In phase III comparative clinical trials for a new drug application in Japan, a test drug is accepted if the efficacy and/or usefulness of the test drug shows equal or more than equal to that of the control drug (not a placebo). Hence, the needs of statistical tests for testing equivalence, or more than equivalence is increasing. Therefore, we established the following two null hypotheses for testing equivalence, or more than equivalence which adjust for prognostic factors by stratification. 1) Pi11 = ƒPi01 i=1,2,..,L (0<ƒ<1,ƒis a given constant) 2) (Pi11 (1—Pi01)) / ((1—Pi11) Pi01) =ψio i=1,2,..,L (0<ψi0 <1,ψi0 is a given constant), where Pi11 and Pi01 are efficacy ratio of the test drug and control drug, respectively, in i-th stratum. Developing Mantel-Haenszel type test statistics for these null hypotheses and studying their characteristics, this paper proposes methods for testing equivalence, or more than equivalence of two drugs.
We briefly review the literature dealing with the effect of covariate measurement errors on the parameter estimation for censored survival models. As compared to non-censored errors-in-variables models, the area has not been developed very well. Corrected scores as applied to the proportional hazards model is reviewed in detail with application to A-bomb survivors data in which estimated doses for the survivors were obtained from inaccurate information and subject to appreciable measurement errors.
Orthogonal series estimate of additive model in which independent variables are represented as distributions is proposed. Two methods to realize this methodology are developed: (1)Orthogonal functions are given beforehand. Regressed functions are derived as a linear combination of the functions. This method ends up with ridge regression. Hence, hat matrix and related statistics such as GCV are derived easily. Smoothing splines are considered special cases of this method. Further, neural network is also associated with this method. (2) Orthogonal functions are created from data using Gram-Schmidt’s orthogonalization process. Regressed curves are obtained without procedure of least squares. Linear filters are used to smooth the curves. This regression needs a smaller amount of computational cost than generalized smoothing splines.
Let us consider a strip-wise grazing pasture, likc a corridor, to simplify the subject mathematically, and suppose that the length of pasture is θ meters and there are n individuals of cattle. Here, we define that the spatial pattern of individuals is random if the n distances from the left end of pasture to each individual follow a uniform distribution on the strip. Under such an assumption, the variance of distances between any two neighbors is given by n θ2(n+1)-2(n+2)-1; and the variance between n+1 distances formed by n individuals from the left end to the right end of pasture, is given by θ2(n+1)-1(n+2)-1. These two kinds of variance can be used for determining (1) spatial pattern of a cattle population on the strip and (2) spatial pattern of individuals within the cattle population, by comparing with the variances calculated from data. From analysis of data observed at an 88m×6m experimental pasture, where 6 individuals of cattle were released, the following results were obtained: (1) the individuals were not randomly dispersed on the whole area of strip, but crowded at some part on the strip, and (2) the individuals distributed randomly or exclusively within the population.
Applying a log-linear model, we analyzed stomach cancer mortalities during 1973-90 for 47 prefectures in Japan. The model we dealt with is based on a poisson distribution in which the expected number of deaths from stomach cancer is expressed as nrij exp(μr+αi+τrj), for ith age group and jth calendar year, for prefecture c; here nrij denotes the population size of (i, j) category in region r. Risk of stomach cance mortality decreases almost exponentially in prefectures in this period for both sexes; the decreasing rate in female is larger than that in male for all prefectures. High correlation between risk of stomach cancer mortality in male and that in female exists. Two geographical clusters of high risk for stomach cancer mortality exist; the one of them is west side of Touhoku area, and the other is southwest part of Kinki area. There is a trend such that the risk decreases more rapidly in the area of higher risk especially for male.