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.^

Whence a healthy mind: Correlation of physical fitness and academic performance among schoolchildren

Background. Public schools are a key forum in the fight for child health because of the opportunities they present for physical activity and fitness surveillance. However, because schools are evaluated and funded on the basis of standardized academic performance rather than physical activity, empirical research evaluating the connections between fitness and academic performance is needed to justify curriculum allocations to physical activity. ^ Methods. Analyses were based on a convenience sample of 315,092 individually-matched standardized academic (TAKS™) and fitness (FITNESSGRAM®) test records collected by 13 Texas school districts under state mandates. We categorized each fitness result in quintiles by age and gender and used a mixed effects regression model to compare the academic performance of the top and bottom fitness groups for each fitness test and grade level combination. ^ Results. All fitness variables except BMI showed significant, positive associations with academic performance after sociodemographic covariate adjustments, with effect sizes ranging from 0.07 (95% CI: 0.05,0.08) in girls trunklift-TAKS reading to 0.34 (0.32,0.35) in boys cardiovascular-TAKS math. Cardiovascular fitness showed the largest inter-quintile difference in TAKS score (32-75 points), followed by curl-ups. After an additional adjustment for BMI and curl-ups, cardiovascular associations peaked in 8th-9 th grades (maximum inter-quintile difference 142 TAKS points; effect size 0.75 (0.69,0.82) for 8th grade girls math) and showed dose-response characteristics across quintiles (p<0.001 for both genders and outcomes). BMI analysis demonstrated limited, non-linear association with academic performance after adjustment for sociodemographic, cardiovascular fitness and curl-up variables. Low-BMI Hispanic high school boys showed significantly lower TAKS scores than the moderate (but not high) BMI group. High-BMI non-Hispanic white high school girls showed significantly lower scores than the moderate (but not low) BMI group. ^ Conclusions. In this study, fitness was strongly and significantly related to academic performance. Cardiovascular fitness showed a distinct dose-response association with academic performance independent of other sociodemographic and fitness variables. The association peaked in late middle to early high school. The independent association of BMI to academic performance was only found in two sub-groups and was non-linear, with both low and high BMI posing risk relative to moderate BMI but not to each other. In light of our findings, we recommend that policymakers consider PE mandates in middle-high school and require linkage of academic and fitness records to facilitate longitudinal surveillance. School administrators should consider increasing PE time in pursuit of higher academic test scores, and PE practitioners should emphasize cardiovascular fitness over BMI reduction.^

A Bayesian approach to estimating the intraclass correlation coefficient

A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^

Correlation of blood type with thrombosis in pancreatic cancer patients

Objective: The study aimed to identify the risk factors involved in initiating thromboembolism (TE) in pancreatic cancer (PC) patients, with focus on ABO blood type. ^ Methods and Patients: There were 35.7% confirmed cases of TE and 64.3% cases remained free of TE (n=687). There were 12.7% only Pulmonary embolism (PE), 9% only Deep vein thrombosis (DVT), 53.5% only other sites, 3.3% combined PE and DVT, 8.6% combined PE and other sites, 9.8% combined DVT and other sites, and 3.3% all three combined cases. ^ Results: The risk factors for thrombosis identified by multivariate logistic regression were: history of previous anti-thrombotic treatment, tumor site in pancreatic body or tail, large tumor size, maximum glucose category more than 126 and 200 mg/dL. ^ The factors with worse overall survival by multivariate Cox regression and Kaplan Meier analyses were: locally advanced or metastatic stage, worsening performance status, high CA 19-9 levels, and HbA1C levels more than 6 %, at diagnosis. ^ There were 29.1% and 39.1% of the patients with thrombosis in the O and non-O blood type groups respectively. Both Non-O blood type (P=0.02) and the A, B and AB blood types (P= 0.007) were associated with thrombosis as compared to O type. The odds of thrombosis were nearly half in O blood type patients as compared to non-O blood type [OR-0.54 (95% C.I.- 0.37-0.79), P<0.001]. ^ Conclusion: A better understanding of the TE and PC relationship and involved risk factors may provide insights on tumor biology and patient response to prophylactic anticoagulation therapy.^