In the comment of Karl Michaëlsson, Alicja Wolk and Liisa Byberg dated 4th of December 2014, they state the following.
“We note with interest that these authors also reference the incorrect calculations of crude mortality made by Staffan Hellstrand, who is consultant for the Federation of Swedish Farmers, an organization who is owner of milk industries (e.g., Arla Foods). In a previous response (http://www.bmj.com/content/349/bmj.g6015/rr/779932), we have corrected Staffan Hellstrand and guided him to the correct data for use. Despite erroneous figures, Astrup and Givens have chosen to repeat the presentation of Staffan Hellstrand’s incorrect calculations – an interesting action given the fact that Arne Astrup should be an objective key opinion leader in field of nutritional research by his role as editor of the American Journal of Clinical Nutrition. Hopefully, his action to criticize our study by distorted arguments is not related to his financial conflicts of interest, for example research support from Arla Foods (25).”
In a previous commentary I have shown some errors in this passage. In this commentary I will go deeper regarding some challenges in statistical analysis of systems where life is a key system characteristic.
Any one as read the original article; the first commentary of Stefan (not Staffan) Hellstrand; and the first reply of the authors of the original article on my first commentary in parallel; will easily see that the comment of the authors avoids the crucial point put forward in my first response; “that the paper itself with data supplement has not shown in a satisfactory way that the results obtained are results that are valid for the population of humans from which the samples were drawn.”
The figure I presented in the first comment and the calculations made are not incorrect. I clearly defined the measure “mortality” I introduced as the actual fraction that died per subsample. Noteworthy is that another article published in BMJ the 2nd December 2014, in a cohort study relating maternal overweight to risk of infant mortality, gives exactly the same definition of their measure “mortality rate” as the mortality measure I defined in my first comment, see Johansson et al. (2014).
Assume that this measure defined in this way gives incorrect calculations resulting in erroneous figures and conclusions, and that this is in conflict with criteria of good scientific quality regarding among other aspects objectiveness. Then there is a moral obligation for Michaëlsson et al. to guide the scientific community, including Johansson et al. (ibid.) and the editorial board and chief editor of the journal publishing their article, away from this incorrect measure generating erroneous results and conclusions to appropriate methods.
If it is so that the measure I used in my first response, which is the same as the mortality rate in Johansson et al. (ibid.), in some contexts are relevant in cohort studies of human health aspects, then Michaëlsson et al. have some more work to do to show why the measure they have chosen is better, and if the results obtained have such quality after considering strength and weaknesses in their material and the methodology they have chosen given the way they have applied it, that the conclusions they have drawn actually are supported.
The two figures below indicate the challenges they face. In the female cohort study women born in 1913 were included in the same data set as women born in 1951. The first figure shows clearly that women born in 1951 have another phenotype than women born in 1913. If there are differences in the age distribution between the groups with different milk-consumption in Michaëlsson et al. (2014), then this will complicate the statistical analysis.
The second figure illustrates the statistical challenge due to the wide span in the age of women entering the study. The blue line shows the share of all women that lives born in 1915 at different ages, and the red line the same for women born in 1955 in Sweden. They are based on data from Statistics Sweden that are closest to the birth-year for the oldest and youngest women in the study, respectively. The X-marks are for women with the age of 74 when entering the study, and the age of 39, respectively. For women born in 1915, 61.2% are still alive at the age of 74. The study endured for around 20 years. At the age of 94, about 10% were still alive: i.e. 16% of the ones alive at the age of 74. Here the fraction that died during the study was 1 – 0.16 = 0.84.
At the age of 39, 96.2% of all women born in 1955 are still alive, and 20 years later, at the age of 59, around 93% are alive: i.e. 97% of the ones alive at the age of 39. Here the fraction that died during the study was 1 – 0.97= 0.03. If there are differences in the age distribution between the groups with different milk-consumption in Michaëlsson et al. (2014), then this will further complicate the statistical analysis.
From my experiences from analysis of biological systems in agricultural sciences I conclude that some more efforts are needed before we know how Michaëlsson et al. (2014) should be interpreted.
And with the comments of the authors as I have discussed above my final conclusion is that there is a need to further examine to what degree the material and methods of the original article informs of impacts to expect on mortality and fractures of different levels of milk consumption. With that I hold the question open that the authors may have made a valuable contribution. Maybe they have, maybe not. So I end with a question to the authors:
If I specify underlying data that I would like to get access from you in order to further probe the relevance of the statistical processing of data, generating the results presented in the original article, will you support me with that?
Johansson, S., Villamor, E., Altman, M., Edstedt Bonamy, A-K; Granath, F., Cnattingius, S. 2014. Maternal overweight and obesity in early pregnancy and risk of infant mortality: a population based cohort study in Sweden. BMJ 2014;349:g6572.
Competing interests: No competing interests