Statistical analysis
Analyses were performed with SPSS software version 19.0 (SPSS Inc,
Chicago, Illinois, USA), except for the ROC contrast estimation, ROC
contrast test, and 80/20 split-sample cross-validation, which were
performed with SAS Proc LOGISTIC version 9.4 (SAS Institute Inc., Cary,
NC, USA). Normality of distribution was checked with the
Kolmogorov-Smirnov test. Normally distributed data were expressed as
mean ± standard deviation (SD) or 95% Confidence interval (CI).
Non-normally distributed data were expressed as
median and
interquartile ranges (IQR). The
coefficient of variance (CV) was calculated for each continuous
variable. Fisher’s exact test was to analyze intergroup differences for
discontinuous variables. The Mann-Whitney test was performed for the
intergroup comparisons for continuous variables. The association between
different variables was decided by Spearman correlation, since the
Gaussian Approximation was proved for analyzed variables.
The 2 independent variables of interest were assessed by their marginal
effects on the response in a logistic regression model. The prediction
performance of each variable was measured as the AUC of the ROC derived
from the logistic regression models. Furthermore, a multiple logistic
model of the 2 variables was fitted, and the resultant AUC of this
multiple logistic model was used as a measure of the joint prediction
performance. We use the chi-square test proposed by DeLong et al to
determine whether the multiple logistic model would significantly
improve the prediction performance, defined as the AUC, relative to the
marginal models.19
We used MCH bronchial provocation tests as the gold standard for
defining BHR. The optimal value of the single measurement giving the
highest sum of BHR diagnostic sensitivity and specificity was used as a
cut-off value.20-21 Positive predictive values (PPV),
negative predictive values (NPV), and percentages correctly classified
(PCC) were calculated for each cut-off value.22-23 The
corresponding odds ratios, CI, and P values were also calculated.
Continuous
variables were converted to dichotomous-state variables on the basis of
the cut-off values. Subsequently, ROC curves were determined for the
joint models with the dichotomous-state variables.
We constructed and examined all models to predict BHR with repeated
five-fold cross-validation (5 repeats), which partitions the original
sample into 5 disjoint subsets, uses 4 of those subsets in the training
process, and then makes predictions about the remaining subset. The
average AUC of 5 different cross-validation models and the whole-model
AUC using the entire data set were calculated. The Error Rate equals abs
(Average AUC – Whole Model AUC)/(Whole Model AUC). Accurate
classification was also calculated for the test subset.
The threshold for statistical significance for all analyses was set atP < .05.