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. ^

Epidemiologic and methodological issues in serial measurements of blood pressure: The blood pressure study in Mexican children

The Blood Pressure Study in Mexican Children (BPSMC) is a short term longitudinal study of serial blood pressure collected in three observation periods by standardized examinations of 233 female children, 10 to 12 years of age, enrolled in public and private primary schools in Tlalpan, Mexico. Study objectives were: (1) to describe from baseline information the distribution and relationship of blood pressure to age and selected anthropometric factors, as well as to compare the BPSMC results with other blood pressure studies, (2) to examine the sources and amount of variation present in serial blood pressure of 123 children, and (3) to evaluate observer performance by means of intra- and inter-observer variability.^ Stepwise regression results from baseline revealed that of all anthropometric factors and age, weight was the best predictor for blood pressure.^ The results of serial blood pressure measurements show that, besides the known sources of blood pressure variability (subject, day, reading), the physiologic event of menarche has an important bearing upon the variability and characterization of blood pressure in young girls. The assessment of the effects of blood pressure variability and reliability upon the design and analysis of epidemiologic studies, became apparent among post-menarcheal girls; where blood pressure measurements taken from them have low reliability. Research is needed to propose alternatives for assessing blood pressure during puberty.^ Finally, observer performance of blood pressure and anthropometry were evaluated. Anthropometric measurements had reliabilities in excess of R = 0.96. Acceptable reliabilities (R = 0.88 to 0.95) were obtained for systolic and diastolic (phase 4 and 5) blood pressures. The BPSMC showed a 50 percent decrease in measurement error from the first to the third observation periods. ^