Distribution of postpartum blood loss: modeling, estimation and application to clinical trials

Abstract

Background: The loss of large amounts of blood postpartum can lead to severe maternal morbidity and mortality. Understanding the nature of postpartum blood loss distribution is critical for the development of efficient analysis techniques when comparing treatments to prevent this event. When blood loss is measured, resulting in a continuous volume measure, often this variable is categorized in classes, and reduced to an indicator of volume greater than a cutoff point. This reduction of volume to classes entails a substantial loss of information. As a consequence, very large trials are needed to assess clinically important differences between treatments to prevent postpartum haemorrhage.

Methods: The authors explore the nature of postpartum blood loss distribution, assuming that the physical properties of blood loss lead to a lognormal distribution. Data from four clinical trials and one observational study are used to confirm this empirically. Estimates of probabilities of postpartum haemorrhage events 'blood loss greater than a cutoff point' and relative risks are obtained from the fitted lognormal distributions. Confidence intervals for relative risk are obtained by bootstrap techniques.

Results: A variant of the lognormal distribution, the three-parameter lognormal distribution, showed an excellent fit to postpartum blood loss data of the four trials and the observational study. A measurement quality assessment showed that problems of digit preference and lower limit of detection were well handled by the lognormal fit. The analysis of postpartum haemorrhage events based on a lognormal distribution improved the efficiency of the estimates. Sample size calculation for a hypothetical future trial showed that the application of this procedure permits a reduction of sample size for treatment comparison.

Conclusion: A variant of the lognormal distribution fitted very well postpartum blood loss data from different geographical areas, suggesting that the lognormal distribution might fit postpartum blood loss universally. An approach of analysis of postpartum haemorrhage events based on the lognormal distribution improves efficiency of estimates of probabilities and relative risk, and permits a reduction of sample size for treatment comparison.

Trial registration: This paper reports secondary analyses for trials registered at Australian New Zealand Clinical Trials Registry (ACTRN 12608000434392 and ACTRN12614000870651); and at clinicaltrials.gov (NCT00781066).

Keywords: Blood loss distribution; Clinical trials; Digit preference; Limit of detection of blood loss measures; Lognormal; Postpartum blood loss; Postpartum haemorrhage.

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The authors declare not to have any competing interests.

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Figures

Fig. 1

Blood loss volumes (mL) for the Simplified Package of the Active Management trial

Fig. 2

Probability plot for the fit of a two-parameter lognormal distribution for the Simplified Package of the Active Management trial

Fig. 3

Probability plot for the fit of a two-parameter lognormal distribution for the Misoprostol treatment of the Misoprostol trial

Fig. 4

Histograms a: showing digit preference (narrow bins) and lognormal fit (red line), and b: masking digit preference (bins of 100 mL) and lognormal fit (red line), Misoprostol treatment, Misoprostol trial

Fig. 5

Empirical cumulative distribution function (black dots) and three-parameter lognormal fit (red line); a: Misoprostol treatment, Misoprostol trial; b: Simplified package, Active Management trial; c: aggregated treatments, CHAMPION trial; d: CCT treatment, Althabe et al. trial, showing also 95% CIs for the fitted lognormal cumulative distribution (red area) and for the empirical cumulative distribution (blue lines); a magnified area is shown for a, b and c in the range of 400 to 1400 mL; only one treatment shown for the first two and the last trial, as the graphs for the two treatments were almost identical

Fig. 6

Quantile-quantile plot of the fitted three-parameter lognormal distribution quantiles versus observed blood loss volume quantiles (mL), showing a good fit up to 1800 mL (Misoprostol treatment, Misoprostol trial, panel a), up to 1500 mL (Active Management trial, panel b), and in all the range (CHAMPION trial, panel c, and Althabe et al. trial, panel d); only one treatment shown for the first two and the last trial, as the graphs for the two treatments were almost identical

Fig. 7

Quantiles reported in Bamberg et al. observational study (dots) and fitted lognormal distribution (full line)