Adjustment with Three Continuous Variables

Spurious association between X and Y may be due to a confounding variable W. Statisticians may adjust for W using a variety of techniques. This paper presents the results of simulations conducted to assess the performance of those techniques under various, elementary, data-generating processes. The results indicate that no technique is best overall and that specific techniques should be selected based on the particulars of the data-generating process. Here we show how causal graphs can guide the selection or design of techniques for statistical adjustment. R programs are provided for researchers interested in generalization

Model-Robust Inference for Clinical Trials that Improve Precision by Stratified Randomization and Adjustment for Additional Baseline Variables

We focus on estimating the average treatment effect in clinical trials that involve stratified randomization, which is commonly used. It is important to understand the large sample properties of estimators that adjust for stratum variables (those used in the randomization procedure) and additional baseline variables, since this can lead to substantial gains in precision and power. Surprisingly, to the best of our knowledge, this is an open problem. It was only recently that a simpler problem was solved by Bugni et al. (2018) for the case with no additional baseline variables, continuous outcomes, the analysis of covariance (ANCOVA) estimator, and no missing data. We generalize their results in three directions. First, in addition to continuous outcomes, we handle binary and time-to-event outcomes; this broadens the applicability of the results. Second, we allow adjustment for an additional, preplanned set of baseline variables, which can improve precision. Third, we handle missing outcomes under the missing at random assumption. We prove that a wide class of estimators is asymptotically normally distributed under stratified randomization and has equal or smaller asymptotic variance than under simple randomization. For each estimator in this class, we give a consistent variance estimator. This is important in order to fully capitalize on the combined precision gains from stratified randomization and adjustment for additional baseline variables. The above results also hold for the biased-coin covariate-adaptive design. We demonstrate our results using completed trial data sets of treatments for substance use disorder, where adjustment for additional baseline variables brings substantial variance reduction

Mild and moderate pre-dialysis chronic kidney disease is associated with increased coronary artery calcium.

BackgroundIt is increasingly evident that patients with chronic kidney disease (CKD) are more likely to die from heart disease than kidney failure. This study evaluated whether pre- dialysis CKD is an independent risk factor for coronary artery calcium (CAC).MethodsA total of 544 consecutive patients who underwent CAC scoring were analyzed. Eleven patients requiring hemodialysis were excluded. Patients were divided into three groups: normal glomerular filtration rate (GFR) (GFR > 90 mL/min/1.73 m²), mild CKD (90 ≥ GFR > 60 mL/min/1.73 m²), and moderate CKD (60 ≥ GFR > 30 mL/min/1.73 m²). Continuous and categorical variables were compared using analysis of variance and the χ² statistic. A multiple logistic regression model was used for detecting the association between total CAC score and GFR. An unadjusted model was used, followed by a second model adjusted for covariates known to be related to CAC. Another multivariable binary logistic model predicting the presence of CAC (>10) was performed and odds of incidence of CAC (>10) were calculated among the three GFR subgroups.ResultsAfter adjustment for covariates, patients with mild CKD had mean CAC scores 175 points higher than those with the referent normal GFR (P = 0.048), while those with moderate CKD had mean CAC scores 693 points higher than the referent (P < 0.001). After adjustment for covariates, patients with mild CKD were found to be 2.2 times more likely (95% confidence interval 1.3-3.7, P = 0.004) and patients with moderate CKD were 6.4 times more likely (95% confidence interval 2.9-14.3, P < 0.001) to have incident CAC compared with the group with normal GFR.ConclusionMild and moderate pre-dialysis CKD are independent risk factors for increased mean and incident CAC

Sleep Patterns and the Behavior of Children in the Second-, Third-, and Fourth-Grades in Urban Public Schools

This investigation examined the relationship between nocturnal sleep patterns and behaviors in the classroom of seventy-four girls and fifty-nine boys from second-, third-, and fourth-grades attending five urban public schools in Norfolk, Virginia. The dependent variables were the classroom behavior that was subdivided into five personality areas for objective assessment of the student\u27s adjustment areas labeled self, social, school, home, and physical. The objective assessment was observed and documented on a seventy-eight item questionnaire by their primary classroom teachers who were familiar with the subjects behavior. The parents observed and recorded data on a sleep log listing independent variables such as length of daytime naps, time to bed, number of hours slept, number of hours in bed, age, and gender. The parents recorded the data on the sleep log for seven nights. Other independent variables were grade ranking and type of lunch subsidy. Stepwise regressions revealed that night awakenings have a significant impact on home, social, self, school, and total adjustment. A one-way MANOVA with hours of sleep as the categorical variable with three levels of sleep indicated that the length of sleep had no impact on a child\u27s adjustment. The levels of sleep were less than nine-hours, 9.00-to-10.45 hours, and 10.5 hours and greater. The recorded time difference between the longest sleeper and the shortest sleeper is only 0.66 hours. Study findings suggest that continuous and uninterrupted sleep is more critical than actual length of sleep. A two-way MANOVA yielded statistically significant main effects of gender and Tukey\u27s HSD test revealed gender effects (self, social, school, and physical but not home) indicating better adjustment for girls than boys. The two-way MANOVA yielded nonsignificant main effects for age. The interaction effect of gender and age was significant. In conclusion, the findings of the current study suggest practical applications to the urban environment. Parents can be educated to direct attention to their children\u27s sleep practices, schedules, and daily stresses in order to enhance continuous and uninterrupted sleep

Increments to life and mortality tempo

This paper introduces and develops the idea of “increments to life.†Increments to life are roughly analogous to forces of mortality: they are quantities specified for each age and time by a mathematical function of two variables that may be used to describe, analyze and model changing length of life in populations. The rationale is three-fold. First, I wanted a general mathematical representation of Bongaart’s “life extension†pill (Bongaarts and Feeney 2003) allowing for continuous variation in age and time. This is accomplished in sections 3-5, to which sections 1-2 are preliminaries. It turned out to be a good deal more difficult than I expected, partly on account of the mathematics, but mostly because it requires thinking in very unaccustomed ways. Second, I wanted a means of assessing the robustness of the Bongaarts-Feeney mortality tempo adjustment formula (Bongaarts and Feeney 2003) against variations in increments to life by age. Section 6 shows how the increments to life mathematics accomplishes this with an application to the Swedish data used in Bongaarts and Feeney (2003). In this application, at least, the Bongaarts-Feeney adjustment is robust. Third, I hoped by formulating age-variable increments to life to avoid the slight awkwardness of working with conditional rather than unconditional survival functions. This third aim has not been accomplished, but this appears to be because it was unreasonable to begin with. While it is possible to conceptualize length of life as completely described by an age-varying increments to life function, this is not consistent with the Bongaarts-Feeney mortality tempo adjustment. What seems to be needed, rather, is a model that incorporates two fundamentally different kinds of changes in mortality and length of life, one based on the familiar force of mortality function, the other based on the increments to life function. Section 7 considers heuristically what such models might look like.adult mortality, increments to life, length of life, life expectancy at birth, mortality, mortality measurement, mortality tempo, mortality tempo adjustment, period-cohort relationships, risk of death, robustness of Bongaarts-Feeney method, tempo adjustment

Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon – the reversal paradox

This article discusses three statistical paradoxes that pervade epidemiological research: Simpson's paradox, Lord's paradox, and suppression. These paradoxes have important implications for the interpretation of evidence from observational studies. This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon – the reversal paradox – depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three. Although the three statistical paradoxes occur in different types of variables, they share the same characteristic: the association between two variables can be reversed, diminished, or enhanced when another variable is statistically controlled for. Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings. These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results