Concomitant Information in Competing Risk Analysis

A competing risk model, accommodating both Type I censoring and random withdrawals, is expanded to incorporate concomitant information by allowing the parameters of the underlying distributions to be a linear function of two covariates. The model is developed for two competing risks, one following a Weibull distribution and the other a Rayleigh distribution, and random withdrawals following a Weibull distribution. A method is developed for testing the equality of the coefficients for a given covariate for each of the competing risks using MLE'.     

Fractional paternity assignment: theoretical development and comparison to other methods

Summary There has recently been a burgeoning interest in the analysis of paternity patterns for natural populations because of its relevance to population genetic phenomena such as the distance between successful mates, relative male reproductive success and gene flow. In this paper we develop a method of analyzing populational patterns of paternity, the fractional paternity method, and compare its performance to two other commonly used methods of paternity analysis (simple exclusion and the most-likely methods). We show that the fractional method is the most accurate method for determining populational patterns of paternity because it assigns paternity to all progeny examined, and because it avoids biases inherent in the other paternity analysis methods when model assumptions are met. In particular, it avoids a systematic bias of the most-likely paternity assignment method, which has a tendency to over-assign paternity of progeny to certain male parents with a greater than average number of homozygous marker loci. We also demonstrate the effect of linkage of some of the marker loci on paternity assignment, showing how the knowledge of the linkage phase of male and female parents in the population can significantly improve the accuracy of the estimates of populational patterns of paternity. Knowledge of the linkage phase of individuals in a population is usually unknown and difficult to assess without progeny testing, which involves considerable labor. However, we show how the linkage phase of hermaphroditic individuals in a population can be obtained in conjunction with the paternity analysis if progeny can be obtained from each hermaphroditic individual in the population, thereby avoiding the problem of traditional progeny testing. Applications of the fractional paternity approach developed herein should contribute significantly to our understanding of the mating patterns in, and hence the evolution of, natural populations.     

Statistical analysis of spatial patterns of the heliozoanActinophrys sol

Summary Cell-to-cell interaction and spatial distribution of the heliozoanActinophrys sol was analyzed with computer-aided video microscopy. By means of goodness-of-fit statistics (² analysis) and a quadrat-count analysis (I-curve analysis), the spatial point pattern of the cells was shown to be of regular distribution, which implies that a regulating mechanism is operating to encourage an even spatial distribution of the cell centers ofActinophrys. An attempt was further made to define a unified model which fitsActinophrys cell distribution observed at different cell densities. For this purpose, the fitting of a parameterized potential function (r)=(/r)¹² was carried out, wherer is the distance between cell centers of two neighboring cells. The scaling parameter a was estimated from the maximum likelihood procedure for obtaining the best fit for the data, which was found to be a decreasing function of the cell density; we obtained = 0.44 mm at a low cell density (0.5 cell/mm²) and =0.10 mm at the highest cell density (6.5 cells/mm²). These results suggest that (1) the possible nearest distance between two neighboring cells is primarily defined by the axopodial length, and (2) at lower cell densities,Actinophrys can recognize the presence of distant neighboring cells by some unknown means.     

Statistical approach for comparison between methods of bacterial enumeration in drinking water

A general statistical procedure based on the likelihood ratio test is presented for the purpose of comparing estimates of mean bacterial density derived from different sets of data. This approach is much more appropriate than the conventional ways of analyzing bacteriological results (e.g., analysis of variance) which usually require previous transformation of the data. An illustrative application of the method compares three distinct titration techniques for enumerating heterotrophic bacteria in drinking water at 20°C incubation temperature. It was shown that both the standard plate count (SPC) and the membrane filter (MF) procedures supplied substantially the same information, whereas the microplate technique using the most probable number (MPN) for total bacterial enumeration could yield considerably different estimates: MPN values were significantly lower in three cases and significantly higher in one case out of a total of five experiments. The results consistently indicate a strong interaction between the technique used and the sample analyzed. Three different media (nutrient agar, R-2A low nutrient agar and m-SPC agar) were then evaluated for enumerating heterotrophic bacteria, using the MF technique at 48, 72 and 96 h of incubation time at 20°C. Although the media recovered approximately the same numbers of bacteria after 96 h of incubation, statistically significant discrepancies occurred after intermediate periods of incubation, perhaps because the relative rates of bacterial growth differed among media.     

A model of the plant-to-plant movement of aphids II. Estimation of parameters and the application

1. It was shown in the previous report that the statistical model of the plant-to-plant movement of aphids could be fitted well to the actual population of barley aphids (Shiyomi , 1967). To examine validity of the model, results of the further experiments were analysed and the methods of estimation of parameters were given in this paper.
2. Comparing the estimates of the parameters obtained by the moment method with those obtained by the maximum likelihood method, the estimates from the latter method were somewhat precise.
3. The theoretical frequency distributions calculated from the model were fitted very well to the observed ones.
4. The model was reexamined with reference to the results obtained byItô (1954, 1960). When the distance between plants was less than 4.5 cm, the farther was the distance between plants, the smaller was the rate of the plant-to-plant movement of aphids. When the distance was greater than 4.5 cm, however, the rate of the plant-to-plant movement was independent of the distance. This result is similar to that ofItô .