Re: Impact of analysis technique on our understanding of the natural history of labour

Dear Dr. Papageorghiou, De Vries et al. used data simulation to create two data sets, based on the Friedman and Zhang labour curve models, respectively, to assess whether the repeatedmeasures polynomial regression and intervalcensored regression used by Zhang et al. are appropriate statistical methods to describe the first stage of labour. It was concluded that these methods do not accurately reflect the underlying data. We respectfully disagree. The key issue regarding the appropriateness of polynomial repeatedmeasures regression hinges on whether the shape of the average labour curve matches the shape of the underlying individual curves. The authors demonstrated that when vaginal examinations are performed 1– 3 hourly or more, the average labour curve is close to the underlying labour pattern (figures 3B, S4 and S5). We suggest that the authors show a similar figure to figures 3B and S4 with an increasing frequency of vaginal examinations, to illustrate how similar the average curve becomes to the underlying labour pattern when the underlying labour pattern is assumed to be progressively accelerating. This evidence indicates that the polynomial regression is a reasonable method to model the labour curve when vaginal examinations are performed at least 1– 3 hourly. Labour patterns vary widely from woman to woman. Any single labour curve cannot truly represent the reality. The Friedman curve is an idealised individual curve. The rigid onecurveforall is too simplistic and has important clinical consequences. Whether the true active phase of labour follows a straight line or exponential curve still remains undetermined. Both trajectories, as well as other patterns, are likely to coexist. It may not be totally accurate to use the piecewise linear curve as the reference standard to judge the appropriateness of a statistical method. The estimate of labour duration, particularly the 95th centile, is influenced by the distribution of the transit time. While figure 1 demonstrated the approximate log normal distribution of the latent phase, active phase and total duration, it is also important to show such a distribution in each cmbycm segment with varying frequency of vaginal examinations. If the distribution is not log normal, the estimate may be biased. In addition, it is overly simplistic to assume that every parturient enters the active phase of labour at 4cm dilatation, which has been opposed by Cohen and Friedman. Such an assumption is likely to result in substantially reduced variations of the average labour duration. Subsequently, the 95th centiles based on the simulated data are much smaller than those based on the real data (table 1). Oladapo et al. used a multistate Markov model and produced very similar results to the interval censored regression, suggesting that the simulated data may be inappropriate to provide realistic results, which have much greater variations than the simulated data. Nonetheless, we agree that the admission time to labour may bias the results of the latent phase through potential selection bias. We had ignored the findings before 3 cm of cervical dilatation for the same reason.