Letters to the Editor Authors’ Response to Kaufman and Muntaner Rosalind Arden, 1 * Michelle Luciano, 2 Ian J. Deary, 2 Chandra A. Reynolds, 3 Nancy L. Pedersen, 4 Brenda L. Plassman, 5 Matt McGue, 6,7 Kaare Christensen 7 and Peter M. Visscher 8 1 Centre for Philosophy of Natural and Social Science, London School of Economics, London, UK, 2 Centre for Cognitive Ageing and Cognitive Epidemiology, Department of Psychology, University of Edinburgh, Edinburgh, UK, 3 Department of Psychology, University of California, Riverside, CA, USA, 4 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden, 5 Department of Psychiatry and Behavioral Sciences, Duke University Medical Center, Durham, NC, USA, 6 DepartmentofPsychology, University of Minnesota, Minneapolis, MN, USA, 7 DanishAging Research Center, University of Southern Denmark, Odense, Denmark and 8 Queensland Brain Institute, University of Queensland Diamantina Institute, Woolloongabba, QLD, Australia *Corresponding author. Centre for Philosophy of Natural and Social Science, London School of Economics, Lakatos Building, Houghton Street, London WC2A 2AE, UK. E-mail: arden.rosalind@gmail.com We thank Kaufman and Muntaner (K&M) for their inter- est in our work. In our response we have not addressed their ideological comments; instead we concentrate on ra- tionale, empirical data and statistical analysis. In our study we asked: ‘Why do brighter people tend to live longer?’ To test this empirical question, we turned to three samples of twin data. All data have limitations. We devoted several para- graphs to discussing those in our data; one anonymous re- viewer noted the ‘honestly portrayed results’. We were constrained to analysing data from twin pairs where at least one member had died and we noted that this reduced mortality variance. We also stated that ideal data would include intelligence assessed in childhood, completed mor- tality data and much larger samples. Regarding statistical analysis, K&M claim that, by re- porting results of null hypothesis testing rather than effect size estimates, we do not follow current conventions. This is an odd complaint since, as readers can see, we report only effect size estimates and no results of null hypothesis tests, in the abstract. Concerning K&M’s complaint that we have no direct measures of genes or environments, the power of pedigree- based studies of trait (co)variation is that genetic param- eters can be estimated without information on individual genes or their effect sizes. Concerning the equal environ- ments assumption in general, empirical data based on most twin studies ever published point to little or no influence of shared environmental factors on twin similarity. 1 K&M assert that the equal environmental similarity assumption invalidates our analysis of twin data. In fact, as we stated in our paper, monozygotic (MZ) twins are more likely to have more similar environments than dizygotic (DZ) twins, but this is because they create this greater similarity. The most comprehensive published evaluation of equal envir- onmental similarity, based on environmental characteris- tics outside the twins’ control, concluded that the available evidence supported the validity of the assumption. 2 With respect to our samples in particular, there is nothing in our ascertainment scheme that implies differential selection on twin zygosity. K&M mention collider variables, but the essential in- formation on which we base our inference is summarized in Figure 1. We do not claim that the slopes in Figure 1 are unbiased estimates of their population parameters, but ra- ther draw conclusions about the differences between them. It is correct that imputed missing data have different variance to observed data. K&M further state that if im- putation and selection cause a greater bias in DZ than MZ twins, then the genetic contribution will be exaggerated. V C The Author 2016; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association 1 International Journal of Epidemiology, 2016, 1–2 doi: 10.1093/ije/dyw020 Int. J. Epidemiol. Advance Access published March 27, 2016 at King's College London on March 27, 2016 http://ije.oxfordjournals.org/ Downloaded from