To the Editor:
We greatly appreciate the readers’1 thorough and critical review of our manuscript2 and welcome suggestions to improve our methodology. The readers note several perceived shortcomings of our study, which we hope to address with the following.
The readers point out a possible discrepancy in the P-value reported in Table 1 and the corresponding value in the text. The P-value of .013 was obtained from univariate logistic regression analysis examining the relationship of body mass index (BMI) to delayed infarction; this value is listed in Table 2, not Table 1, and matches the value provided in the manuscript text. The P-value obtained from the chi-squared test presented in Table 1 (.020) was not mentioned in the text. We agree that Fisher's exact test may have been more appropriate than Pearson's chi-squared test in this instance given the small number of examples; when employing Fisher's test, the P-value for the comparison in question is .026.
Regarding the presentation of BMI as a categorical variable, our intuition is that the effect of increasing BMI on delayed ischemia and infarction may not be linear across the physiological range of BMI, and may emerge only at indices at or above the threshold of obesity. This possibility is suggested by our results, as on linear regression analysis BMI was not significantly associated with delayed infarction (P = .101), whereas when dichotomized to above or below 29.4, BMI was significantly associated with infarction. This phenomenon is evident in the effect of BMI on other outcomes, for example mortality, on which the effect of BMI is bimodal as opposed to linear.3 An additional possibility is that our study was underpowered to detect a relationship between BMI and infarction when BMI was presented as a continuous variable, which we recognize as a limitation of our study. BMI was presented as a continuous variable when assessing its relationship to transcranial doppler (TCD) velocities to provide a graphical representation of the relationship between these two continuous variables. The relationship of BMI as a categorical variable to TCD velocities was also investigated, the results of which is contained in the manuscript text under the subheading “Relationship of BMI to TCD Velocities and Incidence of Angiographic Vasospasm.”
Increased BMI is indeed a risk factor for hypertension, yet the pathophysiology of hypertension is undoubtedly multifactorial. In our cohort, there was not a significant difference in BMI between patients with and without hypertension (29.4 vs 28.3; P = .349). A cohort of patients suffering subarachnoid hemorrhage likely has additional risk factors for hypertension, for example cigarette smoking, in greater proportions than the population at large, which could explain the lack of association of BMI with hypertension among patients in our study. Regardless, the overlapping distribution of BMI in patients with and without hypertension likely accounts for the discordance in P-values noted by the readers.
We recognize the additive likelihood for type 1 error as an increasing number of statistical tests are performed without correction, which must be balanced with the possibility of type II error if a conservative adjustment such as the Bonferroni correction is employed. Given the results of the multivariate analysis, we feel that the association of BMI with delayed infarction is robust, yet the criticisms levied by the readers are valid and warrant consideration. Ultimately, our study was not intended to prove an association of BMI with delayed infarction, and our results require confirmation in additional, larger studies. Finally, the semantic distinction pointed out by the readers is important. As they state, the c-statistic is a measure of the predictive accuracy of the model. The high value reported for the model assessing predictors of delayed infarction (.891) is indeed potentially optimistic, which we hope to potentially validate in future studies.
We sincerely thank the readers for their interest in our study. We will consider their feedback in future investigations.
The authors have no personal, financial, or institutional interest in any of the drugs, materials, or devices described in this article.
1. Fischer I, Mijderwijk H-J, Steiger H-J. Letter: Increased BMI associated with reduced risk of delayed cerebral ischemia and subsequent infarction after aneurysmal subarachnoid hemorrhage. Neurosurgery. Published online ahead of print: September 6, 2018. (doi: 10.1093/neuros/nyy344).
2. Rinaldo L, Rabinstein AA, Lanzino G. Increased body mass index associated with reduced risk of delayed cerebral ischemia and subsequent infarction after aneurysmal subarachnoid hemorrhage. Neurosurgery. Published online ahead of print: 2018. (doi: 10.1093/neuros/nyy104.)
3. Adams KF, Schatzkin A, Harris TB, et al. Overweight, obesity, and mortality in a large prospective cohort of persons 50 to 71 years old. N Engl J Med. 2006;355(8):763–778.