Modeling Study Of The Sustained-release And Controlled-release Formulation Based On The Quadratic Inference Functions

With the rapid development of our society, pharmaceutical technology isexperiencing progressive improvement in the pharmaceutical field. At the same time,it also results in the upgrading of traditional pharmaceutical models and theincreasing use of the sustained-release and controlled-release formulation for thosechronic medicines which are of high toxicity and narrow therapeutic index. In recentyears, with the intensive researches on the sustained-release and controlled-releaseformulation and the ready availability of the sustained-release and controlled-releasematerials, the sustained-release and controlled-release formulation has attracted moreand more attention.In modeling study of the sustained-release and controlled-release formulation,many traditional modeling methods involve quadratic regression modeling andmultiple linear regression modeling. But the response variables of thesustained-release and controlled-release formulation are cumulative release degrees,which display repeated and interrelated measurement data of the release quantity ofdrugs, so the traditional modeling methods are not capable of revealing responsecharacteristics of the data accurately.Considering the correlation feature of duplicate data, the generalized estimatingequations can avoid the problem above. In2012, a member of the research group,applied the generalized estimating equations to the modeling study of thesustained-release and controlled-release formulation and obtained satisfactory results.But generalized estimating equations also has disadvantages: lack of the inferencefunctions of the likelihood ratio test, inability of selecting the modeling methods by using the AIC (Akaike information criterion) and BIC(Bayesian Information Criterion)criterion, sensitivity to the Parameter estimation of outliers, uncertainty of theparameter estimation efficiency when work correlation matrix selection isinappropriate etc..Due to the disadvantages of the generalized estimating equations, this researchapplies a new modeling method----quadratic inference functions, QIF----to themodeling of the sustained-release and controlled-release formulation. Furthermore,QIF is a promotion of GEE method, displaying the estimates of work matrix with theemployment of the linear combination of the elementary matrix. And QIF has thefollowing advantages: it contains a chi-square inference function, which can be usedto do the test of goodness of fit and regression error setting; it is similar to the test ofgoodness of fit of the likelihood ratio test, which can select the modeling methods byusing AIC and BIC criterion. Therefore, QIF can be applied to perfectly solve theproblems caused by the application of GEE in modeling.According to the theoretical research, the modeling effects of the quadraticinference functions are better than that of the generalized estimating equations, andthis modeling method of the quadratic inference functions also received preciouseffects in its application of the modeling in large samples of repeated measurementdata at abroad. However, this method has not been applied to the relatively smallsamples of repeated measurement data in the research of the sustained-release andcontrolled-release formulation in pharmaceutical field, so this research explores themodeling effects of the application of the quadratic inference functions in themodeling of the sustained-release and controlled-release formulation. The researchincludes the following aspects:The first part: The introduction of the information and data characteristics of thesustained-release and controlled-release formulation. This part introduces the concept, dosage forms, release degree index in vitro, data characteristics, dynamic types andthe traditional modeling methods of the sustained-release and controlled-releaseformulation. Furthermore, the response variables of the sustained-release andcontrolled-release formulation are cumulative release degrees, which are of repeatedmeasurement data, possess correlation between different data, and the release quantitymust meet the prescribed release standard at each point, all of these would lead to thedata complexity and modeling difficulties of the sustained-release andcontrolled-release formulation.The second part: The principles of the generalized estimating equations and thequadratic inference functions. This part involves the concept, basic steps and therespective advantages and disadvantages of the generalized estimating equations andthe quadratic inference functions.The third part: According to the cumulative release degrees of different timepoints (three time points, five time points, six time points), apply SAS MACRO QIFprograms to establish an equation, which evaluates the cumulative release degrees ofthe sustained-release and controlled-release formulation. Also employs three differentwork correlation matrix modelings (exchangeable corelation, first-orderautocorrelation, no structure corelation), which obtain a suitable work correlationmatrix type of the sustained-release and controlled-release formulation. By adoptingthe relevant work correlation matrix type, this research then applies QIF and GEE inmodeling; after comparing the modeling effects of the two methods above, theresearch finally obtains a suitable modeling method of the sustained-release andcontrolled-release formulation for promotion.The instance of the cumulative release degree with three time points, it quotesthe data of nimesulide sustained-release tablets and uses the three factors and threelevels orthogonal experiment design, the quadratic inference functions and the generalized estimating equations, which shows exchangeable Q value of thecorrelation matrix, AIC and BIC are minimal, respectively Q=6.29x10-28, AIC=20,BIC=21.972. Thus, the characteristics of data conform to the exchangeable relevantstructure. Based on the same exchangeable relevant matrix model, the SRE value is25.906, which illustrates the QIF modeling effect is better than that of the GEE.The instance of the cumulative release degree with five time points, it quotes thedata of multi-particulate beads and uses central composite design of three factors andthree levels test to observe the five different quadratic inference functions modelingsand generalized estimating equations modelings, which shows exchangeable Q valueof the correlation matrix, AIC and BIC are minimal, respectively Q=0.870, AIC=18.870, BIC=25.824. Thus, the characteristics of data conform to the exchangeablerelevant structure. Based on the same exchangeable relevant matrix model, the SREvalue is1.839, which illustrates the QIF modeling effect is better than that of theGEE.The instance of the cumulative release degree with six time points, it quotes thedata of salbutamol sulfate hydrophilic matrix sustained release tablets and uses fourfactors and five levels of orthogonal experiment design to observe the six differentquadratic inference functions modelings and generalized estimating equationsmodelings, which shows exchangeable Q value of the correlation matrix, AIC andBIC are minimal, respectively Q=1.37212，AIC=25.3721，BIC=42.1865. Thus, thecharacteristics of data conform to the exchangeable relevant structure. Based on thesame exchangeable relevant matrix model, the SRE value is1.281, which illustratesthe QIF modeling effect is better than that of the GEE, and the QIF modeling aremore suitable for the sustained-release and controlled-release formulation.To sum up, the characteristics of data with cumulative release degree ofsustained-release and controlled-release formulation conform to the exchangeable relevant matrix structure. In this modeling, the quadratic inference functions arebetter than that of the generalized estimating equations, can make up the disadvantageof GEE, conclude the value of goodness of fit and provide a feasible method formodeling.