Research
Estimation of New Drug Product Approval Probabilities in Phased Clinical Trials
This paper proposes and presents a method for the estimation of approval probabilities of new drug or product. The proposed method assumes that three evaluation communities are used to assess and evaluate the quality of a new drug or product and that the evaluation is done by the committees in three period phased clinical trials of the drug product using matched samples of subjects at each phase. Estimates of absolute and conditional approval probabilities by various combination evaluation committees at each phase of clinical trials are provided. Test statistics are also developed testing desired hypothesis at each of the phased clinical trials. The proposed method is illustrated with some sample data. It is shown in terms of estimated probability that it is more difficult for all three evaluation committees to be in complex agreement to approve or not approve a new drug or product than for fewer evaluation committees to grant approval.
Simultaneous Estimation of Adjusted Rate of Two Factors using Method of Direct Standardization
This paper presents the use of standardization or adjustment of rates and ratios in comparing two populations using single indices rather than a series of specific rates or ratios. Here the overall adjusted crude rate or the unadjusted crude rate for two populations will have same estimate irrespective of the nature of the standard population distribution. These results are obtained in all cases whenever the two standard distributions are of the total sample. In these cases the overall adjusted crude rates based on the two sets of directly adjusted rates would be equal to each other, although not necessarily always equal to the overall unadjusted crude rate as is found to be the case here. However, if the standard population distribution chosen for a given population is different from that chosen for another, then the two resulting estimated adjusted or standardized crude rates would most likely not be equal to each other.
One Factor Analysis of Variance and Dummy Variable Regression Models
This paper proposes and presents a method that would enable the use of dummy variable regression techniques for the analysis of sample data appropriate for analysis with the traditional one factor analysis of variance techniques with one, equal and unequal replications per treatment combination. The proposed method, applying the extra sum of squares principle develops F ratio-test statistics for testing the significance of factor effects in analysis of variance models. The method also shows how using the extra sum of squares principle builds more parsimonious explanatory models for dependent or criterion variables of interest. In addition, unlike the traditional approach with analysis of variance models, the proposed method easily enables the simultaneous estimation of total or absolute and the so-called direct and indirect effects of independent or explanatory variables on the dependent or criterion variables. The proposed methods are illustrated with some sample data and shown to yield essentially the same results as would the one factor analysis of variance techniques when the later methods are equally applicable.
Semiparametric Estimation of AUC from Generalized Linear Mixed Model
Methods of evaluating the performance of diagnostic tests are of increasing importance in medical science. When a test is based on an observed variable that lies on a continuous scale, an assessment of the overall value of the test can be made through the use of a Receiver Operating Characteristic (ROC) curve. The ROC curve describes the discrimination ability of a diagnosis test for the diseased subjects from the non-diseased subjects. The area under the ROC curve (AUC) represents the probability that a randomly chosen diseased subject will have higher probability of having disease than a randomly chosen non-diseased subject. Semi-parametric being a ROC curve estimation method is widely used in making inferences from diagnostic test results that are at least measurements on ordinal scale. In this paper, we proposed a method of semi-parametric estimation in which predicted probabilities of discordant pairs of observation are obtained from generalized linear mixed model (GLMM) and used in modeling ROC and AUC. The AUC obtained which is time dependent is equivalent to the Mann-Whitney statistic (Hanley and McNeil, 1982) often applied for comparing distributions of values from the two samples.
Generalized Methods for Generating Moments of Continuous Distribution
We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters 1122,,andαβαβin finding the nth moment of the variable ()0,0cdxycd≥≥where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called (,)ngcddefined ()(,),ncdngcdEXYλ=+the nth moment of expected value of the t distribution of the cth power of X and dth power of Y about the constant λ.These moments are obtained by the use of bi-variate moment generating functions, when they exist. The proposed (,)ngcd is illustrated with some continuous bi-variate distributions and is shown to be easy to use even when the powers of the random variables being considered are non-negative real numbers that need not be integers. The results obtained using (,)ngcd are the same as results obtained using other methods such as moment generating functions when they exist.
Two Factor Analysis of Variance and Dummy Variable Multiple Regression Models
This paper proposes and presents a method that would enable the use of dummy variable multiple regression techniques for the analysis of sample data appropriate for analysis with the traditional two factor analysis of variance techniques with one, equal and unequal replications per treatment combination and with interaction. The proposed method, applying the extra sum of squares principle develops F ratio-test statistics for testing the significance of factor and interaction effects in analysis of variance models. The method also shows how using the extra sum of squares principle to build more parsimonious explanatory models for dependent or criterion variables of interest. In addition, unlike the traditional approach with analysis of variance models the proposed method easily enables the simultaneous estimation of total or absolute and the so-called direct and indirect effects of independent or explanatory variables on given criterion variables. The proposed methods are illustrated with some sample data and shown to yield essentially the same results as would the two factor analysis of variance techniques when the later methods are equally applicable.
