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.