A Nonlinear Hierarchical Model for Estimating Prevalence Rates with Small Samples

Estimating prevalence rates with small weighted samples, especially for rare diseases is a challenging task. We encountered such a situation in the recent National Latino and Asian American Study (NLAAS) on mental health. Due to small sizes of the weighted samples in various age groups, the standard designedbased estimators are highly variable. Bayesian hierarchical modeling offers a more workable approach by incorporating our knowledge on the smoothness of the prevalence rates as a function of age. The non-linear nature of this function, however, presents some intricate modeling issues such as the sensitivity to the link function (for converting a rate parameter onto the real line). In this paper we report our findings and some strategies we adopted to combat such problems. 1 Background and NLAAS In the last four decades, the United States has experienced an unprecedented wave of immigration, primarily from Latin America and Asia, which presents considerable challenges for health care delivery systems. Unfortunately, the problems in health-care delivery for immigrants are compounded by incomplete data on these populations. National prevalence estimates of psychiatric disorders for the 41 million people of Latino ancestry living in the United States remain elusive because studies fail to disaggregate them ∗Harvard University †Cambridge Health Alliance and Harvard Medical School ‡Boston University by national origin or nativity groups or to consider the heterogeneity between and within Latino groups. The National Latino and Asian Study (NLAAS) is a nationally representative survey of household residents (ages 18 and older) in the non-institutionalized population of the coterminous United States. Data were collected between May 2002 and November 2003. A total of 4864 individuals, including Latinos, Asians, and whites, were interviewed. Among them, a total of 2554 English and Spanish-speaking Latinos, divided into four strata (Puerto Rican, Cuban, Mexican, and all Other Latinos), comprised the final Latino sample with a response rate of 75.5%. The sample includes an NLAAS Core, designed to be nationally representative of all Latino origin groups regardless of geographic patterns; and NLAAS-HD supplements, designed to oversample geographic areas with moderate to high density (HD) of Latino households. Weighting reflecting the joint probability of selection from the pooled Core and HD samples provides sample-based coverage of the national Latino population. The NLAAS weighted sample is similar to the 2000 Census in gender, age, education, marital status and geographical distribution, but different in nativity and household income, with more U.S. immigrants and lower income respondents in the NLAAS sample. This discrepancy may be due to, among others, Census undercounting of immigrants, non-inclusion of undocumented workers, lack of fully bilingual interviewers of Latino ethnicity conducting Census interviews, or sample recruitment differences of participants.