How mathematics warp biology: round-off of umbilical cord blood gas case value decimals distorts calculation of metabolic acidosis at birth

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To illustrate the impact on settling neonatal metabolic acidosis diagnosis by rounding off pH and base deficit (BD) case value decimals. Design. Comparative study. Setting. University maternity units. Sample. Umbilical cord arterial blood gas values from 18 831 newborns. Main outcome measures. Prevalences of pH <7.05 and metabolic acidosis diagnosis (pH <7.05 plus BD >12.0 mmol/L). Methods. Calculation of BD from pH and pCO2 values, and calculating the prevalences of metabolic acidosis before and after rounding off three-decimal values to two or one decimals. The ‘round to half even’ and ‘round half up’ round-off rules were used for digit 5. Results. Arterial pH was ≤7.049 in 339 newborns (1.8%). In 27 (8.0%) pH was 7.045–7.049, rounded off to 7.05 when truncated to two decimals (crude vs. round-off values; McNemar's test, p<0.000001). Depending on round-offs of pH case value decimals before or after calculation of BD, and round-offs of resulting three-decimal BD values to one decimal, metabolic acidosis ‘disappeared’ or ‘appeared’ in eight of 75 metabolic acidosis cases (10.7%). With different modes of calculation, the number of metabolic acidosis cases varied between 75 and 71 cases (p≥0.1). Conclusion. Due to pH and BD case value decimal round-offs, a diagnostic discrepancy of acidotic pH values occurred in 8%, and of metabolic acidosis diagnosis in 10.7% of cases. A drift of a dichotomy parameter value cut-off due to decimal round-offs will result in a shift in distribution of positive and negative cases in a population sample.

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