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Authors’ Reply

Sir,

We thank Dr Philopoulos1 for his interest in our article on predicting the risk of operative delivery in labouring women with a singleton term pregnancy in cephalic presentation. We developed two models to simultaneously predict the probability of five possible outcome states: spontaneous vaginal delivery (1), instrumental vaginal delivery due to suspected fetal distress (2) or failure to progress (3), and caesarean delivery due to suspected fetal distress (4) or failure to progress (5).2 The models included antepartum characteristics only (model 1) and both antepartum and intrapartum characteristics (model 2). We would like to address the two questions posed by Philopoulos: first, whether there was a near-significant nonlinear relationship between birth weightand caesarean section for failure to progress; and second, on what was the order of imputation and bootstrapping based?

It is known that caesarean section rates at least double at birthweights >4500 g compared with birthweights <4500 g.3 We observed up to a three-fold increase in rates of caesarean sections: 27% of caesarean sections with a failure to progress indication in the birthweights >4500 g and only 9% in birthweights >4500 g. In the prediction models, however, expected birthweight was not included as a binary variable (e.g. <4500 g versus ≥4500 g), but was included as a continuous predictor assuming a linear relation with the outcome. Deviations from this assumption were explored using restricted cubic spline analysis, which did not indicate a nonlinear relation between birthweight and caesarean section with an indication of failure to progress.

In the development of clinical prediction models, several problems can be encountered. Missing data are a frequent problem in any clinical study. Multiple imputation is one of the advocated methods to handle missing data. Another potential problem is overfitting the data; bootstrapping methods are often used to adjust the model for such overfitting. In which order multiple imputation and bootstrapping should be applied is still under debate.4 We first multiply imputed the missing data and then developed the model (per imputed data set) using bootstrapping methods to adjust for overfitting. The rationale behind this was that we used bootstrapping methods to asses the sampling variation in the study sample. Hence, first this full study sample was reconstructed (using multiple imputation) and then the bootstrapping methods were applied. Also, we expected that an imputation model based on bootstrap samples (rather than the original data), would yield too much variation. The sequence of imputation and bootstrapping is probably less relevant when the number of missing values is small or the number of imputation sets and bootstrap samples becomes large.

In women with a singleton term pregnancy in cephalic presentation, both antepartum and intrapartum characteristics influence the probability of an instrumental vaginal delivery or caesarean section for suspected fetal distress or failure to progress. Information on the risk of an instrumental vaginal delivery or caesarean section because of suspected fetal distress or failure to progress can be of great value in counselling women and guiding labour management.

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