WHO MONICA Project e-publications, No. 31

Estimation of an errors-in-variables regression model when the variances of the measurement errors vary between the observations: appendix to a paper published in Statistics in Medicine

December 2010

Sangita Kulathinal¹ and Kari Kuulasmaa²

¹ Indic Society for Education and Development (INSEED), Nashik, India
² Department of Chronic Disease Prevention, National Institute for Health and Welfare, Helsinki, Finland
Correspondence to Kari Kuulasmaa (firstname.lastname@thl.fi)

• Copyright notice
• Document identification:
  • WHO MONICA Project e-publications (ISSN 2242-1246), No. 31
  • URL:http://www.ktl.fi/publications/monica/errors-in-variables/appendix.htm
  • URN:NBN:fi-fe201012083070

Contents

• 1. Introduction
• 2. SAS code
• 3. Example data
• 4. Errata
• References
• Attachments:
  • SAS code
  • Data sets:
    • Case 1
    • Case 2
    • Case 3
    • Case 4
    • MONICA, men
    • MONICA, women

1  Introduction

This document is an appendix to the paper titled "Estimation of an errors-in-variables regression model when the variances of the measurement errors vary between the observations" published in Statistics in Medicine [1]. This contains SAS code for the method developed in the paper, and the data sets used for the examples.

2 SAS code

SAS code to implement the EM algorithm for the bivariate normal model (BVNM) of reference [1] is attached. Instructions on the requirement of input file are given in the SAS file.

3 Example data

Table 1 of  reference [1] used four simulated data sets corresponding to true regression coefficient 0.67. In all four cases the mean vector was (-2, -1), the diagonal elements of the variance-covariance matrix were (3, 4), and the off-diagonal element was 2. The coefficients of attenuation were 1, 1, 0.75 and 0.75. The simulated data sets, containing observed X and Y, and square root of measurement error variances in x and y are at:

• case1.csv: no measurement error, the variances of measurement errors were taken as 0;
• case2.csv: no measurement error in x observations but the variance of measurement error in y observations was taken as 1;
• case3.csv: no measurement error in y observations but the variance of measurement error in x observations was taken as 1;
• case4.csv: measurement errors in both x and y observations with variance 1.

Table 2 of  reference [1] used data which have been published in Table 1 of reference [2].

Table 3 of  reference [1] used data from Tables 1 and 2 of reference [3]. The data sets, including also the standard errors which were not shown in reference [3] are at:

• monica_men.csv for men and
• monica_women.csv for women.

In these data files,  x denotes the Risk score trend and y denotes the Change in coronary-event rate during the lagged period.

4 Errata

Table 3 of reference [1] has misprints for BVNM for Women, : SE(β) is 0.39 (not 0.24) and CI(β) is (-0.08, 1.44).

References

1. Kulathinal SB, Kuulasmaa K, Gasbarra D. Estimation of an errors-in-variables regression model when the variances of the measurement errors vary between the observations. Statistics in Medicine 2002;21(8):1089-1101.
2. Dear KBG, Puterman ML, Dobson AJ. Estimating corre1ations from epidemio1ogica1 data in the presence of measurement error. Statistics in Medicine 1997;16:2177-2189.
3. Kuulasmaa K, Tunstall-Pedoe H, Dobson A, Fortmann S, Sans S, Tolonen H, Evans A, Ferrario M, Tuomilehto J, for the WHO MONICA Project. Estimation of contribution of changes in classic risk factors to trends in coronary-event rates across the WHO MONICA Project populations. Lancet 2000:355;675-87.