The Role of Cell Sterilization in Population Based Studies of Radiogenic Second Cancers Following Radiation Therapy

Advances in radiotherapy have generated increased interest in comparative studies of treatment techniques and their effectiveness. In this respect, pediatric patients are of specific interest because of their sensitivity to radiation induced second cancers. However, due to the rarity of childhood cancers and the long latency of second cancers, large sample sizes are unavailable for the epidemiological study of contemporary radiotherapy treatments. Additionally, when specific treatments are considered, such as proton therapy, sample sizes are further reduced due to the rareness of such treatments. We propose a method to improve statistical power in micro clinical trials. Specifically, we use a more biologically relevant quantity, cancer equivalent dose (DCE), to estimate risk instead of mean absorbed dose (DMA). Our objective was to demonstrate that when DCE is used fewer subjects are needed for clinical trials. Thus, we compared the impact of DCE vs. DMA on sample size in a virtual clinical trial that estimated risk for second cancer (SC) in the thyroid following craniospinal irradiation (CSI) of pediatric patients using protons vs. photons. Dose reconstruction, risk models, and statistical analysis were used to evaluate SC risk from therapeutic and stray radiation from CSI for 18 patients. Absorbed dose was calculated in two ways: with (1) traditional DMA and (2) with DCE. DCE and DMA values were used to estimate relative risk of SC incidence (RRCE and RRMA, respectively) after proton vs. photon CSI. Ratios of RR for proton vs. photon CSI (RRRCE and RRRMA) were then used in comparative estimations of sample size to determine the minimal number of patients needed to maintain 80% statistical power when using DCE vs. DMA. For all patients, we found that protons substantially reduced the risk of developing a second thyroid cancer when compared to photon therapy. Mean RRR values were 0.052±0.014 and 0.087±0.021 for RRRMA and RRRCE, respectively. However, we did not find that use of DCE reduced the number of patents needed for acceptable statistical power (i.e, 80%). In fact, when considerations were made for RRR values that met equipoise requirements and the need for descriptive statistics, the minimum number of patients needed for a micro-clinical trial increased from 17 using DMA to 37 using DCE. Subsequent analyses revealed that for our sample, the most influential factor in determining variations in sample size was the experimental standard deviation of estimates for RRR across the patient sample. Additionally, because the relative uncertainty in dose from proton CSI was so much larger (on the order of 2000 times larger) than the other uncertainty terms, it dominated the uncertainty in RRR. Thus, we found that use of corrections for cell sterilization, in the form of DCE, may be an important and underappreciated consideration in the design of clinical trials and radio-epidemiological studies. In addition, the accurate application of cell sterilization to thyroid dose was sensitive to variations in absorbed dose, especially for proton CSI, which may stem from errors in patient positioning, range calculation, and other aspects of treatment planning and delivery.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports largesample tests for complex survey designs and exact tests for small samples as well as classic large-sample x2-approximation tests based on Pearson’s X2, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read, 1984, Journal of the Royal Statistical Society, Series B (Methodological) 46: 440–464). The complex survey correction is based on the approach by Rao and Scott (1981, Journal of the American Statistical Association 76: 221–230) and parallels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enumeration. mgof also provides an exact one-sample Kolmogorov–Smirnov test for discrete data.

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. ^

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.^

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

A new Stata command called -mgof- is introduced. The command is used to compute distributional tests for discrete (categorical, multinomial) variables. Apart from classic large sample $\chi^2$-approximation tests based on Pearson's $X^2$, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read 1984), large sample tests for complex survey designs and exact tests for small samples are supported. The complex survey correction is based on the approach by Rao and Scott (1981) and parallels the survey design correction used for independence tests in -svy:tabulate-. The exact tests are computed using Monte Carlo methods or exhaustive enumeration. An exact Kolmogorov-Smirnov test for discrete data is also provided.

Statnote 8: statistical power and sample size

Statistical software is now commonly available to calculate Power (P') and sample size (N) for most experimental designs. In many circumstances, however, sample size is constrained by lack of time, cost, and in research involving human subjects, the problems of recruiting suitable individuals. In addition, the calculation of N is often based on erroneous assumptions about variability and therefore such estimates are often inaccurate. At best, we would suggest that such calculations provide only a very rough guide of how to proceed in an experiment. Nevertheless, calculation of P' is very useful especially in experiments that have failed to detect a difference which the experimenter thought was present. We would recommend that P' should always be calculated in these circumstances to determine whether the experiment was actually too small to test null hypotheses adequately.

Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression

Moderating effects of management control systems and innovation on performance. Simple methods for correcting the effects of measurement error for interaction effects in small samples

In the accounting literature, interaction or moderating effects are usually assessed by means of OLS regression and summated rating scales are constructed to reduce measurement error bias. Structural equation models and two-stage least squares regression could be used to completely eliminate this bias, but large samples are needed. Partial Least Squares are appropriate for small samples but do not correct measurement error bias. In this article, disattenuated regression is discussed as a small sample alternative and is illustrated on data of Bisbe and Otley (in press) that examine the interaction effect of innovation and style of use of budgets on performance. Sizeable differences emerge between OLS and disattenuated regression

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

Study of heat capacity measurement methods for small samples

Methods of measuring specific heats of small samples were studied. Three automated methods were explored, two of which have shown promising results. The adiabatic continuous heating method, has provided smooth well behaved data but further work is presently underway to improve on the results obtained so far . The decay method has been success fully implemented demonstrating reasonable agreement with accepted data for a copper test sample.

Moderating effects of management control systems and innovation on performance. Simple methods for correcting the effects of measurement error for interaction effects in small samples

In the accounting literature, interaction or moderating effects are usually assessed by means of OLS regression and summated rating scales are constructed to reduce measurement error bias. Structural equation models and two-stage least squares regression could be used to completely eliminate this bias, but large samples are needed. Partial Least Squares are appropriate for small samples but do not correct measurement error bias. In this article, disattenuated regression is discussed as a small sample alternative and is illustrated on data of Bisbe and Otley (in press) that examine the interaction effect of innovation and style of use of budgets on performance. Sizeable differences emerge between OLS and disattenuated regression

Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression