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Foot & Ankle International 40(9)
data treatment (n=107) and no missing data treatment, are
reported for the logistic regression of the score (n=91).
The data were processed using Stata, version 11.2
(StataCorp LP, College Station, TX).

Results

Figure 4.  Flowchart showing the patient exclusion criteria and
the number of patients available for analysis. TTA, talar tilt angle.

In addition, the likelihood ratio and Wald chi-square were
used to select the final model. Hazard ratios and the P values are reported. After the model was created, a test of proportional hazards assumption (ph-test) was performed and
considered acceptable if the probability was greater than
.15 (P > .15).
All significant variables included in the multivariate
survival model were used to construct a score. The value
of 1 was assigned if the risk variable was present; otherwise, it was assigned a value of 0. A binomial regression
analysis was used to determine if the score should be
weighted. Given that the odds ratio of the independent
variables was similar with respect to the score, a nonweighted score was constructed. Then a univariate Cox
proportional hazards model was estimated, using the
score as the independent variable. Additionally, the phtest was performed after this model, and considered
acceptable if probability was greater than 0.15 (P > .15).
The power (1 - β) was calculated by a Wald test for a
Cox proportional hazards model.
Finally, a univariate logistic regression model was
estimated using failure as the dependent variable and the
score as the independent variable. Then, a receiver operating characteristic (ROC) curve was calculated and
interpreted according to Hosmer and Lemeshow's recommendations.19 For internal validation of our predictive
score, bootstrap (200 replicates) and jackknife estimations were utilized. The probability of failure by each
outcome of the score is reported with confidence intervals of 95%.
No missing data were found in the failure group for the
variables included in the score (n=12/107), but 16 missing
were found in the control group. Using missing imputation, values were estimated by linear regression and multivariate normal regression. Both results, with missing

A total of 107 TAA (104 patients) met the inclusion criteria;
85 Hintegra and 22 Infinity TAA (Figure 4). Twelve patients
(11%) had a TAA failure: 11 patients were revised for aseptic loosening and 1 for periprosthetic infection. The median
follow-up was 49 months (18-131 months), the total time at
risk was 503 years, and the median time to failure was 40
months (24-114 months) (Figure 5). All radiographic measurements demonstrated at least fair reliability (T-T ratio),
but most of them showed good to excellent, inter- and intraobserver reliability (see Table 2).
The results of the univariate analyses are summarized in
Table 3. The preoperative AOS score greater than 63, "normal" gamma angle, and previous SF-36 were the significant
variables.
After the multivariate analysis, 4 variables were found
to have a probability less than .10 to predict failure: the
presence of diabetes mellitus (DM), a baseline AOS score
>63, a gamma angle >19 degrees, and a T-T ratio <0.32
or >0.39 (see Table 4). This model with 4 variables has
an acceptable prediction power with a Harrell C of 88%
or Somers D of 75%.36 Compared with a model that
included only DM and baseline AOS scores, the model
with the 4 variables in it was significantly better by loglikelihood ratio test (P = .01) and Wald χ2 test (P = .05).
Because of these results, the model with 4 variables was
kept. As such, a predictive score was developed using
these 4 variables and the above values that were associated with failure. The value of 1 was assigned if the risk
variable was present; otherwise, it was assigned a value
of 0. For example, a patient with DM who had an AOS
score before surgery of 30 and a gamma angle of 15
degrees and a T-T ratio of 0.30 scores 2 points (1+0+0+1).
The binomial regression showed equivalent odds ratio for
each variable of the score, so no factor was added to the
sum of each variable (Table 5). The predictive score has a
hazard ratio of 10.51 (2.57-42.94), a ph-test of 0.21, and
a power (1 - β) of 0.93.
The probability of TAA failure in the time studied, for
each possible value of the score in this predictive model
was obtained by a logistic regression with 200 replicates
bootstrap estimation and 89 Jackknife replicates (Figure 6).
The ROC curve is shown in Figure 7, the area under the
ROC curve was 0.83 (0.71-0.94), which is considered "very
good" discrimination according to Hosmer and Lemeshow.19
Also, the probabilities with missing data imputation are
shown in Figure 6.
Foot & Ankle International - September 2019

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