nach oben

Demography

Erschienen in:

01.04.2013

Estimation of Covariate Effects With Current Status Data and Differential Mortality

verfasst von: Alberto Palloni, Jason R. Thomas

Erschienen in: Demography | Ausgabe 2/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The assessment of the impact that socioeconomic determinants have on the prevalence of certain chronic conditions reported by respondents in population surveys must confront two problems. First, the self-reports could be in error (false positives and false negatives). Second, those reporting are a selected sample of those who ever experience the problem, and this selection is heavily influenced by excess mortality attributable to the condition being reported. In this article, we use a combination of empirical data and microsimulation to (a) assess the magnitude of the bias attributable to the selection problem, and (b) suggest an adjustment procedure that corrects for this bias. We find that the proposed adjustment procedure considerably reduces the bias arising from differential mortality.

Vorheriger Artikel Paradox Revisited: A Further Investigation of Racial/Ethnic Differences in Infant Mortality by Maternal Age

Nächster Artikel The Contribution of Smoking to Black-White Differences in U.S. Mortality

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

See Weinberg et al. (1993, 1994) for research on the consequences of erroneously assuming stationarity when analyzing retrospective data.

Lin et al. (1998) studied the case of differential mortality and proposed a model for current-status data collected in an experimental setting in which all subjects are observed (and the monitoring time depends on the event of interest). We consider a different situation in which current-status data are randomly sampled from a population and differential mortality is more likely to prevent population members who experience the event of interest, relative to those who do not, from surviving to (and thus being observed at) the time of the survey (for individuals of a given age).

See Palloni and Thomas (2011) for an additional example concerning trends in the prevalence of disability in the United States.

The standard expression for SMAM is

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Equa_HTML.gif

where

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Figbb_HTML.gif

is the proportion single in the age group (x _i, x _i + 1). This expression assumes that there is no marriage before age 15 or after age 50.

In what follows, risk homogeneity refers to a situation in which the risk of attrition before (and hence not being observed by) the time of a census or survey is independent of the event being studied. Conversely, risk heterogeneity is a situation in which precensus (survey) attrition occurs differentially among those who do and those who do not experience the event of interest.

Again, see Weinberg et al. (1993, 1994) for research on the consequences of erroneously assuming stationarity when analyzing retrospective data.

See Goldman (1993) for a simulation study of the roles of marital selection and marital protection in producing mortality differences between the married and single populations.

Results of simulated values of SMAM under different conditions are available on request.

See Palloni and Thomas (2011) for a derivation of these results from first principles.

To move from Eq. (1) to Eq. (2), combine the terms in the second factor involving

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Fige_HTML.gif

and note that the terms

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Figf_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Figg_HTML.gif

combine to form the density function, which yields

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Figh_HTML.gif

—that is, the distribution function, when integrated.

If functional forms other than the logistic are deemed appropriate, the same conclusions about biases and inferential difficulties apply and only the functional form of the adjustment factor changes.

It is also worth noting that

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-012-0160-6/MediaObjects/13524_2012_160_Figv_HTML.gif

, so 1 minus the estimated coefficient for the integrated hazard provides an estimate of the mortality difference between those with and without the disease.

We simulate growing birth cohorts simply to mimic real populations. All results apply if all rates of growth are set equal to zero, or if there are no calendar time effects on fertility, mortality, or the incidence of diabetes.

Although we started with a large number of simulations, a small number was enough to produce sufficient Monte Carlo variation. As a consequence, we settled on a total of 25 replicas.

Some researchers (e.g., Smith 2007) prefer to fit probit models to prevalence data to make inferences about incidence. We have not investigated the magnitude of the biases when the researcher estimates a probit rather than a logit model.

Recall that in the simulated data, this coefficient has a true value equal to 1.0.

In the sensitivity analysis, there is no mortality difference among the high-education group, but in the low-education group, mortality is 4.48 times higher among diabetics compared with nondiabetics. The mean errors are smaller than those presented in Fig. 5 when the mortality differential decreases.

Although these panel data can be used to obtain (noisy or error-ridden) estimates of diabetes incidence for any subgroup, we cannot do so before ages 50 (Mexico) or 60 (Puerto Rico). Because diabetes in these countries has a relatively early onset, the set of observed incidence rates is too incomplete to retrieve reliable effects of covariates. Additional information can be obtained online (http://prehco.rcm.upr.edu for PREHCO, and http://www.mhas.pop.upenn.edu/english/home.htm for MHAS).

Low education is defined as less than 6 years of schooling, and high education is defined as 6 years or more.

This is a refinement that we can introduce only due to the panel nature of the data.

Aguilar-Salinas, C. A., Rojas, R., Gόmez-Pérez, F. J., García, E., Valles, V., Ríos-Torres, J. M., . . . Rull, J. A. (2002). Prevalence and characteristics of early-onset type 2 diabetes in Mexico. American Journal of Medicine, 113, 569–574.

Andersen, P. K., & Væth, M. (1989). Simple parametric and nonparametric models for excess and relative mortality. Biometrika, 45, 523–535.

Berk, R. A. (1983). An introduction to sample selection bias in sociological data. American Review of Sociology, 48, 298–386.

Bloom, D. E., & Killingsworth, M. R. (1985). Correcting for truncation bias caused by a latent truncation variable. Journal of Econometrics, 27, 131–135.CrossRef

Coale, A. J., Demeny, P., & Vaughan, B. (1983). Regional model life tables in stable populations. New York: Academic Press.

Coale, A. J., & McNeil, D. R. (1972). The distribution by age of the frequency of first marriage in female cohort. Journal of the American Statistical Association, 67, 743–749.CrossRef

Dalstra, J. A. A., Kunst, A. E., Borrell, C., Breeze, E., Cambios, E., Costa, G., . . . Mackenbach, J. P. (2005). Socioeconomic differences in the prevalence of common chronic diseases: An overview of eight European countries. International Journal of Epidemiology, 34, 316–326.

Diamond, I. D., & McDonald, J. (1991). The analysis of current status data. In J. Trussell, R. Hankinson, & J. Tilton (Eds.), Demographic applications of event history analysis (pp. 231–252). Oxford, UK: Oxford University Press.

Ederer, F., Axtell, L. M., & Cutler, S. J. (1961). The relative survival rate: A statistical methodology. National Cancer Institute Monographs, 6, 101–121.

Fligstein, N., & Wolf, W. (1978). Sex similarities in occupational status attainment: Are the results due to the restrictions on the sample to employed women? Social Science Research, 7, 197–212.CrossRef

Goldman, N. (1993). Marriage selection and mortality patterns: Inferences and fallacies. Demography, 30, 189–208.CrossRef

Greene, W. H. (1981). Sample selection bias as a specification error: A comment. Econometrica, 49, 795–798.CrossRef

Hajnal, J. (1953). Age at marriage and proportions marrying. Population Studies, 72, 111–136.

Hajnal, J. (1965). European marriage patterns in perspective. In D. V. Glass & D. E. C. Eversley (Eds.), Population in history: Essays in historical demography (pp. 101–143). London, UK: Edward Arnold.

Heckman, J. (1979). Sample selection bias as a specification error. Econometrica, 47, 153–161.CrossRef

Heckman, J., & Singer, B. (1984). A method for minimizing the impact of distributional assumptions in econometric models of duration data. Econometrica, 52, 271–320.CrossRef

Hougaard, P. (2000). Analysis of multivariate survival data. New York: Springer.CrossRef

Hu, Y., & Goldman, N. (1990). Mortality differentials by marital status: An international comparison. Demography, 27, 233–250.CrossRef

Jewell, N. P., & Van der Laan, M. J. (2004). Current status data: Review, recent developments and open problems. In N. Balakrishnan & C. R. Rao (Eds.), Handbook of statistics: Advances in survival analysis (pp. 625–643). Amsterdam, The Netherlands: Elsevier.

Keiding, N. (1991). Age-specific incidence and prevalence: A statistical perspective. Journal of the Royal Statistical Society: Series A, 154, 342–371.

Keiding, N. (2006). Event history analysis and the cross-section. Statistics in Medicine, 25, 2343–2364.CrossRef

Keiding, N., Begtrup, K., Scheike, T. H., & Hasibeder, G. (1996). Estimation from current-status data in continuous time. Lifetime Data Analysis, 2, 119–129.CrossRef

Keiding, N., Holst, C., & Green, A. (1989). Retrospective estimation of diabetes incidence from information in a prevalent population and historical mortality. American Journal of Epidemiology, 130, 588–600.

Kisker, E. E., & Goldman, N. (1987). Perils of single life and benefits of marriage. Social Biology, 34, 125–152.

Lin, D. Y., Oakes, D., & Ying, Z. (1998). Additive hazards regression with current status data. Biometrika, 85, 289–298.CrossRef

Little, R. J. A. (1995). Modeling the drop-out mechanism in repeated-measures studies. Journal of the American Statistical Association, 90, 1112–1121.CrossRef

Livi-Bacci, M. (1985). Selectivity of marriage and mortality: Notes for future research. In N. Keyfitz (Ed.), Population and biology (pp. 99–108). Liege, Belgium: Ordina Editions.

Maddala, G. S. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge, UK: Cambridge University Press.CrossRef

Manton, K. G., & Stallard, E. (1981). Methods for evaluating the heterogeneity of aging processes in human populations using vital statistics data: Explaining the black/white mortality crossover by a model of mortality selection. Human Biology, 53, 47–67.

McLaren, L. (2007). Socioeconomic status and obesity. Epidemiologic Reviews, 29, 29–48.CrossRef

Monteiro, C. A., Conde, W. L., Lu, B., & Popkin, B. M. (2004). Obesity and inequities in health in the developing world. International Journal of Obesity, 28, 1181–1186.CrossRef

Palloni, A., & Thomas, J. (2011). Estimation of health status inequalities from prevalence data: A risky business (CDE Working Paper No. 2011-09). Madison: Center for Demography and Ecology, University of Wisconsin.

Popkin, B. M. (1998). The nutrition transition and its health implications in lower-income countries. Public Health Nutrition, 1, 5–21.CrossRef

Robbins, J. M., Vaccarino, V., Zhang, H., & Kasl, S. V. (2001). Socioeconomic status and type 2 diabetes in African American and non-Hispanic white women and men: Evidence from the third National Health and Nutrition Examination Survey. American Journal of Public Health, 91, 76–83.CrossRef

Robbins, J. M., Vaccarino, V., Zhang, H., & Kasl, S. V. (2005). Socioeconomic status and diagnosed diabetes incidence. Diabetes Research and Clinical Practice, 68, 230–236.CrossRef

Smith, J. P. (2007). Nature and causes of trends in male diabetes prevalence, undiagnosed diabetes, and the socioeconomic status health gradient. Proceedings of the National Academy of Sciences of the United States of America, 104, 13225–13231.CrossRef

Sun, J., & Kalbfleish, J. D. (1993). The analysis of current status data on point processes. Journal of the American Statistical Association, 88, 1449–1454.CrossRef

Trussell, J., & Richards, T. (1985). Correcting for unmeasured heterogeneity in hazard models using the Heckman-Singer procedure. In N. Tuma (Ed.), Sociological methodology (pp. 242–276). San Francisco, CA: Jossey-Bass.

Trussell, J., & Rodríguez, G. (1990). Heterogeneity in demographic research. In J. Adams, D. Lam, A. Hermalin, & P. Smouse (Eds.), Convergent issues in genetics and demography (pp. 111–132). New York: Oxford University Press.

Vaupel, J. W., Manton, K. G., & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454.CrossRef

Vaupel, J. W., & Yashin, A. I. (1985). Heterogeneity’s ruses: Some surprising effects of selection on population dynamics. The American Statistician, 39, 176–185.

Weinberg, C., Baird, D. D., & Rowland, A. S. (1993). Pitfalls inherent in retrospective time-to-event studies: The example of time to pregnancy. Statistics in Medicine, 12, 867–879.CrossRef

Weinberg, C., Baird, D. D., & Wilcox, A. J. (1994). Sources of bias in studies of time to pregnancy. Statistics in Medicine, 13, 671–681.CrossRef

Wooldridge, J. M. (1995). Selection corrections for panel data models under conditional mean independence assumptions. Journal of Econometrics, 68, 115–132.CrossRef

Titel: Estimation of Covariate Effects With Current Status Data and Differential Mortality
verfasst von: Alberto Palloni
Jason R. Thomas
Publikationsdatum: 01.04.2013
Verlag: Springer US
Erschienen in: Demography / Ausgabe 2/2013
Print ISSN: 0070-3370
Elektronische ISSN: 1533-7790
DOI: https://doi.org/10.1007/s13524-012-0160-6

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2013

Erratum to: Trends in Occupational Segregation by Gender 1970–2009: Adjusting for the Impact of Changes in the Occupational Coding System

Returns on Lifetime Investments in Children in Egypt

Family Instability and Early Initiation of Sexual Activity in Western Kenya

Integration or Fragmentation? Racial Diversity and the American Future

Trends in Occupational Segregation by Gender 1970–2009: Adjusting for the Impact of Changes in the Occupational Coding System

Maternal Education, Birth Weight, and Infant Mortality in the United States