Detection of nonrandom association of alleles from the distribution of the number of heterozygous loci in a sample.

The distribution of the number of heterozygous loci in two randomly chosen gametes or in a random diploid zygote provides information regarding the nonrandom association of alleles among different genetic loci. Two alternative statistics may be employed for detection of nonrandom association of genes of different loci when observations are made on these distributions: observed variance of the number of heterozygous loci (s2k) and a goodness-of-fit criterion (X2) to contrast the observed distribution with that expected under the hypothesis of random association of genes. It is shown, by simulation, that s2k is statistically more efficient than X2 to detect a given extent of nonrandom association. Asymptotic normality of s2k is justified, and X2 is shown to follow a chi-square (chi 2) distribution with partial loss of degrees of freedom arising because of estimation of parameters from the marginal gene frequency data. Whenever direct evaluations of linkage disequilibrium values are possible, tests based on maximum likelihood estimators of linkage disequilibria require a smaller sample size (number of zygotes or gametes) to detect a given level of nonrandom association in comparison with that required if such tests are conducted on the basis of s2k. Summarization of multilocus genotype (or haplotype) data, into the different number of heterozygous loci classes, thus, amounts to appreciable loss of information.

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.^

Design of long-term animal bioassay for low-dose extrapolation using a multistage model

Conventional designs of animal bioassays allocate the same number of animals into control and dose groups to explore the spontaneous and induced tumor incidence rates, respectively. The purpose of such bioassays are (a) to determine whether or not the substance exhibits carcinogenic properties, and (b) if so, to estimate the human response at relatively low doses. In this study, it has been found that the optimal allocation to the experimental groups which, in some sense, minimize the error of the estimated response for low dose extrapolation is associated with the dose level and tumor risk. The number of dose levels has been investigated at the affordable experimental cost. The pattern of the administered dose, 1 MTD, 1/2 MTD, 1/4 MTD,....., etc. plus control, gives the most reasonable arrangement for the low dose extrapolation purpose. The arrangement of five dose groups may make the highest dose trivial. A four-dose design can circumvent this problem and has also one degree of freedom for testing the goodness-of-fit of the response model.^ An example using the data on liver tumors induced in mice in a lifetime study of feeding dieldrin (Walker et al., 1973) is implemented with the methodology. The results are compared with conclusions drawn from other studies. ^

THE RECOVERY OF ENTEROPATHOGENS FROM CONTAMINATED COOKED FOODS AT HOLDING TEMPERATURES

Hot foods served in foodservice establishments, institutions and homes, have always been regarded as safe, since cooking temperatures are more likely to kill the bacterial agents that may cause foodborne diseases. However, foods that are otherwise served hot have been epidemiologically incriminated for causing foodborne diseases. This situation arises due to the possible post-cooking food contamination. Post-cooking contamination of hot-held food is most threatening for it gives the contaminating agents the possibility of proliferation. On one hand, post-cooking contamination is least understood and on the other, hot-holding of food gives the consumer a false sense of freedom from foodborne diseases. In this study, the dynamics of food contamination before or after cooking and during hot-holding are discussed and a food contamination dynamics model is presented.^ The literature on foodborne cholera, cholera-like diarrhea, shigellosis and E. coli gastroenteritis together with the literature on the occurrence and growth of the causative enteropathogens; 01 V. cholerae, non-01 V. cholerae, S. sonnei, S. flexneri and E. coli were reviewed. The literature on the infective doses of these organisms were also cited.^ In the study, four cooked food types held hot at 40-60(DEGREES)C were deliberately contaminated with 01 V. cholerae, non-01 V. cholerae, S. sonnei, S. flexneri and E. coli, one at a time at each of the hot-holding temperatures. Tested food samples for the recovery of these enteropathogens were withdrawn at various time intervals of hot holding.^ The results showed bacterial recovery to decline with increasing temperature and with increasing hot-holding time within each holding temperature. All the bacterial types except V. cholerae were recovered even after holding the food at 60(DEGREES)C for one hour. V. cholerae was not recovered after hot-holding the food at 50-60(DEGREES)C at certain holding periods. After 48 hrs incubation, V. cholerae was recovered on TCBS agar plates that read negative after the initial 24 hrs of incubation. Effective hot-holding temperatures were determined for each of the food types contaminated by each of the bacterial types.^ Statistical analysis of the collected data showed temperature, bacterial type and their interaction to be significant in enteropathogen recovery. Food type and its interactions with temperature and bacterial type were found not significant. ^