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. ^

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.

Contribution of the genes of the renin-angiotensin system to interindividual differences in blood pressure levels in Caucasians from Rochester, Minnesota

The Renin-Angiotensin system (RAS) regulates blood pressure through its effects on vascular tone, renal hemodynamics, and renal sodium and fluid balance. The genes encoding the four major components of the RAS, angiotensinogen, renin, angiotensin I-converting enzyme (ACE), and angiotensin II receptor type 1 (AT1), have been investigated as candidate genes in the pathogenesis of essential hypertension. However, studies have primarily focused on small samples of diseased individuals, and, therefore, have provided little information about the determinants of interindividual variation in blood pressure (BP) in the general population.^ Using data from a large population-based sample from Rochester, MN, I have evaluated the contribution of variation in the region of the RAS genes to interindividual variation in systolic, diastolic, and mean arterial pressure in the population-at-large. Marker genotype data from four polymorphisms located within or very near these genes were first collected on 3,974 individuals from 583 randomly ascertained three-generation pedigrees. Haseman-Elston regression and variance component methods of linkage analysis were then carried out to estimate the proportion of interindividual variance in BP attributable to the effects of variation at these four measured loci.^ A significant effect of the ACE locus on interindividual variation in mean arterial pressure (MAP) was detected in a sample of siblings belonging to the youngest generation. After allowing for measured covariates, this effect accounted for 15-25% of the interindividual variance in MAP, and was even greater in a subset with a positive family history of hypertension. When gender-specific analyses were carried out, this effect was significant in males but not in females. Extended pedigree analyses also provided evidence for an effect of the ACE locus on interindividual variation in MAP, but no difference between males and females was observed. Circumstantial evidence suggests that the ACE gene itself may be responsible for the observed effects on BP, although the possibility that other genes in the region may be at play cannot be excluded.^ No definitive evidence for an effect of the renin, angiotensinogen, or AT1 loci on interindividual variation in BP was obtained in this study, suggesting that the impact of these genes on BP may not be great in the Caucasian population-at-large. However, this does not preclude a larger effect of these genes in some subsets of individuals, especially among those with clinically manifest hypertension or coronary heart disease, or in other populations. ^

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Upregulation of defensins in burn sheep small intestine.

OBJECTIVE: The aim of this study was to visualize and localize the sheep antimicrobials, beta-defensins 1, 2, and 3, (SBD-1, SBD-2, SBD-3), sheep neutrophil defensin alpha (SNP-1), and the cathelicidin LL-37 in sheep small intestine after burn injury, our hypothesis being that these compounds would be upregulated in an effort to overcome a compromised endothelial lining. Response to burn injury includes the release of proinflammatory cytokines and systemic immune suppression that, if untreated, can progress to multiple organ failure and death, so protective mechanisms have to be initiated and implemented. METHODS: Tissue sections were probed with antibodies to the antimicrobials and then visualized with fluorescently labeled secondary antibodies and subjected to fluorescence deconvolution microscopy and image reconstruction. RESULTS: In both the sham and burn samples, all the aforementioned antimicrobials were seen in each of the layers of small intestine, the highest concentration being localized to the epithelium. SBD-2, SBD-3, and SNP-1 were upregulated in both enterocytes and Paneth cells, while SNP-1 and LL-37 showed increases in both the inner circular and outer longitudinal muscle layers of the muscularis externa following burn injury. Each of the defensins, except SBD-1, was also seen in between the muscle layers of the externa and while burn caused slight increases of SBD-2, SBD-3, and SNP-1 in this location, LL-37 content was significantly decreased. CONCLUSION: That while each of these human antimicrobials is present in multiple layers of sheep small intestine, SBD-2, SBD-3, SNP-1, and LL-37 are upregulated in the specific layers of the small intestine.

Oncogenic activation of c-Abl tyrosine kinase in non-small cell lung cancer: FUS1 tumor suppressor down-regulates c-Abl tyrosine kinase

The FUS1 tumor suppressor gene (TSG) has been found to be deficient in many human non-small cell lung cancer (NSCLC) tissue samples and cell lines (1,2,3). Studies have shown potent anti-tumor activity of FUS1 in animal models where FUS1 was delivered through a liposomal vector (4) and the use of FUS1 as a therapeutic agent is currently being studied in clinical human trials (5). Currently, the mechanisms of FUS1 activity are being investigated and my studies have shown that c-Abl tyrosine kinase is inhibited by the FUS1 TSG.^ Considering that many NSCLC cell lines are FUS1 deficient, my studies further identified that FUS1 deficient NSCLC cells have an activated c-Abl tyrosine kinase. C-Abl is a known proto-oncogene and while c-Abl kinase is tightly regulated in normal cells, constitutively active Abl kinase is known to contribute to the oncogenic phenotype in some types of hematopoietic cancers. My studies show that the active c-Abl kinase contributes to the oncogenicity of NSCLC cells, particularly in tumors that are deficient in FUS1, and that c-Abl may prove to be a viable target in NSCLC therapy.^ Current studies have shown that growth factor receptors play a role in NSCLC. Over-expression of the epidermal growth factor receptor (EGFR) plays a significant role in aggressiveness of NSCLC. Current late stage treatments include EFGR tyrosine kinase inhibitors or EGFR antibodies. Platelet-derived growth factor receptor (PDGFR) also has been shown to play a role in NSCLC. Of note, both growth factor receptors are known upstream activators of c-Abl kinase. My studies indicate that growth factor receptor simulation along deficiency in FUS1 expression contributes to the activation of c-Abl kinase in NSCLC cells. ^

Genome instability quantified in constitutive tissues as well as putatively stable tumor tissue in hereditary non -polyposis colon cancer patients by small pool PCR

Microsatellite instability (MSI) is a hallmark of the mutator phenotype associated with Hereditary Non-Polyposis Colon Cancer (HNPCC). The MSI-High (MSI-H) HNPCC population has been well characterized, but the microsatellite low and stable (MSI-L/MSS) HNPCC population is much less understood. We hypothesize there are significant levels of MSI in HNPCC DNA classified as MSI-L/MSS, but no single variant allele makes up a sufficient population in the tumor DNA to be detected by standard analysis. Finding variants would suggest there is a mutator phenotype for the MSI-L/MSS HNPCC population that is distinct from the MSI-H HNPCC populations. This study quantified and compared MSI in HNPCC patients previously shown to be MSI-H, MSI-L/MSS and an MSI-H older, sporadic colorectal cancer patient. Small-pool Polymerase Chain Reactions (SP-PCRs) were conducted where the DNAs from each sample and controls are diluted into multiple pools, each containing approximately single genome equivalents. At least 100 alleles/sample were studied at six microsatellite loci. Mutant fragments were identified, quantified, and compared using Poisson statistics. Most of the variants were small deletions or insertions, with more mutants being deletions, as has been previously described in yeast and transgenic mice. SP-PCR, where most of the pools contained only 3 or less fragments, enabled identification of variants too infrequent to be detected by large pool PCR. Mutant fragments in positive control MSI-H tumor samples ranged from 0.26 to 0.68 in at least 4 of the 6 loci tested and were consistent with their MSI-H status. In the so called MSS tumors and constitutive tissues (normal colon tissue, and PBLs) of all the HNPCC patients, low, but significant levels of MSI were seen in at least two of the loci studied. This phenomenon was not seen in the sporadic MSI constitutive tissues nor the normal controls and suggests haploinsufficiency, gain-of-function, or a dominant/negative basis of the instability in HNPCC patients carrying germline mutations for tumor suppressor genes. A different frequency and spectrum of mutant fragments suggests a different genetic basis (other than a major mutation in MLH1 or MSH2) for disease in MSI-L and MSS HNPCC patients. ^