Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

Hypertension control and related variables among urban and rural adults in Taiwan

Literature on hypertension treatment has demonstrated that a healthy life style is one of the best strategies for hypertension control. In exploring the mechanisms of behavioral change for hypertension control, a comprehensive study based on the Transtheoretical Model was carried out in Taiwan during the summer of 2000 with a sample of 350 hypertensive adults living in Taipei urban and rural areas. ^ The relationships among stages of change, processes of change and demographic factors were analyzed for six health behaviors—low fat food consumption, alcohol use, smoking, physical activity, weight control, and routine blood pressure checkups. In addition, differences were assessed between urban and rural populations in changing their behavior for hypertension control. ^ The results showed that rural populations had more difficulties than urban populations in avoiding smoking and engaging in physical activity, and the processes of change being used by urban populations were significantly greater than rural populations. The study findings support a strong association between processes and stages of change. ^ Individuals who use more processes of change will be more inclined to move from precontemplation stage to maintenance stage. Counterconditioning, which is the substitution of alternatives for the problem behaviors, in this study, significantly helped people to change diet, engage in physical activity, and check blood pressure regularly. For example, counterconditioning is eating more vegetables instead of meat, or engaging in physical activity as a time to relax rather than another task to accomplish. ^ In addition, self-reevaluation was the most important process for helping people to engage in physical activity; and social liberation was the most important process for changing diet behavior. The findings in this study may be applied to improve health behaviors among rural populations with low income and low education; however, at the same time, the obesity problems among urban populations should be prevented to control hypertension in Taiwan. ^

Ethnic comparisons of adolescent sexual risk -taking and preventive behavior

For adolescents, unprotected sexual intercourse is the primary cause of sexually transmitted disease (STD), including Human Immunodeficiency Virus (HIV) infection (virus which causes Acquired Immunodeficiency Syndrome (AIDS)), and pregnancy. Although many studies on adolescent sexual behavior have addressed racial/ethnic differences, few studies have examined the relation between race/ethnicity while controlling for other sociocultural and psychosocial variables. The purpose of this study is to examine the relationship between racial/ethnic categories and selected sociocultural and psychosocial variables, with reported adolescent sexual risk-taking and preventive behavior.^ A self-administered questionnaire was used to collect information from 3132 students in a Texas school district (Section 3.5.2). The instrument contained approximately 100 questions on demographic characteristics, sexual behavior, and psychosocial determinants of sexual behavior. Based on the findings of this study, the following major conclusions are made: (1) There are differences in reported sexual risk-taking and preventive behavior among Black, Hispanic and White adolescents in this study. The stratified analysis by gender further suggests significant gender differences in reported sexual behavior among the three racial/ethnic groups. (2) Gender, living arrangement, academic grades, and language spoken at home modified the association between reported sexual risk-taking and preventive behavior and race/ethnicity in this study. This suggests that these sociocultural variables should be considered in future research and practice involving multicultural populations. (3) There are differences in selected psychosocial determinants among the three racial/ethnic groups and between males and females. These differences were consistent with the reported sexual risk-taking and preventive behaviors among race/ethnicity and gender for adolescents in this study. The findings support the consideration of psychosocial determinants in research and interventions addressing adolescent sexual behavior among different racial/ethnic groups.^ Based on the results of this study, two recommendations for practice are made. First, health professionals developing interventions for adolescents from different cultural backgrounds and gender need to be familiar with the specific sociocultural and psychosocial factors which will reduce risky sexual behavior, and promote protective behavior. Second, the need for immediate, realistic, and continuous HIV/STD and pregnancy prevention programs for children and adolescents should be considered. ^