Correspondence

Meta-Analysis of Radiotherapy for Small-Cell Lung Cancer

N Engl J Med 1993; 328:1425-1426May 13, 1993

Article

To the Editor:

There are several errors in the meta-analysis by Pignon et al.1. Our analysis of their data fails to support their conclusion that a statistically significant benefit has been demonstrated for radiotherapy combined with chemotherapy.

Specifically, we were unable to reproduce the estimates of relative risk (odds ratios) for the individual studies and for the pooled estimate, as well as the values and variances for the observed number of deaths minus the expected number (O - E) shown in their Figure 1 when we used the (Peto) method cited2. Using the standard formula, we obtained the O - E value of 0.47 for the National Cancer Institute (NCI) study instead of -8.9. The NCI study has counts of 46 deaths among 48 patients enrolled (95.8 percent) in the chemotherapy-plus-radiotherapy group and 46 of 49 patients (93.9 percent) in the chemotherapy-alone group. When the basic definitions are used, the relative risk is 1.02 [(46/48) / (46/49)], and the odds ratio is 1.5 [(46/2) / (46/3)]. Our application of the Peto method produced an odds ratio (which Pignon et al. use to estimate the relative risk) of 1.48. The relative risk reported in their Figure 1 is 0.66. Data for the Eastern Cooperative Oncology Group study are not provided but can be derived by subtracting the other values listed from the totals. We obtained the values of -12.1 for the total O - E and 49.8 for the total variance, which produce an odds ratio of 0.78 and a 95 percent confidence interval of 0.59 to 1.04 (two-sided P value, 0.086), indicating a trend in favor of radiotherapy plus chemotherapy but having only borderline statistical significance at best. Analysis with a random-effects model,3 which explicitly accounts for variability among studies, yields an odds ratio of 0.82, with a much wider 95 percent confidence interval of 0.53 to 1.29 (two-sided P value, 0.4). We were also unable to replicate the authors' results from the data presented in Figure 3. The origin of these data and the description of the method of pooling are not evident.

Although there is a trend in favor of radiotherapy plus chemotherapy, statistical significance cannot be claimed. The Peto method estimates the odds ratio, and the use of the odds ratio to approximate the relative risk is suboptimal when the event rates are high, as in these studies.

Joseph Lau, M.D.
New England Medical Center, Boston, MA 02111

Jesse Berlin, Sc.D.
University of Pennsylvania School of Medicine, Philadelphia, PA 19104

Thomas C. Chalmers, M.D.
Harvard School of Public Health, Boston, MA 02115

3 References

1. 1

   Pignon J-P, Arriagada R, Ihde DC, et al. A meta-analysis of thoracic radiotherapy for small-cell lung cancer. N Engl J Med 1992;327:1618-1624
   Full Text | Web of Science | Medline

2. 2

   Early Breast Cancer Trialists' Collaborative Group (EBCTCG). Treatment of early breast cancer. Vol. 1. Worldwide evidence 1985-1990: a systematic overview of all available randomized trials of adjuvant endocrine and cytotoxic therapy. Oxford, England: Oxford University Press, 1990.
   

3. 3

   DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials 1986;7:177-188
   CrossRef | Medline

Author/Editor Response

The authors reply:

To the Editor: We thank Lau et al. for providing us with the opportunity to comment on the statistical methods used in our paper, given that some of the details were deleted during the review process. We disagree with our learned colleagues about the alleged errors in our paper. We have performed a log-rank analysis, stratified on trials, using data on individual patients and exact dates of death1. This is certainly not equivalent to the simple computation performed by Lau et al., which summarizes each study according to the proportion of deaths in each treatment group, ignoring the follow-up time and therefore sacrificing part of the available information and thus the statistical power. The method presented by Lau et al. is generally used in literature-based meta-analysis, for want of better data2. In our paper, Figure 1 is typical of the meta-analysis based on the Mantel-Haenszel-Peto method1. The same kind of figure is used to present both types of analyses, and in both cases the computation can be checked from the figure. The error of Lau et al. stems from using the less efficient method. The advantages of a meta-analysis based on individual data as compared with a literature-based meta-analysis have been discussed recently3,4. Stewart and Parmar3 report another example in which the more precise analysis and the analysis based on published data led to discrepant results.

Jean-Pierre Pignon, M.D.
Rodrigo Arriagada, M.D.
Institut Gustave-Roussy, 94805 Villejuif, France

4 References

1. 1

   Early Breast Cancer Trialists' Collaborative Group (EBCTCG). Treatment of early breast cancer. Vol. 1. Worldwide evidence 1985-1990: a systematic overview of all available randomized trials of adjuvant endocrine and cytotoxic therapy. Oxford, England: Oxford University Press, 1990.
   

2. 2

   Warde P, Payne D. Does thoracic irradiation improve survival and local control in limited-stage small-cell carcinoma of the lung? A meta-analysis. J Clin Oncol 1992;10:890-895
   Web of Science | Medline

3. 3

   Stewart LA, Parmar MKB. Meta-analysis of the literature or of individual patient data: is there a difference? Lancet 1993;341:418-422
   CrossRef | Web of Science | Medline

4. 4

   Pignon JP, Arriagada R. Role of thoracic radiotherapy in limited-stage small-cell lung cancer: quantitative review based on the literature versus meta-analysis based on individual data. J Clin Oncol 1992;10:1819-1820
   Web of Science | Medline

Citing Articles (1)

Citing Articles

1. 1

   Claus A. Kristensen, Peter B. Jensen, Hans S. Poulsen, Heine H. Hansen. (1996) Small cell lung cancer: biological and therapeutic aspects. Critical Reviews in Oncology/Hematology 22:1, 27-60
   CrossRef