameters. Thus, the synovial fluid white blood-cell cut-point decreased going from an elevation of erythrocyte sedimentation rate or C-reactive protein level to an elevation of both erythrocyte sedimentation rate and C-reactive protein level (e.g., going from "or" to "and"). As there was no benefit in considering white blood-cell count in patients without erythrocyte sedimentation rate and C-reactive protein level elevations, differential dependencies between erythrocyte sedimentation rate, C-reactive protein level, and white blood-cell count support the need for sequential preoperative testing of the erythrocyte sedimentation rate and C-reactive protein level, followed by the synovial fluid white blood-cell count.
We viewed the infection rates at synovial fluid white blood-cell counts of >3000 and >9000 in the absence of erythrocyte sedimentation rate and C-reactive protein level to be unnecessary, holding a view similar to that expressed by McCullagh and Nelder1 on "nuisance parameters." We thought that these parameters were largely irrelevant to the conclusions. When the synovial fluid white blood-cell count was examined independently of the erythrocyte sedimentation rate, C-reactive protein level, and other clinical parameters, we chose to report the parameters at a cut-point of >4200, the cut-point at which statistical parameters were at maxima (Table IV in our study).
We provide the summaries of statistical parameters at synovial fluid white blood-cell cut-points of >3000 and >9000 in Table I of this letter.
Given the group definitions provided, the marginal statistical parameters provided in Table I of this letter cannot be compared against the statistical parameters that we presented in Table V of our study. This is because the summaries that we present in Table I of this letter include patients both without an elevated erythrocyte sedimentation rate and without an elevated C-reactive protein level. The addition of these patients has increased misclassification and has led to lower statistical parameters. This explains why a seemingly "paradoxical" increase in statistical parameters was obtained in stratified analyses.
We appreciate Dr. Liao's and Dr. Lin's concern regarding the statistical parameters that we presented in Table VI of our study. That table contained errors that were missed during review. We provide corrections in Table II of this letter.
During our further review of this manuscript, two additional areas for clarification were identified. First, the units for the synovial fluid white blood cell count were reported as being measured per mL (milliliter), when in fact the accurate label is per µL (microliter). The second correction is regarding the units reported for the C-reactive protein level; these were reported in our manuscript as mg/dL, when in fact the appropriate label is mg/L. We apologize for these oversights.
The additional information provided in Table I of this response and the corrections to Table VI of our study (provided in Table II of this response) do not affect our original conclusions. We maintain that a synovial fluid cell count of >3000 white blood cells/µL was the most predictive perioperative testing modality for determining the presence of periprosthetic infection when combined with an elevated preoperative erythrocyte sedimentation rate and C-reactive protein level in patients undergoing revision total hip arthroplasty.