Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Tracking of plasma lipids and lipoproteins, within-person and year-to-year variability in plasma cholesterol levels among participants from age 8 to 18 in Project HeartBeat!

Coronary heart disease remains the leading cause of death in the United States and increased blood cholesterol level has been found to be a major risk factor with roots in childhood. Tracking of cholesterol, i.e., the tendency to maintain a particular cholesterol level relative to the rest of the population, and variability in blood lipid levels with increase in age have implications for cholesterol screening and assessment of lipid levels in children for possible prevention of further rise to prevent adulthood heart disease. In this study the pattern of change in plasma lipids, over time, and their tracking were investigated. Also, within-person variance and retest reliability defined as the square root of within-person variance for plasma total cholesterol, HDL-cholesterol, LDL-cholesterol, and triglycerides and their relation to age, sex and body mass index among participants from age 8 to 18 years were investigated. ^ In Project HeartBeat!, 678 healthy children aged 8, 11 and 14 years at baseline were enrolled and examined at 4-monthly intervals for up to 4 years. We examined the relationship between repeated observations by Pearson's correlations. Age- and sex-specific quintiles were calculated and the probability of participants to remain in the uppermost quintile of their respective distribution was evaluated with life table methods. Plasma total cholesterol, HDL-C and LDL-C at baseline were strongly and significantly correlated with measurements at subsequent visits across the sex and age groups. Plasma triglyceride at baseline was also significantly correlated with subsequent measurements but less strongly than was the case for other plasma lipids. The probability to remain in the upper quintile was also high (60 to 70%) for plasma total cholesterol, HDL-C and LDL-C. ^ We used a mixed longitudinal, or synthetic cohort design with continuous observations from age 8 to 18 years to estimate within person variance of plasma total cholesterol, HDL-C, LDL-C and triglycerides. A total of 5809 measurements were available for both cholesterol and triglycerides. A multilevel linear model was used. Within-person variance among repeated measures over up to four years of follow-up was estimated for total cholesterol, HDL-C, LDL-C and triglycerides separately. The relationship of within-person and inter-individual variance with age, sex, and body mass index was evaluated. Likelihood ratio tests were conducted by calculating the deviation of −2log (likelihood) within the basic model and alternative models. The square root of within-person variance provided the retest reliability (within person standard deviation) for plasma total cholesterol, HDL-C, LDL-C and triglycerides. We found 13.6 percent retest reliability for plasma cholesterol, 6.1 percent for HDL-cholesterol, 11.9 percent for LDL-cholesterol and 32.4 percent for triglycerides. Retest reliability of plasma lipids was significantly related with age and body mass index. It increased with increase in body mass index and age. These findings have implications for screening guidelines, as participants in the uppermost quintile tended to maintain their status in each of the age groups during a four-year follow-up. The magnitude of within-person variability of plasma lipids influences the ability to classify children into risk categories recommended by the National Cholesterol Education Program. ^

DNA nucleotide excision repair gene single nucleotide polymorphisms and hereditary nonpolyposis colorectal cancer

Hereditary nonpolyposis colorectal cancer (HNPCC) is an autosomal dominant disease caused by germline mutations in DNA mismatch repair(MMR) genes. The nucleotide excision repair(NER) pathway plays a very important role in cancer development. We systematically studied interactions between NER and MMR genes to identify NER gene single nucleotide polymorphism (SNP) risk factors that modify the effect of MMR mutations on risk for cancer in HNPCC. We analyzed data from polymorphisms in 10 NER genes that had been genotyped in HNPCC patients that carry MSH2 and MLH1 gene mutations. The influence of the NER gene SNPs on time to onset of colorectal cancer (CRC) was assessed using survival analysis and a semiparametric proportional hazard model. We found the median age of onset for CRC among MMR mutation carriers with the ERCC1 mutation was 3.9 years earlier than patients with wildtype ERCC1(median 47.7 vs 51.6, log-rank test p=0.035). The influence of Rad23B A249V SNP on age of onset of HNPCC is age dependent (likelihood ratio test p=0.0056). Interestingly, using the likelihood ratio test, we also found evidence of genetic interactions between the MMR gene mutations and SNPs in ERCC1 gene(C8092A) and XPG/ERCC5 gene(D1104H) with p-values of 0.004 and 0.042, respectively. An assessment using tree structured survival analysis (TSSA) showed distinct gene interactions in MLH1 mutation carriers and MSH2 mutation carriers. ERCC1 SNP genotypes greatly modified the age onset of HNPCC in MSH2 mutation carriers, while no effect was detected in MLH1 mutation carriers. Given the NER genes in this study play different roles in NER pathway, they may have distinct influences on the development of HNPCC. The findings of this study are very important for elucidation of the molecular mechanism of colon cancer development and for understanding why some mutation carriers of the MSH2 and MLH1 gene develop CRC early and others never develop CRC. Overall, the findings also have important implications for the development of early detection strategies and prevention as well as understanding the mechanism of colorectal carcinogenesis in HNPCC. ^

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^

Diabetes genes and risk of prostate cancer in the Atherosclerosis Risk in Communities study

Prostate cancer (PrCa) is a leading cause of morbidity and mortality, yet the etiology remains uncertain. Meta-analyses show that PrCa risk is reduced by 16% in men with type 2 diabetes (T2D), but the mechanism is unknown. Recent genome-wide association studies and meta-analyses have found single nucleotide polymorphisms (SNPs) that consistently predict T2D risk. We evaluated associations of incident PrCa with 14 T2D SNPs in the Atherosclerosis Risk in Communities (ARIC) study. From 1987-2000, there were 397 incident PrCa cases ascertained from state or local cancer registries among 6,642 men (1,560 blacks and 5,082 whites) aged 45-64 years at baseline. Genotypes were determined by TaqMan assay. Cox proportional hazards models were used to assess the association between PrCa and increasing number of T2D risk-raising alleles for individual SNPs and for genetic risk scores (GRS) comprised of the number of T2D risk-raising alleles across SNPs. Two-way gene-gene interactions were evaluated with likelihood ratio tests. Using additive genetic models, the T2D risk-raising allele was associated with significantly reduced risk of PrCa for IGF2BP2 rs4402960 (hazard ratio [HR]=0.79; P=0.07 among blacks only), SLC2A2 rs5400 (race-adjusted HR=0.85; P=0.05) and UCP2 rs660339 (race-adjusted HR=0.84; P=0.02), but significantly increased risk of PrCa for CAPN10 rs3792267 (race-adjusted HR=1.20; P=0.05). No other SNPs were associated with PrCa using an additive genetic model. However, at least one copy of the T2D risk-raising allele for TCF7L2 rs7903146 was associated with reduced PrCa risk using a dominant genetic model (race-adjusted HR=0.79; P=0.03). These results imply that the T2D-PrCa association may be partly due to shared genetic variation, but these results should be verified since multiple tests were performed. When the combined, additive effects of these SNPs were tested using a GRS, there was nearly a 10% reduction in risk of PrCa per T2D risk-raising allele (race-adjusted HR=0.92; P=0.02). SNPs in IGF2BP2, KCNJ11 and SLC2A2 were also involved in multiple synergistic gene-gene interactions on a multiplicative scale. In conclusion, it appears that the T2D-PrCa association may be due, in part, to common genetic variation. Further knowledge of T2D gene-PrCa mechanisms may improve understanding of PrCa etiology and may inform PrCa prevention and treatment.^

BEST SUBSET SELECTION FOR CATEGORICAL DATA

When choosing among models to describe categorical data, the necessity to consider interactions makes selection more difficult. With just four variables, considering all interactions, there are 166 different hierarchical models and many more non-hierarchical models. Two procedures have been developed for categorical data which will produce the "best" subset or subsets of each model size where size refers to the number of effects in the model. Both procedures are patterned after the Leaps and Bounds approach used by Furnival and Wilson for continuous data and do not generally require fitting all models. For hierarchical models, likelihood ratio statistics (G('2)) are computed using iterative proportional fitting and "best" is determined by comparing, among models with the same number of effects, the Pr((chi)(,k)('2) (GREATERTHEQ) G(,ij)('2)) where k is the degrees of freedom for ith model of size j. To fit non-hierarchical as well as hierarchical models, a weighted least squares procedure has been developed.^ The procedures are applied to published occupational data relating to the occurrence of byssinosis. These results are compared to previously published analyses of the same data. Also, the procedures are applied to published data on symptoms in psychiatric patients and again compared to previously published analyses.^ These procedures will make categorical data analysis more accessible to researchers who are not statisticians. The procedures should also encourage more complex exploratory analyses of epidemiologic data and contribute to the development of new hypotheses for study. ^

Exploration of genetic susceptibility to pancreatic cancer: A GWAS approach

Pancreatic cancer is the 4th most common cause for cancer death in the United States, accompanied by less than 5% five-year survival rate based on current treatments, particularly because it is usually detected at a late stage. Identifying a high-risk population to launch an effective preventive strategy and intervention to control this highly lethal disease is desperately needed. The genetic etiology of pancreatic cancer has not been well profiled. We hypothesized that unidentified genetic variants by previous genome-wide association study (GWAS) for pancreatic cancer, due to stringent statistical threshold or missing interaction analysis, may be unveiled using alternative approaches. To achieve this aim, we explored genetic susceptibility to pancreatic cancer in terms of marginal associations of pathway and genes, as well as their interactions with risk factors. We conducted pathway- and gene-based analysis using GWAS data from 3141 pancreatic cancer patients and 3367 controls with European ancestry. Using the gene set ridge regression in association studies (GRASS) method, we analyzed 197 pathways from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. Using the logistic kernel machine (LKM) test, we analyzed 17906 genes defined by University of California Santa Cruz (UCSC) database. Using the likelihood ratio test (LRT) in a logistic regression model, we analyzed 177 pathways and 17906 genes for interactions with risk factors in 2028 pancreatic cancer patients and 2109 controls with European ancestry. After adjusting for multiple comparisons, six pathways were marginally associated with risk of pancreatic cancer ( P < 0.00025): Fc epsilon RI signaling, maturity onset diabetes of the young, neuroactive ligand-receptor interaction, long-term depression (Ps < 0.0002), and the olfactory transduction and vascular smooth muscle contraction pathways (P = 0.0002; Nine genes were marginally associated with pancreatic cancer risk (P < 2.62 × 10−5), including five reported genes (ABO, HNF1A, CLPTM1L, SHH and MYC), as well as four novel genes (OR13C4, OR 13C3, KCNA6 and HNF4 G); three pathways significantly interacted with risk factors on modifying the risk of pancreatic cancer (P < 2.82 × 10−4): chemokine signaling pathway with obesity ( P < 1.43 × 10−4), calcium signaling pathway (P < 2.27 × 10−4) and MAPK signaling pathway with diabetes (P < 2.77 × 10−4). However, none of the 17906 genes tested for interactions survived the multiple comparisons corrections. In summary, our current GWAS study unveiled unidentified genetic susceptibility to pancreatic cancer using alternative methods. These novel findings provide new perspectives on genetic susceptibility to and molecular mechanisms of pancreatic cancer, once confirmed, will shed promising light on the prevention and treatment of this disease. ^