Quantifying the Family Frailty Effect in Infant and Child Mortality by Using Median Hazard Ratio (MHR)

Abstract Most microlevel studies in the social sciences have focused on the impact of different measured variables. While some studies have also dealt with unobserved variation, it has usually only been controlled for to perfect the estimates of the observables. In this article, the authors applied a modified version of a recently developed method designed to quantify the effect of unobserved variation in continuous time multilevel models, called a median hazard ratio. It allows a direct comparison of the effect of unobserved heterogeneity with standard relative risks. The method is used in an analysis of infant and child mortality in southern Sweden during the period 1766–1895. The empirical findings indicate that unmeasured differences between families were more important than either socioeconomic status or gender throughout this period. Keywords: child mortalityfamily clusteringfrailtyinfant mortalitymedian hazard ratiosmedian odds ratios (MORs)multilevel analysisunobserved heterogeneity Notes The main text was written by Tommy Bengtsson and Martin Dribe. The appendix was written by Jan Lanke. Martin Dribe acknowledges financial support from the Swedish Council for Working Life and Social Research. We are grateful to Juan Merlo at Lund University and Klaus Larsen at the Hvidovre University Hospital for guidance regarding the MHR. We also thank Göran Broström, Jim Oeppen, and participants at the IUSSP workshop Space and Time in Historical Demographic Research: New Methods and Models (Minnesota Population Center), the Social Science History Association, CitationMinneapolis, MN, 2006, and the Population Association of America, New York, 2007, for comments on previous versions of this article. 1. The estimations were made using the eha package in R (R Development Core Team 2006).The eha package was developed by Göran Broström at Umeå University, Sweden. 2. The data is maintained by the Scanian Demographic Database, a collaborative project between the Regional Archives in Lund and the Centre for Economic Demography, Lund University. The source material is described in Elisabeth Reuterswärd and CitationFranceska Olsson (1993), and the quality of data is analyzed in Tommy Bengtsson and CitationChrister Lundh (1991). 3. We have used 1/16 mantal (a rough measure of the productive potential of the farm) as the limit of subsistence, which is also the way the contemporary society defined it (see CitationDribe 2000, chap. 2 for a discussion).