Statistical analysis
To evaluate the learning curve of robot-assisted laparoscopy, a
risk-adjusted cumulative sum (RA-CUSUM) statistical analysis was
performed. The cumulative sum (CUSUM) procedure has been validated to
monitor surgical outcomes and is able to detect small changes over time
in the surgical performance.25,26 The RA-CUSUM is an
extension of this statistical method by adjusting for each patient’s
individual risk of surgical failure through the use of a
likelihood-based scoring method25. We defined surgical
failure as cervical cancer recurrence. As the estimated risk of
recurrence varies among patients, a multivariate risk adjustment is
essential. The probability of recurrence for each patient was modelled
by a logistic regression analysis. The variables included in the risk
model were based on prior results.27 We limited this
model to 3 degrees of freedom to prevent overfitting. Sensitivity
analyses with different models were tested in the RA-CUSUM to ensure
that the presented data is robust.
The RA-CUSUM chart plots the function:
\begin{equation}
{\left(1\right)\text{\ \ \ X}}_{t}=\max{\ \left(0,X_{t-1}+\ W_{t}\right),\ \ t=1,2,3,\ldots}\nonumber \\
\end{equation}Where \(X_{0}=0\) and \(W_{t}\) is the weight assigned to the \(t\)he
procedure. In this study, each value of \(t\) corresponds to a new
patient receiving a robot-assisted procedure. The weights \(W_{t}\ \)are
given by:
\begin{equation}
(2)\ \ \text{\ W}_{t}=\left\{\begin{matrix}\log\left[\frac{1-p_{t}+R_{0}p_{t}}{1-p_{t}+R_{A}p_{t}}\right]\text{\ \ if\ patient\ t\ develops\ no\ recurrence}\\
\log{\left[\frac{(1-p_{t}+R_{0}p_{t})R_{A}}{(1-p_{t}+R_{A}p_{t})R_{0}}\right]\text{\ \ }}\text{if\ patient\ t\ develops\ recurrence}\\
\end{matrix}\right.\ \nonumber \\
\end{equation}Where \(p_{t}\) is the probability of recurrence for each patient
calculated from the probability of recurrence model;\(\ R_{0}=1\)represents the odds ratio under the null hypothesis; \(R_{A}\)represents the odds ratio under the alternate hypothesis. Following
Steiner et al. we used two RA-CUSUM procedures.25 The
first, here referred to as RA-CUSUM+, is designed to detect a doubling
of the odds of recurrence (\(R_{A}=2\)). The second one, here referred
to as RA-CUSUM-, is designed to detect a halving of the odds of
recurrence (\(R_{A}=0.5\)) (based on a similar analysis in
robot-assisted hemicolectomy by Parisi et al.28).
Both RA-CUSUM procedures can be presented in one plot, with RA-CUSUM+
plotting the function \(\mathrm{X}_{\mathrm{t}}\) as described above
(1), and RA-CUSUM- plotting the function:
\begin{equation}
\left(3\right)\text{\ \ \ }Z_{t}=\min{\ \left(0,Z_{t-1}-\ W_{t}\right),\ \ t=1,2,3,\ldots}\nonumber \\
\end{equation}Where \(Z_{0}=0\) and \(W_{t}\) is provided by the formerly described
function (2).
To summarise, the RA-CUSUM plots the difference between the cumulative
expected occurrence of an event (here: recurrence) and the actual
observation. In the upper RA-CUSUM+ chart, the curve moves up for every
case with recurrence and down for every case without recurrence. The
magnitude by which the line ascends or descends is determined by the
difference between the observed and expected probability of recurrence.
For instance, if a patient modelled as having a high probability of
recurrence subsequently develops a recurrence, the curve ascends less
(i.e. small penalty) than it would if a recurrence is diagnosed in a low
risk modelled patient (i.e. larger penalty). In the lower RA-CUSUM-
chart, surgical success is indicated by a negative drift of the curve.
Based on the RA-CUSUM plot, the “learning phase” of robot-assisted
laparoscopy at our institution was determined. The procedures performed
during this first phase were compared with the rest of the procedures
performed thereafter. The Statistical Package for the Social Sciences
version 25.0.2 (SPSS; International Business Machines, Armonk, NY USA)
was used for modelling analysis and the RA-CUSUM analyses were performed
using Microsoft Excel 2010 for Windows. As we performed an
intention-to-treat analysis, cases where radical hysterectomy was
aborted because of positive lymph nodes were included in the analysis.
Comparisons of continuous variables were conducted using the
Mann-Whitney U test. Categorical data were reported as proportions and
compared between groups using χ2-test or Fisher exact
test as appropriate.
Survival curves for both groups were estimated using Kaplan Meier method
and differences between the two groups were compared using log-rank
test. Statistical tests were two-sided with significance set at P< 0.05, with confidence intervals (CI) at the 95% level.