Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

The impact of 1995--1996 health sector reforms in the effectiveness of malaria control program in the state of Orissa, India

Malaria poses a significant public health problem worldwide. The World Health Organization indicates that approximately 40% of the world's population and almost 85% of the population from the South–East Asian region is at risk of contracting malaria. India being the most populous country in the region, contributes the highest number of malaria cases and deaths attributed to malaria. Orissa is the state that has the highest number of malaria cases and deaths attributable to malaria. A secondary data analysis was carried out to evaluate the effectiveness of the World bank-assisted Malaria Action Program in the state of Orissa under the health sector reforms of 1995-96. The secondary analysis utilized the government of India's National Anti Malaria Management Information System's (NAMMIS) surveillance data and the National Family Health Survey (NFHS–I and NFHS–II) datasets to compare the malaria mortality and morbidity in the state between 1992-93 and 1998-99. Results revealed no effect of the intervention and indicated an increase of 2.18 times in malaria mortality between 1992-1999 and an increase of 1.53 times in malaria morbidity between 1992-93 and 1998-99 in the state. The difference in the age-adjusted malaria morbidity in the state between the time periods of 1992-93 and 1998-99 proved to be highly significant (t = 4.29 df=16, p<. 0005) whereas the difference between the increase of age-adjusted malaria morbidity during 1992-93 and 1998-99 between Orissa (with intervention) and Bihar (no intervention) proved to be non significant (t=.0471 df=16, p<.50). Factors such as underutilization of World Bank funds for the malaria control program, inadequate health care infrastructure, structural adjustment problems, poor management, poor financial management, parasite resistance to anti-malarial drugs, inadequate supply of drugs and staff shortages may have contributed to the failure of the program in the state.^

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

A descriptive study of comprehensive and categorical services for pregnant and parenting adolescents in West Dallas

This study evaluates the effectiveness of the Children and Youth Projects' Adolescent Family Life Program, a comprehensive program serving pregnant and parenting adolescents in the economically disadvantaged area of West Dallas. The underlying question asked is what are the relative contributions of the comprehensive, school-linked Adolescent Family Life (AFL) Program compared with the Maternal Health and Family Planning Program (MHFPP), a categorical provider of family planning and reproductive services, towards meeting the immediate and intermediate term needs of adolescent mothers. Also addressed are the protective effects of participation in the Dallas Independent School District Health Special Program, a segregated school for pregnant adolescents.^ A cohort of 339 West Dallas adolescent mothers who delivered babies during a two-year period, 1986 through 1987, are monitored by linking records from Parkland Hospital, the primary provider to hospital services to indigent women in Dallas, the Dallas Independent School District, and the prenatal care providers, the AFL and MHFP Programs. Information is collected on each teen describing her demographic, fertility, service utilization and educational characteristics.^ The study tests the hypothesis that adolescents receiving services from the comprehensive AFL program will be less likely to have a repeat birth and to discontinue school during the 24 month study period, compared with categorical provider clients. Although the study finds that there are no statistically significant differences in repeat deliveries, using survival analysis, or in school continuation between programs, important findings are revealed about the ethnic differences. Black and Hispanic fertility and educational behaviors are compared, and their implications for program design and evaluation discussed. ^

Isolation and characterization of a novel human Mix -like homeobox gene MIXL

Molecular events involved in specification of early hematopoietic system are not well known. In Xenopus, a paired-box homeodomain family (Mix.1–4) has been implicated in this process. Although Mix-like homeobox genes have been isolated from zebrafish (bon), chicken (CMIX) and mice (MmI/MIXL1), isolation of a human Mix-like gene has remained elusive. ^ We have recently isolated and characterized a novel human Mix-like homeobox gene with a predicted open reading frame of 232 amino acids designated the Mix.1 homeobox (Xenopus laevis)-like gene (MIXL). The overall identity of this novel protein to CMIX and MmI/MIXL1 is 41% and 69%, respectively. However, the identity in the homeodomain is 66% to that of Xenopus Mix.1, 79% to that of CMIX, and 94% to that of MmI/MIXL1. In normal hematopoiesis, MIXL expression appears to be restricted immature B and T lymphoid cells. Several acute leukemic cell lines of B, T and myeloid lineages express MIXL suggesting a survival/block in differentiation advantage. Furthermore, Xenopus animal cap assay revealed that MIXL could induce expression of the α-globin gene, suggesting a functional conservation of the homeodomain. ^ Biochemical analysis revealed that MIXL proteins are phosphorylated at multiple sites. Immunoprecipitation and immunoblotting confirmed that MIXL is tyrosine phosphorylated. Mutational analysis determined that Tyr20 appears to be the site for phosphorylation. However, deletion analysis preliminarily showed that the proline-rich domain appears not to be necessary for tyrosine phosphorylation. The novel finding will help us make a deeper understanding of the regulation on homeodomain proteins by rarely reported tyrosine phosphorylation. ^ Taken together, isolation of the MIXL gene is the first step toward understanding novel regulatory circuits in early hematopoietic differentiation and malignant transformation. ^