Statistical Studies For Drug Clinical Trials Designs And Gene-Disease Association

The journey from initial medical research to the bottle in our family's medicine cabinet is very complex. To be brief, the process can be divided into two stages: preclinical (or laboratory) research and clinical trials. The clinical testing of experimental drugs is normally done in three phases. Phase I clinical trials are primarily concerned with assessing the drug's safety, and one of the main objectives is to estimate maximum tolerated dose (MTD); once a drug has been shown to be safe, it must be tested for efficacy in phase II; in phase III studies, a drug is tested in several hundred to several thousand patients. This large-scale testing provides with a more thorough understanding of the drug's effectiveness.Although this process is very complex, time-consuming and expensive, it is reliable after all~[62] By now, many countries and districts in the world have their special drug management organization. Prom the development and the assessment of new drugs to the testing of their effectiveness, many developed countries have set up a systematic, scientific assessing and censoring procedure in the whole process, and the statistical inference methods are needed in almost all steps. The research on the statistical analysis methods on new drugs has been a focus in biostatistics, which can be seen from the publications in top-ranking journals. Although our country has set up a special drug management organization, the statistical analysis and research in drug trials falls behind the developed countries. Now, our country has joined into WTO, it is imperative to speed up the research in this field. It is well known that traditional Chinese medicine is a treasure in our country's medical treasure-house, which has many advantages in comparison with western drugs. How to utilize its advantages and make it stride toward international markets in a faster and better fashion presses for the guidance of scientific methods~[62].With the rapid development of science and technology, new drugs and therapies are developed one after another, many incurable diseases are easily handled today. In recent years, with the advancement of molecular biology, it is very glad to see that some gene drugs have shown up. However, no drug is perfect—on the one hand, it can cure anyone; on the other hand, it has no any adverse effect on patients. Clinical trials are the most objective means and procedures on the assessment of the performance of the drugs.The paper mainly contains:(1) Stepwise method based on asymmetry confidence bound and information incorporation for identifying the maximum tolerated doseThe clinical testing of an experimental drug is normally done in three phases. A phase I clinical trial is primarily concerned with assessing the drug's toxicity, and the main objective of a phase I clinical trial is to estimate the maximum tolerated dose (MTD) of the drug. By now, several designs have been proposed for this purpose.Up-and-down design method proposed by Storer (1989)~[47] needs neither assuming models nor complex calculations, hence it is still in dominant posi-tion in the stage I clinical trials in America at present. But this method has quite some drawbacks, e.g., that it cannot account for indication or patient population specific DLT rates, the precision of the estimator of the MTD is fairly imprecise. However, without effective prepared method, it is kept using in many stage I clinical trials. In 1990, for the first time, O'Quigley, Pepe and Fasher ^ proposed Bayesian clinical design method which was applied in estimating MTD alternative. It was called CRM (Continual Reassessment Method). It is a Bayesian procedure that takes a prior distribution of a parameter of a one parameter dose-response model as a starting point. This distribution is updated according to Bayes theorem as soon as new information about the occurrence of DLTs becomes available. The method can account for different numbers of patients per dose and can be targeted to any preselected DLT rate and even cope with the situation when investigators feel they have to overrule the proposal by the CRM for the next dose to be used. It fixed the total number of patients trials, until everybody finished it. The dose level could both rise and fall. In comparison with the traditional up-and-down design method, The CRM is superior to the up-and-down design in terms of more accurate recommendation of the target level, more efficient use of accrued information, and, in particular, as the trial continues, the property of convergence to the target level (see [38], [44], [37]). The up-and-down schemes being memoryless sample more or less widely around some percentile but do not converge (see [32], [29]). However, some serious objections have been raised to the CRM: the CRM method tends to treat more patients above the MTD than the traditional method, and CRM may lead the patients to take higher toxicity dosage, more would be toxic, even seriously toxic to die. On the other hand, CRM need assume the dose-toxicity model beforehand and select theprior information of the corresponding parameter, refer to the complex calculation. It is difficult to give a good prior information and model which meets the reality. Hence, from the proposal of CRM till now, many authors (e.g. [6], [7], [17], [21], [31], [25], [35], [39]) have modified, advanced and applied it.In this paper, profiting from some advantages of the existing methods, we propose a new stepwise method based on asymmetry confidence bound and information incorporation for the identifying the maximum tolerated dose. The method is based on the following intuitional idea: in view of practice and ethics, in order to treat patients more humanely, patients were enrolled to be engaged in the trial continuously by sequence idea. In the mean time, the total trial time should be short, and the number of patients who take part in the trial should be small. And the number of patients treated in the dosage level without the healing effect and of low toxicity should reach the smallest, but one should avoid bring unnecessary risks to those who were more exposed. Our design adopts start-up rule and takes distance into consideration, that is, if the present dosage level is far away from the DLT, the trial proceeds rapidly, as the trial continues, the dosage level gradually approximate to the DLT, the number of toxic patients increases. In order to suggest the dosage more precisely, based on this dosage level, we add a group of patients to make trial to get much more and precise information, then combine the trial information to make decisions, and for precisely identifying MTD and avoiding increasing the dosage so rapid that leading the patients to be seriously toxic for taking the dosage level of high toxicity, even die from it, we make the trial in increasing one by one form. This design meets the needs of practice and ethics, the patients are treated more humanely, the number of patients attending the trial is small and they are safe, suggest the MTD more precisely, the time and money is saved, it ismore easily accepted by clinical trials.(2) Extended up-and-down design based on toxicity grade information for the identifying the maximum tolerated dosePhase I cancer clinical trials are studies in which a new drug is first tried in humans. Their purpose is to select a dose, called the maximum tolerated dose (MTD), for use in subsequent phase II and phase III trials. Ideally, the MTD is high enough that the drug may prove efficacious, but not so high as to represent unacceptable risk of severe or fatal toxicity to the patients. These goals are complicated by the fact that usually little is known about the activity or toxicity profile of the drug in humans, and by the fact that the patients are already likely to be at high risk of death under any treatment regimen. The competing needs of the study thus require that the trial design be optimized to allow for quick dose escalation, in order to minimize the number of patients treated at very low, non-therapeutic doses, but also to protect against exposing patients to unnecessary added risk.In many phase I cancer trials, patients are evaluated for drug related toxicity using standard World Health Organization (WHO) ^ guidelines. A 5 point ordinal scale is used to describe the severity of each type of toxicity, with grade 1 representing no toxicity, grade 2 minor toxicity, grade 3 moderate toxicity, grade 4 severe toxicity and grade 5 very severe or life threatening toxicity. For standard phase I designs, the up-and-down designs, toxicity is dichotomized into "acceptable" toxicity or "unacceptable" toxicity. Though several types of toxicity are typically used in this formulation, for the purposes of illustration we consider a single scale. For example, using the 5 point ordinal scale described above, we might define grades 1, 2 and 3 to be acceptable toxicity and grades 4 and 5 to be unacceptable toxicity. The MTD is thendenned as the dose where a patient has a given probability of experiencing unacceptable toxicity.One family of designs for dose-response studies is up-and-down design. Anderson, McCarthy and Tukey (1946) ^ nrst brought these designs to the attention of.the statistical community. Dixon and Mood (1948)'10' analyzed a more tractable version of such designs, namely, one specifically designed for estimating the 50th percentile of the response function. Up-and-down designs have been studied by many authors, including Brownlee, Hodges & Rosenblatt (1953)[5], Derman (1957)(8], Wetherill (1963)[57], Dixon (1965)[9], Tsutakawa (1967)[50], Wetherill and Glazebrook (1986)^, Storer (1989)[47] and Durham and Flournoy (1993, 1994)[11], among others.A simple sequential design that addresses these ethical concerns is the up-and-down biased coin design (BCD) of Durham and Flournoy (1994)'ul Giovagnoli and Pintacuda (1998)'20' have shown that the BCD is optimal in a large class of generalized up-and-down biased coin designs in the sense that the dose distribution is most peaked around target dose. For a review of the characteristics and application of the BCD, see Durham k Flournoy(1994)'12', Durham, Flournoy & Montazer-Haghighi (1995)'13', Durham, Flournoy, and Rosenberger (1997)[14].This class of rules that are up-and-down designs. These designs are particularly attractive for their simplicity in implementation since the decision rule does not involve any complicated calculations and there is no assumed model. However, in the up-and-down designs family, the severity level of graded toxicity of a previous patient's response would not be a differentiated factor for the next dose level assignment and doses that are too toxic may also be recommended, designs for phase I trials with differentiation of graded toxicityhas received little attention in the literature. In this study, we extend the up-and-down procedure incorporating the idea on the assessments of graded toxicity in the dose escalation. We investigate the operating characteristics of this approach under a variety of dose-toxicity associations and comparison with up-and-down family show that particularly the extended up-and-down procedure would minimize the number of patients treated at very low, non-therapeutic doses, but also to protect against exposing patients to unnecessary added risk. In addition, the more accuracy of targeting the maximum tolerated dose is also preserved in the extended up-and-down procedure, that it can achieve significant improvements to the doses recommended during the phase I trial.(3) The method based on the isotonic regression estimation for identifying the maximum tolerated doseIn phase I clinical trials, common assumptions are that the toxicity increases with increasing dose. We estimate the toxicity probability according to the ratio of patients' toxicity respond at each dose, it may not be the non-decreasing function of dose level. Naturally, we use the isotonic regression to adjust the toxicity estimation at different dose to ensure a nondecreasing order. For this up-and-down design, an isotonic regression estimate of the target dose has been shown to perform well relative to other estimators in terms of mean square error (see [49], [23]). Stylianou, Proschan and Flournoy (2003)'281 use the biased coin up-and-down design to allocate and three isotonic regression to estimates toxicity probabilities and determine the MTD. Moreover, for extend up-and-down design based on toxicity grade information, we give the method based on the isotonic regression estimation for identifying MTD . Through much simulation, it shows that extend up-and-down design based on isotonicregression for identifying the maximum tolerated dose has improved the accuracy of recommending MTD and preciseness of suggestion. It apparently decreases the opportunity of recommend the dose level higher than MTD, protects patients efficiently and prevents patients from excessive trials under the higher toxicity dose level and meet the demands of practice, ethics and design. Therefore, extend up-and-down design and the isotonic regression estimation make great signficance in phase I clinical trials design.(4) Unassociated condition of a marker gene and the diseaseIn 1990, NIH and DOE addressed American Human Genome Project (HGP) (see [66]), they spent three billion dollars on that from Oct. 1. 1990 to Sep. 30. 2005. The Human. Genome Project of our country started in 1993, great progress has been made in recent years, and HGP will promote the development of the Whole Life Science.The aim of HGP is to set up the dense dual gene set (SNPs) (see [54]) in Human genome, and this project will provide many genetic markers, which can be used to construct gene map of complex trait. According to the statement of these governments and financial groups, the number of collected SNPs has exceeded 100 thousand, and all these SNPs have been fixed in human genome by ray-mix-map method or fixed in the gene draft by in sillco-map method (http://snp.cshl.org). The aim of these financial groups is to make the number of SNPs exceed three billion by 2002. Then, how to use these collected SNPs efficiently? One way is to use case-control study, which has many advantages (see [30], [41], [53], [22]) in genetic analysis of complex trait. But case-control study will lead pseudo association because of population hierarchy. When sampling from special sub-population, the probability that a case-individual is affected will increase, then the disease frequency among thesub-populations will change, and pseudo association will appear. In that case, the high-frequency markers in these special population are associated with phonotype (see [15], [40]). So one alternative way—pedigree method is widely used. In this method, sampling based on pedigree, can avoid the influence of population hierarchy (see [16], [46], [45], [15], [26], [61]). Although this method is general and successful, case-control study will lead to pseudo association, the latter still has great attractiveness, because case-control study is always more effective than pedigree method when performing test (see [30], [41], [53]), no matter from the qualitive aspect or the quantitive aspect, and case-control study have more practical value than pedigree method. Since we can sample from case or control non-related individuals in case-control study, but we must sample from mutual related individuals in pedigree study; and the data in control genotype data sets can be reused, which reduces much expense and that is economical in practice.According to Simpson's Paradox we study the association between genetic markers and disease in medical statistics by defining association measurer with the method of case-control study, obtain the condition that gene and disease are not associated, i.e., in normal state, when the probabilities that gene appears are equal or the prevalances are equal. When not considering population hierarchy, the condition is sufficient condition, specially, when population noly consists of two sub-populations the condition is necessary and sufficient condition; when considering population hierarchy (no matter how to hierarchize), the condition is its necessary and sufficient condition.In this paper, we propose some improved methods in drug trials. Recently, with the rapid development of molecular biology and clinical genetics, the traditional assessment is challenged by new gene therapies and drugs. By...