COMMENTARY

Planned Home vs Hospital Birth: A Meta-Analysis Gone Wrong

Carl A. Michal, PhD; Patricia A. Janssen, PhD; Saraswathi Vedam, SciD; Eileen K. Hutton, PhD; Ank de Jonge, PhD

April 01, 2011

Paradoxical Results

The main conclusion of the analysis by Wax and coworkers that planned home and planned hospital births exhibit similar perinatal mortality rates, but home births are characterized by 2-3 times higher neonatal death rates,^[1] is drawn from data that are self contradictory. The mortality rates reported in the paper are reproduced in Table 1. CIs for these proportions were not provided in the article.

Table 1: Perinatal and Neonatal Death Rates Reported by Wax and Colleagues

	Planned Home Birth (%)	Planned Hospital Birth (%)
Perinatal death
All	0.07	0.08
Nonanomalous	0.07	0.08
Neonatal death
All	0.20	0.09
Nonanomalous	0.15	0.04

Adapted from Wax JR, et al. Am J Obstet Gynecol. 2010;203:243:e1-e8.^[1]

Wax and colleagues defined perinatal death as stillbirth of at least 20 weeks or 500 g, or death of a liveborn infant within 28 days of birth. Neonatal deaths are defined as deaths of liveborn infants within 28 days of delivery.^[1] With the definitions chosen by these investigators, neonatal deaths are a subset of perinatal deaths. As can be seen in Table 1, however, the investigators' results show that for planned home births, the neonatal death rates are actually far higher than the corresponding perinatal death rates. According to the investigators' definitions, these results are impossible. This is not unique to the planned home birth statistics, and in fact the neonatal death rate for all hospital births is also greater than the corresponding perinatal death rate. These paradoxical results arise from the dramatic differences in outcomes among the included studies, as will be described. It is clear, however, that the perinatal and neonatal death results cannot possibly represent comparable populations.

Because the perinatal death statistics are drawn from more than 500,000 births, whereas the neonatal death statistics are drawn from fewer than 50,000 births (and for many other reasons described below), the neonatal death statistics in the study by Wax and colleagues cannot be defended.

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Cite this: Carl A. Michal, Patricia A. Janssen, Saraswathi Vedam, et. al. Planned Home vs Hospital Birth: A Meta-Analysis Gone Wrong - Medscape - Apr 01, 2011.

Appendix. An Analysis of "Meta5.doc," The Computational Tool Used For Random-Effects Meta-Analysis

The random effects calculations in the study by Wax and colleagues made use of a meta-analysis calculator implemented in a spreadsheet that was embedded in a Microsoft® Word document.^{1} The spreadsheet is based upon formulae found in Petitti's meta-analysis text.^{2} The formulae in question are in Table 7-7 on page 102 and on pages 116-117.

Specifically, the errors in the spreadsheet are:

In cell W10, which contains Petitti's D value (Δ² in DerSimonian and Laird's notation^{3}), any negative value for D should be replaced with 0. The spreadsheet, however, contained no logic to replace negative values. In cases where D is negative, this could dramatically alter the weightings of the datasets.
In the calculation of the adjusted weights (w_i*), which should be given by w_i* = 1/(D+(1/w_i )), the spreadsheet cell reference to the cell containing D was entered not as an absolute cell reference (eg $W$10) but as a relative cell reference (W10), so that it referred to the (possibly incorrect, due to error 1) D value in cell W10, for only the first study. For subsequent studies, the value taken to be D was whatever value happened to be in cells W11, W12, W13, etc. As a consequence of the layout of the spreadsheet, those cells are generally blank, returning values of 0.
In the calculation of the CI limits, rather than employing the sum of the adjusted variances (variance_s*), the sum of the raw variances was used. To correct this, the references to cell H10 in cells I10 and J10 should be replaced by 1/sqrt(U14).
The spreadsheet provides a negative value for the Q statistic. Because Q is a weighted sum-of-squares, this cannot be correct. Q should have been taken from cell S14.

It is possible that the spreadsheet will be corrected. The original version of the spreadsheet can be found on the Internet archive "Wayback Machine."

After making the described corrections, the spreadsheet appears to implement correctly Petitti's description of the DerSimonian-Laird method. However, the results provided by the spreadsheet still show minor deviations from their expected values. This is the result of a discrepancy between Petitti's algorithm and DerSimonian and Laird's paper. In particular, Petitti makes use of the Mantel-Haenszel variance and OR in calculating the adjusted weights w_i ^*. These do not appear to agree with the variance (s_i ² ) and weighted (natural log of) OR (y_w ) indicated for OR calculations in DerSimonian and Laird's original paper.

As an example of the possible consequences of using the spreadsheet, we consider a random effects model calculation combining the 2 datasets shown below.

	Disease (exposed)	Disease (nonexposed)	Nondiseased (exposed)	Nondiseased (nonexposed)
Study 1	920	480	1216	1588
Study 2	160	172	235	157

The spreadsheet provides a random effects OR of 0.64, with 95% confidence bounds of 0.55-0.73. Simply exchanging the order of the 2 studies changes the result to OR = 2.48 (95% CI, 2.15-2.85).

The correct results from a DerSimonian-Laird random effects calculation^{1} is OR, 1.26 (95% CI, 0.32-4.92). The correct results in this example were calculated using the rmeta package^{4} for the R statistical analysis environment^{5} and verified by hand calculations.

These analyses are shown in the forest plot in the Figure. Clearly, either of the 2 incorrect results (shown in blue and red) would lead to incorrect conclusions -- both results spuriously suggest statistical significance, although the conclusion on the direction of the effect depends on the order in which the studies are entered into the spreadsheet.

Figure. Forest plot showing ORs and CIs for a random-effects meta-analysis of the example data sets. The correct result is represented by the long thin black diamond. The red and blue diamonds represent the 2 possible incorrect results produced by the faulty spreadsheet.

References

Basu A. Calculation of summary effects using random effects method. Available at: https://www.pitt.edu/~super1/lecture/lec1171/meta5.doc Accessed January 28, 2011.
Petitti DB. Meta-Analysis, Decision Analysis, and Cost-Effectiveness Analysis. 2^nd Ed. Oxford University Press; New York; 2000.
DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7:177-188.
Lumley, T. rmeta: Meta-analysis. September 29, 2009. Available at: https://cran.r-project.org/web/packages/rmeta/index.html Accessed January 26, 2011.
R. The R Project for Statistical Computing. Available at: https://www.r-project.org Accessed January 26, 2011.

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