Normalization is a basic step in microarray data analysis. A proper normalization procedure ensures that the intensity ratios provide meaningful measures of relative expression values.We propose a robust semiparametric method in a two-way semi-linear model (TW-SLM) for normalization of cDNA microarray data. This method does not make the usual assumptions underlying some of the existing methods. For example, it does not assume that: (i) the percentage of differentially expressed genes is small; or (ii) the numbers of up- and down-regulated genes are about the same, as required in the LOWESS normalization method. We conduct simulation studies to evaluate the proposed method and use a real data set from a specially designed microarray experiment to compare the performance of the proposed method with that of the LOWESS normalization approach.The simulation results show that the proposed method performs better than the LOWESS normalization method in terms of mean square errors for estimated gene effects. The results of analysis of the real data set also show that the proposed method yields more consistent results between the direct and the indirect comparisons and also can detect more differentially expressed genes than the LOWESS method.Our simulation studies and the real data example indicate that the proposed robust TW-SLM method works at least as well as the LOWESS method and works better when the underlying assumptions for the LOWESS method are not satisfied. Therefore, it is a powerful alternative to the existing normalization methods. Microarray technology has become a useful tool for quantitatively monitoring gene expression patterns and has been widely used in functional genomics ,2. In a A basic question in analyzing cDNA microarray data is normalization, the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range. A proper normalization method ensures that the normalized intensity ratios provide meaningful measures of relative expression levels. Normalization is needed because many factors, including different efficiency of dye incorporation, difference in the amount of RNA labeled between the two channels, uneven hybridizations, difference in the printing pin heads, among others, may cause bias in the observed expression values. Therefore, proper normalization is a critical component in the analysis of microarray data and can have important impact on higher level analysis such as detection of differentially expression genes, classification, and cluster analysis.invariant genes that are likely to be constantly expressed and then carrying out LOWESS normalization using this set of genes. But as pointed out by Tseng et al., selected invariant genes may not cover the whole dynamic range of the expression values, and extrapolation is needed to fill in the gaps that are not covered by the invariant genes. Kepler et al. [Many normalization methods have been proposed in the literature. The earliest normalization method for cDNA microarray data goes back to Chen et al.  who propr et al.  also firr et al.  proposedr et al.  used arrr et al.  comparedr et al.  used a mr et al.  considerr et al.  generalir et al.  proposedIt is well known that the least squares method is not resistant to outliers which arise often in cDNA microarray experiments because of many sources of variations. In this paper, we propose a robust method for normalization in the framework of the TW-SLM. We conduct simulation studies and use a real cDNA microarray data set to compare the proposed method with the LOWESS normalization method.jth gene is calculated as the following:Simulation was conducted to compare the mean square errors (MSE) and biases of estimated gene expression levels between the proposed robust TW-SLM and LOWESS normalization methods, between the proposed method and the TW-SLM using OLS. The MSE for the , where N is the total number of replicates for each simulation, J is the number of unique genes, βj is the true gene expression level  for gene j,  is the estimated value for βj,  is the mean of  for N replicates, j = 1, 2,..., J, where J is the total number of genes. The data simulation procedure is based on the method proposed by Balagurunathan et al. [that is, n et al. . In eachj using the exponential distribution with the mean of 3,000, i.e. Ij ~ exp(λ = 1/3000), for j = 1,..., J;1. Simulate true signal intensity for each gene αrj and αgj, respectively, then the fluorescent intensity on the two channels can be generated by the normal distribution with mean Ij and standard deviations αrjIj and αgjIj for the red channel and the green channel, respectively. Let Rj and Gj represent simulated fluorescent intensity for the Cy5 channel and the Cy3 channel for gene j, respectively;2. Simulate fluorescent intensity for the Cy5 channel and the Cy3 channel with the normal distribution, respectively. Suppose the coefficients of variation for intensity in the Cy5 channel and the Cy3 channel are γ × 100% genes are differentially expressed in the whole simulated gene set, then the ratio of the expression level for gene j can be generated by tj = 10b ±with b ~ Beta(1.7,4.8). The sign ± will determine if the gene is up- or down-regulated. The probability of the up-regulated genes within those γ × 100% differentially expressed genes is given as an input parameter. For the genes that are not differentially expressed, the b takes value zero;3. Simulate differentially expressed genes. Suppose tj into signal intensity of gene j. The Rj and Gj will be adjusted by adding the simulated expression ratio tj through the following formulae:  for j = 1,..., J;4. Incorporate the 5. Simulate a fluorescent system with the imperfect response characteristics. Due to various reasons, such as the unequal amount of mRNA for the two channels, different labeling efficiencies, or uneven laser powers at the scanning stage , actual  and , respectively. So four parameter values need to be determined for each channel before simulation. Different parameter values in the two channels will control the shape of the ratio vs. signal intensity plots (R-I plots);to distort the response characteristic functions of observed fluorescent intensity for the two channels, which are expressed as αbr and αbg for the Cy5 channel and the Cy3 channel, respectively. These two parameters are the ratios between the mean and the standard deviations of background noise for the two channels, respectively. Simulated signal intensity for the two channels,  and , are adjusted by subtracting background noise in each channel. Let  and  still denote background adjusted signal intensity for the two channels;6. Simulate background noise for each channel. The mean of background noise is determined by one input parameter: the signal to noise ratio (SNR) and the true mean of signal. The SNR is the ratio between the true mean of the signal and the true mean of background noise. The SNR controls variability of background noise. The normal distribution with a given mean value is used in simulating background noise. Variance of background noise will be controlled by the input parameters 7. Add noise to the signal intensity for each channel. Finally, the signal intensity of each channel is generated by, where α1 ~ U (a1, b1), α2 ~ U (c1, d1), α3 ~ U (a2, b2), α4 ~ U (c2, d2). The a1, b1, c1, d1, a2, b2, c2, d2 are given as input parameters to control variability of fluorescent signal intensity.with We simulated two situations, one is the no-dye bias case and another one is the shape case (dye bias exists). R-I plots of twelve blocks on one slide for two simulated cases are shown in Figures The trend of MSEs and biases of estimated gene expression levels are similar between the robust TW-SLM and the LOWESS normalization methods across different levels of the ratios between the up-regulated genes and the down-regulated genes. This trend also exists in the extreme case. We present the results of the following two scenarios: (a) a 9:1 ratio between the number of the up-regulated genes and that of the down-regulated genes and, (b) the extreme case. Tables Comparing the different robust weight functions, means of MSEs are slightly smaller using Tukey's weight function than that using Huber's weight function. These results are observed across different percentage levels of differentially expressed genes. Biases for estimated gene expression levels distributed similarly between the proposed method and the LOWESS normalization method. But the ranges of the biases for the proposed method are smaller than those of the LOWESS normalization method and the TW-SLM using OLS, respectively. These observations are true in both simulated situations.The extreme case is an example where the proposed method does better than the LOWESS method Tables  and 7. EThe distributions of MSEs and biases between the TW-SLM using OLS and the LOWESS method are similar for cases where there is a relatively small percentage of differentially expressed genes. However, the TW-SLM with OLS performs better than the LOWESS when a larger proportion of genes are differentially expressed. It appears that the more deviation from the two assumptions required by the LOWESS, the better the TW-SLM performs. This trend is consistent with findings in our previous work .In this section, a real data set was analyzed to compare consistency of the LOWESS normalization method and the proposed robust TW-SLM method. A collection of human placenta cDNAs comprising 7,042 clones was identified and used as the probe set for cDNA microarray fabrication in this study .in vitro transcription from a pool of cDNAs in equal amount comprising the entire probe set (PS); (ii) the "Universal Human Reference RNA" from Stratagene, a pool of RNAs derived from 10 different cell lines; and (iii) human full-term placenta RNA. The original goal of the study was to evaluate the performance of the PS RNA as a reference RNA in comparison with that of Stratagene's universal reference RNA.Three kinds of RNA samples were used which include: (i) a common reference RNA obtained by In this study, the Universal Human Reference RNA and the human placenta RNA were treated as two experimental samples. The PS RNA was used as the reference against which the two other bio-samples were compared. In the simple direct comparison, gene expression values were obtained through direct hybridizations between the human placenta RNA and the Universal Human Reference RNA. In the indirect comparison using the PS set as the common reference, hybridizations were performed between the human placenta RNA and the PS reference RNA, and between the Universal Human Reference RNA and the PS reference RNA. The design of this experiment is depicted in Figure After hybridization, slides were scanned with the Axon instruments 4000B scanner. The 633 and 532 lasers are used for excitation of the Cy5 and Cy3 fluorophores, respectively. For each of the three types of hybridizations , there are four slides, including two dye-swapped slides. Each clone was printed three times on different blocks on each slide. Background adjusted medians for the Cy5 and Cy3 channels were used as expression levels. We removed negative controls including "Human Cot1", "PolyA" and "Empty" in the analysis.To evaluate the proposed method, we compare it with the LOWESS method by examining which method produces more consistent results between the direct comparison and the indirect comparison of human placenta and universal human reference RNA samples as described above  in the direct comparison and about 61% (1713/2791) in the indirect comparison.We used 10-5 in the direct comparison and 1,045 in the indirect comparison. The number of overlapping genes with p-value less than 10-5 is 467, which is around 32% (467/1447) in the direct comparison and about 44% (467/1045) in the indirect comparison. It is clear that the proposed method performs more consistent between the direct comparison and the indirect comparison.In comparison, using the LOWESS normalization and the t-tests, there are 1,447 genes with p-value less than 10We also examined overlap between the LOWESS and robust TW-SLM methods for the two comparisons. In the direct comparison, about 79% (1141/1447) of the genes found to be significant based on the LOWESS method are also found to be significant based on the robust TW-SLM method. But they only account for about 40% (1141/2907) of the significant genes detected based on the robust TW-SLM method. In the indirect comparison, about 71% (738/1045) of the significant genes based on the LOWESS method are also found to be significant based on the robust TW-SLM method. But they only account for about 26% (738/2791) significant genes detected based on the robust TW-SLM method.In our analysis, we used background adjusted intensity values. How to adjust background is an important issue in microarray data analysis. To evaluate if background affects our conclusions, we repeated the comparison analysis without adjusting background for the intensity values in both channels, the results are presented in Tables Therefore, the robust TW-SLM method yields more consistent results between the direct comparison and the indirect comparison with the human placenta and the universal human reference RNA samples. In addition, the robust TW-SLM method detects more significant genes for a given cutoff p-value. This makes sense biologically because most of the 7,042 genes specifically discovered from human placenta are expected to have differential expressions relative to the universal reference RNAs. We would expect that the similar comparison results will be got if we compare the TW-SLM using OLS or Huber's weight function with the LOWESS method because the normalization curves for the TW-SLMs (TW-SLM:OLS, TW-SLM:Huber, TW-SLM:Tukey) are similar, but all these three curves are different from the LOWESS normalization curve Figure .βj as the thread linking these slides. In addition, in the proposed method, the normalization curves φi and gene effects βj are estimated simultaneously. With this approach, there is no need to assume that the percentage of genes with differential expression levels is small or the expression levels of up- and down-regulated genes are symmetric, or when one of these assumptions is not satisfied, to use dye-swap normalization, which in turn requires the assumption that the two normalization curves are symmetric.  An underlying condition required for the proposed method is independence of arrays, which is satisfied in a typical microarray experiment. Further theoretical conditions for the TW-SLM can be found in the paper by Huang et al. [We have proposed a robust TW-SLM normalization method for cDNA microarray data. It is interesting to compare the proposed normalization method with the existing methods, such as the widely used LOWESS normalization proposed by Yang et al. (2001)  and furtg et al. .We have only considered the proposed robust TW-SLM method for the simple direct comparison design described in the Methods section. We can easily extend the method to more complicated designs. For example, we can adapt the proposed robust method to the TW-SLM that accommodates the design where a gene is printed multiple times. Such a design is helpful for improving the precision and for assessing the quality of an array using the coefficient of variation . We canR package which is available from the corresponding authors.In our simulation studies, the proposed method performs better than the LOWESS normalization method in terms of MSEs of estimated gene effects in the simulation models we considered. Analysis of the probe set reference data set  shows thn be the number of slides, and J be the number of genes in the study. Let Rij represent background corrected signal intensity from the Cy5 channel and Gij the background corrected signal intensity from the Cy3 channel, and let yij = log2(Rij/Gij), xij = (1/2) log2(Rij × Gij), for gene j on slide i. We assume that there is only one spot for each gene on each slide. The TW-SLM [We first describe the TW-SLM. For simplicity, we focus on the case of comparing two cell populations, in which two cDNA samples from the respective cell populations are competitively hybridized on the same array. Let e TW-SLM  isyij = φi (xij) + βj + ∈ij, i = 1,..., n, j = 1,..., J     (1)φi which is the intensity dependent normalization curve for slide i, the second component is βj which represents the relative expression value of the jth gene after normalization, the last one is the residual error term. Let  be a robust estimator of the ith normalization curve φi based on this model described above. The normalized data areIn this model, the observed log intensity ratio is decomposed into three components. The first component is φi and βj in the TW-SLM. However, it is well known that least squares estimates are not robust against outliers which often arise in microarray experiments. Therefore, we propose to use the robust method [φi and βj. This is done by minimizing the objective functionHuang et al. 2004)  consider04  consiρ is an appropriately chosen function for robust estimation, λ is the collection of the coefficients in the spline representations of φi described below, σ is the scale parameter, and α is a constant to be described below. We note here that estimation of φi, βj are done jointly and uses data from all the arrays. This is different from the LOWESS normalization method in which estimation of normalization curves are done array by array.where ρ functions: Huber's ρ function and Tukey's biweight function. Huber's ρ function isWe consider two Tukey's biweight function isρ, ψ and χ, will be used repeatedly in the description of the algorithm below. They are defined asTwo other usefull functions derived from ψ(x) = ρ'(x), χ(x) = xψ(x) - ρ(x).     (4)H = 1.345 and k = 4.685. The influence of the choice of these constants on normalization methods is beyond the scope of this study.The expressions of these functions are given in the Appendix. We choose commonly used constants in the literature for Huber's and Tukey's functions, i.e., φi. Specifically, let b1,..., bK be K B-spline basis functions. We approximate φi byWe use the cubic B-splines ,22 to apb(x) = (1, b1(x),..., bK(x))' and λi = (λi0, λi1,..., λiK)'.where We estimate the parameters in model (1) by minimizing objective function (3) using an iterative procedure. Two steps, a location step and a scale step, will be used in the computation.We use the following vector and matrix notations in describing the location step:Bi = (b(xi1), b(xi2),..., b(xiJ))',i y= (yi1, yi2,..., yiJ)'.Letand leti = 1,..., n. Given the scale parameter σ,  and  satisfy the equations:for  and  because of identifiability requirement in the TW-SLM. We can solve these equations iteratively to obtain  and . The derivations of these equations are given in the Appendix.where σ isAccording to Huber's proposal , the estrij = yij - b'(xij) , and N is the total number of observations in the data set. In general, equation (8) does not have an explicit solution. So we use the following updating equation to compute the estimated scale parameter σ,where , we used the constant suggested by Huber [In order to obtain the consistent scale estimator at the normal distribution and obtain the classic estimates when using the least squares objective function, i.e., by Huber ,EΦ denotes expectation with respect to the standard normal distribution function Φ.where The procedure described above is called an iterative reweighted least squares (IWLS) algorithm that is used in many non-least squares estimation problems. The implementation of the IWLS algorithm can be carried out using the following steps: for j = 1,..., J and σ(0) = 1, , for i = 1,..., n, j = 1,..., J;1. Initialize  according to equation (6) given βm-1)(, σm-1)  (by equation (9) given , , σm-1)(, and , and set σm-1) (= σm)(,  and σm) (according to equation (5), and set ;5. Calculate weight βm) (given σm-1) (and  using equation (7), and set ;6. Calculate 7. Go to step 2 and iteratively update the estimators of parameters and the weights between steps 2 and 6 until convergence.DW devised and implemented the procedure described in the paper, drafted and finalized the manuscript. JH helped with writing and revising the manuscript. JH and MBS supervised and provided support for this work. HX and LM conducted the experiment that generated the data set used in the example.Methods section in this appendix. Again the notations from the Methods section:We derive estimation equations for location parameters presented in the b(x) = (1, b1(x),..., bK(x))',λi = (λi0, λi1,..., λiK)'.φi(xij) can be approximated by a linear combination of B-spline basis functions, i.e. b'(xij)λi, where bk(xij) is the kth B-spline basis function of xij. Let A = (a1, a2,..., an)', C = (c1, c2,..., cn)', and defineσ, the first partial derivatives of S(λ, β, σ) (3) with respect to λ and β can be expressed in the matrix form asGiven scale parameter iB; = (b(i1x), b(i2x),..., b(iJx))', i y= (yi1, yi2,..., yiJ)', ψ(x) = ρ'(x). As defined in equation (5)where andWi = diag(wi1, wi2,..., wiJ),Wi into equations (10) and (11) and setting them to zeros, and solving these two equations and yielding estimation equations for  in equation (6) and  in equation (7). They arePlugging Letthen equation (7) can also be expressed as = (Z'WZ)-1 Z'W(y - B).Z'WZ)-1 can be explicitly calculates using the following matrix,The solution of .for ψ and χ functions derived from Huber's ρ(z) function areThe The related weight function has the formwhere H is a constant.α used in the scale step for Huber's robust estimation can be calculated as the followingThe constant Φ is the distribution function of the standard normal distribution, N is the total number of observations in the dataset, and p is the total number of parameters in the model.where ψ and χ functions derived from Tukey's ρ(z) function areThe The associated weight function has the formk is a constant and the constant a in the scale step takes valuewhere  is the Chi-square probability function with n degrees of freedom evaluated at s.where σ instead of iteratively updating equation (9) in our R program. It can be shown that equation (8) for Tukey's χ(z) function has an unique real root. This real root is just the solution for the estimator of σ. Let n* be the total number of observations that satisfy the second case of Tukey's χ function, i.e. | z | >k, let J* be the total number of clones that satisfy the first case of the χ, i.e. | z | ≤ k. Replacing z by  and plugging Tukey's χ into equation (8), we getWhen Tukey's weight function is used, equation (8) is solved directly for the estimator of whereLetThen equation (12) becomesax3 + bx2 + cx + d = 0.     (13)x = y - b/3a, divided by a in the both sides of equation (13), and plugs x into equation (13), then we get the Cardan's cubic equationLet p = c/a - b2/3a2, q = d/a - bc/(3a2) + 2b3/(27a3), the above equation becomesLet y3 + py + q = 0.     (15)The determinant for Cardan's equation (15) isq cannot be zero. If we can show that the p is greater or equal to zero, then the Δ must be positive. BecauseIt can be shown that the determined function Δ must be positive. The first term in the determinant equation must be positive because of the square function and ac - b2 is non-negative. We can see thatSo the Δ is positive if only if 3According to the Cauchy inequality , we havep must be non-negative and the Δ must be positive. Thus there is only one real root for equation (15), that isTherefore, the σ in equation (12) isThen the solution for


Two or more factor mixed factorial experiments are becoming increasingly common in microarray data analysis. In this case study, the two factors are presence (Patients with Alzheimer's disease) or absence (Control) of the disease, and brain regions including olfactory bulb (OB) or cerebellum (CER). In the design considered in this manuscript, OB and CER are repeated measurements from the same subject and, hence, are correlated. It is critical to identify sources of variability in the analysis of oligonucleotide array experiments with repeated measures and correlations among data points have to be considered. In addition, multiple testing problems are more complicated in experiments with multi-level treatments or treatment combinations.α-level (αnew = 0.0033) determined by the FDR procedure. Since simple effects may be examined for the genes with significant interaction effect, we adopt the protected Fisher's least significant difference test (LSD) procedure at the level of αnew to control the family-wise error rate (FWER) for each gene examined.In this study we adopted a linear mixed model to analyze oligonucleotide array experiments with repeated measures. We first construct a generalized F test to select differentially expressed genes. The Benjamini and Hochberg (BH) procedure of controlling false discovery rate (FDR) at 5% was applied to the P values of the generalized F test. For those genes with significant generalized F test, we then categorize them based on whether the interaction terms were significant or not at the A linear mixed model is appropriate for analysis of oligonucleotide array experiments with repeated measures. We constructed a generalized F test to select differentially expressed genes, and then applied a specific sequence of tests to identify factorial effects. This sequence of tests applied was designed to control for gene based FWER. Experiments in which subjects are assigned randomly to levels of a treatment factor (or treatment combinations of more than one factor) and then are measured for trends at several sampling times, spaces or regions (within-subject factors) are increasingly common in clinical and medical research. The analysis of interaction, main effects and simple effects are appropriate for analyzing these types of experiments . Main efIt has been shown that replication is the key not only to increasing the precision of estimation but also to estimating errors associated with tests of significance . PreviouAttention to the multiplicity problem in gene expression analysis has been increasing. Numerous methods are available for controlling the family-wise type I error rate (FWER) -17. Sincet al., 2001, Chu et al., 2002, Kerr et al., 2000, and Wernisch et al., 2002 [In this paper, we present a method for analyzing oligonuleotide array experiments with repeated measures using a linear mixed model, which allows us to model variance-covariance structures associated with such complicated experiments. Our method is also related to that of Wolfinger l., 2002 ,9-11. Inl., 2002 . The cerBased on the statistical methods described (see Methods), 708 genes were considered to be significant by the procedure of controlling FDR at 5% for multiple testing across genes. The largest P-value considered to be significant was 0.0033 determined by the FDR procedure. Among the 708 genes, 137 show significant interaction at the level of 0.0033, 49 genes with significant disease effect (32 were up-regulated and 17 were down-regulated in AD patients) and 559 genes with significant regional effects (331 were up-regulated and 228 were down-regulated in the OB)  between AD and control in OB are in the opposite directions compared to the changes between AD and control in CER. In a magnitudinal interaction, the directions of the changes between AD and control are the same but the magnitudes of changes are significantly different. The gene LOC91614 (UniGene Cluster Hs.180545), which encodes novel 58.3 kDa protein, is an example with directional interaction effect. As shown in Figure et al., 2000), and with the slight increase in lysosomal density in the CER compared with the pronounced increase in sites of the AD brain with significant neuropathology . The paIn the absence of interaction effects, main effects are often meaningful. The genes that have either significant main effect of Disease or Region were also identified and characterized by examining the average difference between AD and controls or the average difference between OB and CER. Main effects can also be illustrated by the simple diagrams described above, in which the lines are often parallel. Four genes were used as examples to illustrate main effect of Disease and main effect of Region Table .HMGN2 and TSG101 both have significant effect of Disease  was significantly down-regulated  in the OBs of AD patients compared to elderly non-demented controls; there was no significant difference in mean expression levels in the OB and CER as shown in Figure TSG101, was up-regulated 1.51 fold (p = 0.0021), with no significant differences in expression levels in the OB and CER. The encoded protein is a member of the mammalian class E vps proteins, which mediate ubiquitination-dependent receptor sorting within the endosomal pathway. The up-regulation of TSG101 suggests a potential disruption of OB neurogenesis.The genes se Table . HMGN2 (RELN and B2M (Table RELN is expressed at lower levels in the OB than in the CER (2.7 fold, p <0.0005) as shown in Figure B2M, the gene encoding β2 microglobulin, is expressed at 2.2-fold higher levels in the OB than in the CER (p < 0.0002). One potential explanation for the higher levels of B2M expression in the OB than the CER is that antigens can enter the brain directly along the pathway provided by the axon of the olfactory receptor neuron or within the sheath of the olfactory nerve; numerous proteins and pathogens enter the brain via this route  and control subjects enrolled in the Biologically Resilient Adults in Neurological Studies (BRAiNS) project of the Sanders-Brown Center on Aging. At autopsy, OBs and pieces of the lateral tip of the cerebellums were removed from 6 females, 3 with AD  and 3 controls , and immediately placed in liquid nitrogen. BRAiNS control subjects had no clinical evidence of dementia or other neurological problems and scored within the normal range on yearly mental status tests; on neuropathological examination, their brains exhibited age-related but not disease-related changes. AD patients received a diagnosis of probable AD in the Memory Disorders Clinic; on neuropathological examination, their brains met multiple criteria for definite AD and exhibited no indications of complications from cerebrovascular disease .OBs and cerebellum were homogenized in TRI-Reagent (Molecular Research, Inc., Cincinnati, OH), and total RNA was extracted according to the manufacturer's protocol. RNA concentration was determined spectrophotometrically; its integrity and quality were assessed by spectrophotometry, agarose gel electrophoresis, and Bioanalyzer (Agilent, Technologies, Wilmington, DE) virtual gels. Following target preparation, the samples were hybridized onto the Affymetrix Human Genome U133_A and _B GeneChips at the University of Kentucky Microarray Core Facility according to Affymetrix protocols.μg RNA from the OB and CER of each individual were hybridized with Affymetrix Human Genome U133_A and _B chips . Data from U133_A and _B chips for each RNA sample were combined to give 12 data sets with signal intensities for 44828 targets. Under the assumption of independence among genes, we have a 2 × 2 factorial design for each gene with one factor being either control or AD and with repeated measures (regions, OB or CER) on each subject. The arrangement for the 2 × 2 mixed factorial design in this experiment is shown as in Table 11μ, 12μ, 21μ, and 22 μdenotes the average log 2 based expression levels measured in OB of controls, CER of controls, OB of AD patients and CER of AD patients respectively. Corresponding measurements from the same subject are correlated and they are marked as same color. Our primary interests are to identify various sources of variability and differentially expressed genes.OBs and pieces of the lateral tip of the cerebellums were previously removed from each of 3 control subjects and 3 patients with AD . Total RNA was extracted from OB and CER tissues for each subject. Five Background correction and initial total intensity normalization were first performed for the microarray raw data using Affymetrix Version 5 software , resultiet al., 2003 [In our study, all positive control genes and genes that resulted in an "absent" call for all chips were removed from further analysis. If there was no evidence that these genes were expressed in any of the samples, then these genes can be removed to reduce problems associated with multiple comparisons. Other methods of removing low intensity points were also suggested by Bolstad l., 2003 . All ESTWe use a linear mixed model to describe the experiment.gijk be the base-2 logarithm of background-corrected and normalized intensity of the gth gene, g = 1, ..., 10590, in the ith Treatment group i = 1, 2, from the jth Region, j = 1, 2, on the kth subject k = 1, 2, 3. "Treatment" here signifies the health condition of the subjects (controls or AD patients). A complete linear mixed model for this experiment:Let Ygijk = μ + Di + Sik + Rj + (DR)ij + Aijk + Gg + (GD)gi + (GR)gj + (GDR)gij + εgijk,     (1)Yμ is the grand mean, Di and Rj and are the main effects of treatments, regions respectively, and (DR)ij are the treatment-region interaction effects. Here Sik are the random effects of subjects within disease group and Aijk are the random effects of chips. The symbols Gg, (GD)gi, (GR)gj and (GDR)gij represent the main effect of gene, gene-treatment interaction effects, gene-region interaction effects, gene-treatment-region interaction effects, while εgijk are the additive stochastic errorswhere et al., 2001 [i, Rj and (DR)ij is orthogonal to the design matrix for the fixed effects involving each gene, including Gg, (GD)gi, (GR)gj and (GDR)gij. Therefore, the normalization model has no effect on the inference for each gene under the assumption in (1). A simpler model can be adopted for each gene, and the random effect Sik is absorbed by Sgik terms and Aijk is absorbed by εgijk terms. We make standard stochastic assumptions that the random effects Sgik, and εgijk are normally distributed with zero means with variances σgs2, and σg2 respectively. These random effects are assumed to be independent both across their indices. The model equation then becomesIn general, it is impractical, using currently available software, to fit linear models such as (1) with microarray data involving manipulation of the full covariance matrix of observation variables that usually contains thousands of levels. To be conceptually and computationally more efficient, Wolfinger l., 2001  suggestegijk = μg + Dgi + Rgj + (DR)gij + Sgik + εgijk.     (2)YIn matrix notation, the model equation for each gene can be writtenY = β X+ Zu + ε,     (3)Y is a vector of observations, X and Z are matrices of known constants for the fixed effects and random effects, respectively, β is a vector containing fixed effect parameters Dgi, Rgj, and (DR)gij, u is a vector of random effects, and ε is the error or residual vector. Therefore, Y ~ MVN (β,VX) where V = ZDZ' + Σ. The covariance matrices D = var(u) and Σ = var(ε) can have any valid variance-covariance matrix form. The variances of gene specific subject effects S can vary for different treatments and different genes, while ε effects can have different variances for different treatments, regions and different genes. The remaining terms are fixed effects. All effects and variance components in the model can be estimated using the method of restricted maximum likelihood (REML) [where d (REML) .gV, is block diagonal whereIn the homogeneous variance case assumed here, since observations across subjects are independent, the variance-covariance matrix for gene g, g V= diag (gΣ)andg Σto vary across disease groups.If the assumption of homoscedasticity is not viable, the variance-covariance for gene g can easily be accommodated by allowing β, which containing treatment, region effects and treatment-region interaction for each gene. For each gene, β is estimated byThe estimate of primary interest is  has covarianceThe estimated V are replaced by their REML estimates. See Verbeke and Molenberghs (2000) [where in practice components of s (2000)  for meth11 μ= 12 μ= 21 μ= 22μ, is rejected. Because of the specific variance-covariance structure for a repeated measures experiment with two levels of the within subject factor, it is convenient to test the equivalent composite hypothesis for each gene g which is stated in terms of the main effects and the interaction. Specifically, we considerGenes showing significant interaction effects are defined as those in which the difference in expression levels between control and AD is not the same with the difference between OB and CER. Main effects are meaningful in the absence of interaction effect. Genes showing a significant disease-related effect or main effect of disease are defined as those either under- or over-expressed by AD patients compared to controls at the same extent in both OB and CER, while genes with significant main effect of region are those either under- or over-expressed in OB compared to CER at the same extent by both AD and controls. If the expression levels for a gene are the same across all treatment-region combinations, then there will be neither significant interaction nor main effects; therefore this gene should be excluded from further analysis. The expression of other genes may be altered by treatment or/and region effects, and further analysis of these genes is needed to characterize the experimental effects. Therefore the first step to select differentially expressed genes in factorial designs is to choose those for each of which the hypothesis of equality of all cell means, L be the 3 × 8 matrix containing the coefficients of the 3 contrasts, then o His simplified as β L= 0, where β Lis estimable, and can be tested using the generalized F testWe can test this composite null hypothesis of no interaction and main effects simultaneously by setting up 3 corresponding linear contrasts listed in Table oH, the generalized F is distributed approximately as Snedecor's F with degrees of freedom rank(L) and ν (Fν][rank(L), ). Since the variance-covariance matrix V satisfies a compound symmetry condition, in our example this statistic is distributed as F[3, 4]. Under other assumptions of the variance-covariance structures, the denominator degrees of freedom ν can be approximated by the degrees of freedom to estimate -1 X)-1 L' L from list I and, for genes in list II, to test the simple effects. By complete enumerating of all possible combinations of main effects and interaction effect, one can prove that αnew is an appropriate choice to control the FWERs while selecting genes with either significant interaction or main effects in 2 × 2 factorial experiments. From the remaining genes, significant main effects of either disease or region (list III) were selected. In the example used in this study, αnew = 0.0033.4. Using Data normalization and generation of simulated data were performed using S-plus version 6.1. We used SAS (version 9.0) proc mixed procedure to do Model fitting and significance analysis. The SAS program implementing linear mixed models for the AD data is available on request from the first author.We constructed a generalized F test to select differentially expressed genes (see method). To assess the performance of the constructed generalized F test with small sample sizes, we performed simulation studies. Since expression levels of genes in the OB or CER from an individual (either a control or patient with AD) are considered to be repeated measures, correlated data should be generated for the simulations. First, we studied the case (case I) with equal variance and covariance structure for each individual subject (control or AD patient). We generated 10,000 sets of correlated data; each set has 6 bivariate observations, with mean 20 and the following covariance structure for each subject under either Disease condition :gijk and Ygij'k are measurements from the jth and j'th levels of Region for the kth subject in the ith level of Disease for gene g. The generalized F-statistics were computed for each of the 10,000 data sets and the histogram of the generalized F-statistics was compared with that of randomly generated F values from a F[3, 4] distribution as shown in figure α = 0.05] [3, 4, = 6.59 was 5.12%, instead of the nominal 5%, 4.97% random generated F values were smaller than 6.59.where YMore complicated variance and covariance structure can also be assumed. For example, the controls and AD patients may have a different covariance matrix. We then generated simulated data to study cases like above (case II). Using the same covariance structure as above, we generate 10,000 sets of data for controls. For AD, we generated 10,000 sets of data using a different covariance structureThen we computed the generalized F-statistics and compared them with randomly generated F values described above Figure . The hisHL carried out the study. AJS, and CLW supervised the study. TVG and MLG carried out the molecular genetics studies. All authors contributed to the writing of this manuscript. All authors read and approved the final manuscript.


Under the same conditions, the rate of end-dependent filament disassembly (koff) is 123 ± 16 monomers per minute per filament end. This rate of disassembly requires a tight coupling of the ATP hydrolytic cycles of adjacent RecA monomers. The relationship of kcat to koff infers a filament state in which waves of ATP hydrolysis move unidirectionally through RecA filaments on dsDNA, with successive waves occurring at intervals of approximately six monomers. The waves move nearly synchronously, each one transiting from one monomer to the next every 0.5 s. The results reflect an organization of the ATPase activity that is unique in filamentous systems, and could be linked to a RecA motor function.The RecA protein forms nucleoprotein filaments on DNA, and individual monomers within the filaments hydrolyze ATP. Assembly and disassembly of filaments are both unidirectional, occurring on opposite filament ends, with disassembly requiring ATP hydrolysis. When filaments form on duplex DNA, RecA protein exhibits a functional state comparable to the state observed during active DNA strand exchange. RecA filament state was monitored with a coupled spectrophotometric assay for ATP hydrolysis, with changes fit to a mathematical model for filament disassembly. At 37 °C, monomers within the RecA-double-stranded DNA (dsDNA) filaments hydrolyze ATP with an observed  The RecA filament plays a key role in bacterial DNA recombination and repair. Biochemical studies now reveal some unexpected properties of the filament There are three prominent protein families that both form filaments and hydrolyze nucleoside triphosphates (NTPs). These include the tubulins ,2,3, theThe bacterial RecA protein promotes the central steps of recombinational DNA repair ,22. In vRecA filaments are assembled and disassembled in an end-dependent fashion. Filament assembly proceeds in steps, with a slow nucleation followed by a very rapid 5′ to 3′ extension phase to coat the available DNA ,23,24,25The RecA protein also binds to dsDNA, but nucleation onto dsDNA is much slower than onto ssDNA ,30. Nuclkcat values for ssDNA and dsDNA-dependent ATP hydrolysis rates are approximately 30 and 20 min−1, respectively, as determined in multiple trials over the past two decades [1-ATPase [RecA protein within a filament hydrolyzes ATP in a reaction that is almost completely DNA-dependent under standard reaction conditions . Under o decades ,11,12. A decades . ATP hyd decades . In the  decades ,39,40. H decades ,32,33,34 decades ,42, DNA  decades , and DNA decades ,45. It i decades  and the 1-ATPase . Models 1-ATPase .2+ concentration. However, all RecA filaments on ssDNA hydrolyze ATP with a kcat of approximately 30 min−1. Addition of a second DNA strand to a RecA filament, as in a filament bound to dsDNA or a filament promoting DNA strand exchange, converts the filament to the P state. The P state is characterized by 30% lower rates of ATP hydrolysis [There is now evidence for at least four different functional states of RecA protein, occurring at different reaction stages. These have recently been designated O, Ac, Ao, and P ,48,49 F. The O sdrolysis ,60, highdrolysis ,62, and drolysis ,49,61 thKD, for monomer addition to either filament end cannot be different unless an independent source of chemical energy is provided to affect the binding to one end or the other. As noted above, filament assembly does not require ATP hydrolysis, but filament disassembly does [How can RecA monomers be added to one end of a filament and deleted from the other end in the same test tube? The monomer-monomer interfaces are presumably the same at either end (and everywhere else) in the filament. As pointed out by Wegner , the disbly does ,32,33,34bly does ,61,64. AWithin a RecA filament, ATP hydrolysis could occur at random, or it could be highly organized as cooperative waves traveling through the filament. There is no convenient method for monitoring the effects of ATP hydrolysis in the middle of a RecA filament. However, important clues can be ascertained by examining one effect of ATP hydrolysis: the 5′ to 3′ end-dependent filament disassembly process. In effect, we cannot see waves of ATP hydrolysis within a filament, but we can monitor one of the waves—the one occurring at the disassembling filament end.−1 on ssDNA, each RecA monomer is hydrolyzing one ATP molecule every 2 s. If the ATP hydrolytic cycles of adjacent monomers are not coupled in any way, this will be reflected in a predictable rate of filament disassembly. When the end monomer hydrolyzes ATP and dissociates, the next monomer in line could be at any point within its ATP hydrolytic cycle. However, in a large population of filaments, the next monomer will be on average halfway through the cycle, and it will hydrolyze ATP (and dissociate) one second later. Dissociation of one RecA monomer per second will lead to a measured disassembly rate of 60 monomers of RecA per minute per filament end. This is close to the situation observed for RecA monomers formed on ssDNA , which disassemble with a rate of 60–70 monomers per minute per filament end [The rate of disassembly can lead directly to an assessment of the degree of coupling of the ATP hydrolytic cycles of adjacent RecA monomers within the filament. For example, since RecA hydrolyzes ATP at a rate of approximately 30 minment end . Note thi, between successive waves within the entire filament. For example, consider monomers within RecA filaments on dsDNA that are hydrolyzing ATP at approximately 20 min−1 (or one ATP every 3 s). If ATP hydrolytic cycles of adjacent monomers are coupled within the filament so that ATP hydrolysis is organized in waves  is added at the time of the pH shift [A model system has been developed that allows the rate of end-dependent RecA filament disassembly from ssDNA to be determined quantitatively by monitoring the rate of ATP hydrolysis during the disassembly process ,27. The pH shift ,65,66,67knuc is the rate of renucleation of RecA filaments to vacated DNA during the disassembly process, koff is the end-dependent disassembly rate as noted in the Introduction, ntot is the total number of RecA protein binding sites on the DNA molecule used as substrate, [D-ends] is the concentration of disassembling ends, and kcat is the turnover number for ATP hydrolysis by RecA monomers in the filament.The process in kcat for RecA-mediated ATP hydrolysis does not change in the range used for the pH shifts. This is documented elsewhere [The derivation of lsewhere ,27,30.On dsDNA, the situation becomes more complicated because it is more difficult to define the orientation of the filaments. RecA protein binds to the two strands of a duplex DNA unequally. One strand is bound at the site normally occupied by ssDNA. This strand orients the filament, and it is protected from nuclease digestion better than the second strand of a duplex ,68. We wTo isolate the disassembly process so that it can be measured accurately, we must limit the rate of RecA rebinding to DNA that has been vacated as the RecA dissociates. Several parameters can be adjusted to accomplish this. The first one is pH. The rate of RecA protein disassembly reaches an apparent maximum at pH 8 and above . The ratkcat for ATP hydrolysis is reported as the measured rate of ATP hydrolysis prior to the pH shift (in μM min−1), divided by the initial concentration of bound RecA protein (in 2 μM).Optimizing all of these considerations, the general protocol for these experiments is outlined in koff, is obtained by fitting the equation to the ADP production curve. There is just one caveat. The renucleation onto the vacated DNA must be suppressed sufficiently so that there is, to a reasonable approximation, no more than one disassembling RecA filament end per bound DNA. If multiple filaments formed on the vacated dsDNA as a result of renucleation, this process would not be properly modeled by With the filaments uniquely oriented on the tailed DNA and encompassing the entire length of the DNA, koff and knuc, as well as several known parameters. All concentrations are in μM, and all times are in minutes. The data from ATP hydrolysis assays were converted to [ADP], plotted as a function of time, and fit to ntot, and [RecA] were known for each experiment and held constant for fitting. The terms koff and knuc were the fitting parameters. The apparent kcat for ATP hydrolysis was determined independently as the rate of ATP hydrolysis before the pH shift and initiation of net filament disassembly divided by the concentration of bound RecA protein. However, kcat can be determined as a fitting parameter as well. Therefore, each dataset was fit to kcat held constant at the value measured prior to the pH shift, and once with kcat as a fitting parameter in addition to knuc and koff. The fit parameters for both fittings were compared. Experiments were discarded in which the measured and fit kcat did not agree to within 40%, or the measured kcat was less than 18 min−1 . For the 3 kbp substrate used in A typical experiment is illustrated in kcat fixed at the average value measured prior to the pH shift, kcat = 19.5 ± 0.6 min−1, yields the best-fit values (averaged over 12 experiments) of koff = 120 ± 20 min−1 and knuc = 4.6 ± 0.75 × 10−5 μM−1 min−1. When kcat was allowed to vary as a fitting parameter along with koff and knuc, the parameters were again obtained from the best-fit curves and averaged. This yielded kcat = 21.6 ± 4.4 , koff = 133 ± 24 min−1, and knuc = 5.1 ± 0.89 × 10−5 μM−1 min−1 for the 12 datasets. The reasonable agreement between the measured and fit kcat values in most trials helped provide confidence that the kcat measured prior to the pH shift was consistent with the observed reaction progress curve obtained after the pH shift.The plot in koff to values 10% above and 10% below the value obtained by fitting the data in The fitting process is quite sensitive to small changes in the fitting parameters. As long as the stated constraints on the use of kcat and koff values remaining constant  as a function of DNA length as summarized in kcat to the value measured before the pH shift (average 20.9 ± 0.6 min−1) yields the best-fit values of koff = 125 ± 9 min−1 and knuc = 1.0 ± 0.075 × 10−4 μM−1 min−1. In the same manner, the 4-kbp DNA substrate yielded average values of koff = 124 ± 19 min−1 and knuc = 2.5 ± 0.52 × 10−5 μM−1 min−1 with a measured kcat = 21.7 ± 1.8 min−1. When kcat was allowed to vary as a fitting parameter along with koff and knuc, the best-fit values for the 2-kbp DNA substrate averaged kcat = 20.5 ± 2.4 min−1, koff = 121 ± 10 min−1, and knuc = 9.9 ± 0.76 × 10−5 μM−1 min−1 for the 12 datasets. The 4-kbp DNA substrate yielded best-fit values of kcat = 23.6 ± 3.0 min−1, koff = 136 ± 14 min−1, and knuc = 2.8 ± 0.26 × 10−5 μM−1 min−1 for the 14 datasets. All of this work is summarized in kcat to the value measured before the pH shift are kcat = 20.8 ± 1.5 min−1 and koff = 123 ± 16 min−1. When kcat was not constrained, the values were kcat = 22 ± 3.5 min−1 and koff = 130 ± 18 min−1. Unlike the other parameters, the nucleation of filament formation as expressed in knuc should be affected by factors such as G:C content and sequence structure in the duplex DNA [knuc was quite reproducible.The results agreed very well with those obtained with the 3-kbp DNA, with the knuc and the length of the DNA, and thus varies somewhat.Representative trials using the 2-, 3-, and 4-kbp DNA substrates are compared in −1 min−1. The average final steady-state rate of ATP hydrolysis is 1.23 μM−1 min−1, or 6.3% of the rate observed prior to disassembly. This final rate corresponds to 6.3% occupancy of the available RecA binding sites, or 0.063 μM bound RecA protein. We estimate that the average filament at steady state occupies one-quarter of the available RecA binding sites in the DNA to which it is bound from the following considerations. When a new RecA filament nucleates onto the vacated DNA, the nucleation could occur anywhere along the length of the DNA. On average, the nucleation would occur at the center of the DNA, and the fast unidirectional filament extension phase would quickly coat the DNA from that point to one end, so that the typical new filament would occupy half of the available RecA binding sites on the DNA to which it was bound. At steady state, filaments would be disassembling at a rate that just balances the rate of renucleation of filaments to replace them (with the rate of disassembly much slower than filament extension). A given filament could be anywhere in the disassembly process, but the average filament bound at steady state will have lost half of its length. The average filament at steady state will thus occupy one-quarter of the RecA binding sites on a given DNA molecule. If 6.3% of the available DNA binding sites are occupied by RecA thus distributed in filaments that coat one-quarter of a DNA molecule, then we can estimate that 25.2% of the DNA molecules have some bound RecA protein. About 6% of the DNAs ([0.252]2, or approximately 0.06) will have two filaments bound. Half of these will have two filaments with the same orientation, and thus effectively have only one end where net disassembly will occur. The remaining 3% of DNAs with the potential for two bound filaments and two disassembling ends represent the maximum percentage of DNAs in this condition, and this maximum can only be approached late in the disassembly process after the DNA initially bound by oriented filaments has been vacated completely. Since the potential for multiple filaments is limited early in the dissociation curve, and 3% in any case is well within the error limits of our measurements, we have not adjusted our model or corrected our reported rates for this effect. To the extent that multiple disassembling ends contribute to the observed rates, they would lead to a very slight overestimate of the disassembly rate.As already noted, i, is koff /kcat. We calculate i to be 6.0 ± 0.5, 6.2 ± 1.1, and 5.8 ± 1.1 monomers for the 2-, 3-, and 4-kbp DNA substrates, respectively. As with the other parameters, these values agree well and are identical within experimental error. When averaged across all 38 trials, i is 6.0 ± 0.9 monomers if kcat is constrained and 6.0 ± 0.8 monomers if kcat is not constrained  is plotted against i, an optimum is seen at i = 6.4 monomers for the 3-kbp DNA substrate (i = 5.9 monomers for the 2-kbp DNA substrate, and at i = 5.8 monomers for the 4 kbp-DNA substrate (unpublished data).The interval between waves of ATP hydrolysis, ined see . As noteubstrate . The optkcat of 20.8 ± 1.5 min−1. The ratio koff/kcat gives i, the interval between the waves of hydrolysis within the filament. The koff/kcat = i = 6.0 ± 0.9 monomers. These results are taken from data in which the kcat for ATP hydrolysis was constrained to the value measured prior to the pH shift. The results are quite similar when kcat is not so constrained  is 123 ± 16 RecA monomers per minute per filament end, under the conditions of these experiments. While this is occurring, ATP is being hydrolyzed by monomers within the filament with a measured strained . Given tstrained . These “−1), obtained by Libchaber and colleagues [The rate of filament disassembly that we measure is consistent with a rough estimate of 2.4 monomers per second , 10 mM magnesium acetate, 5% (v/v) glycerol, 1 mM dithiothreitol, 3 mM potassium glutamate, 3 mM ATP, an ATP regenerating system (10 units/ml pyruvate kinase and 3 mM or 2 mM PEP), and concentrations of DNA and RecA protein as described below and in figure legends. The coupled spectrophotometric assay also contained 10 units/ml lactate dehydrogenase and 3 mM NADH. Specific buffers used are described below and in the figure legends. DNA and protein concentrations are indicated for each experiment. Reactions were incubated for 10 min before ATP was added to start the reaction.−1 cm−1 was used to calculate rates of ATP hydrolysis.A coupled spectrophotometric assay was used to measure DNA-dependent ATP hydrolysis by the RecA protein ,93. The kcat for bound RecA protein (one monomer per three available DNA base pairs) of 18–24 min−1. The few reactions displaying initial rates reflecting a kcat less than 18 min−1 generally reflected a problem with one or another reagent, and were discarded. After preincubation to achieve a DNA substrate saturated with RecA protein, the solution was subjected to a pH shift. The 200 μl reaction was diluted with gentle mixing into 200 μl of a solution , containing 25 mM Tris-acetate (30% cation, pH 8.50) buffer, 10 mM magnesium acetate, 5% (v/v) glycerol, 1 mM dithiothreitol, 3 mM potassium glutamate, 3 mM ATP, an ATP regenerating system (10 units/ml pyruvate kinase and 3 mM or 2 mM PEP), and 0.3 μM SSB. The final pH of the reaction after the pH shift was 8.00. The RecA and DNA concentrations were halved as a result of the pH shift, but the concentrations of ATP, Mg2+, and ATP regeneration system components were kept constant. Following the pH shift, the production of ADP was monitored spectrophotometrically as the RecA filaments disassembled. The rate of ATP hydrolysis declined, eventually settling to a slow steady-state rate of ATP hydrolysis that reflects the minimal amount of bound RecA protein for a given experiment (see Results).ATP hydrolysis reactions were started as described above in 25 mM MES/NaOH (76% anion, pH 6.62) buffer. Reactions contained 12 μM RecA protein, 12 μM  linear duplex DNA, and the ATP and ATP regeneration conditions indicated above. These were incubated for approximately 20 min to reach a stable steady-state rate of ATP hydrolysis. The rate was determined and reflected a virtually complete binding of all available DNA by RecA protein. Under these conditions, we routinely achieved rates reflecting an apparent Video S1This movie illustrates the model of (148 KB MOV).Click here for additional data file.


Rivastigmine, a butyl- and acetylcholinesterase inhibitor, is approved for symptomatic treatment of Alzheimer's disease (AD). Data supporting the safety and efficacy of second-generation cholinesterase inhibitors, such as rivastigmine, are available for treatment up to 1 year, with limited data up to 2 1/2 years. The purpose of this report is to present safety and effectiveness data for rivastigmine therapy in patients with mild to moderately severe AD receiving treatment for up to 5 years.An observational approach was used to study 37 patients with originally mild to moderate AD receiving rivastigmine as a therapy for AD in an open-label extension (ENA713, B352 Study Group, 1998).The initial trial demonstrated rivastigmine was well-tolerated and effective in terms of cognition, global functioning and activities of daily living. In this open label extension, high-dose rivastigmine therapy was safe and well tolerated over a 5-year period. Two thirds of the participants still enrolled at week 234 were in the original high-dose rivastigmine group during the double-blind phase, suggesting that early therapy may confer some benefit in delaying long-term progression of symptoms.Long-term cholinesterase inhibition therapy with rivastigmine was well tolerated, with no dropouts due to adverse effects past the initial titration period. Early initiation of treatment, with titration to high-dose therapy, may have an advantage in delaying progression of the illness. Alzheimer's disease (AD) is the most common form of dementia affecting elderly people in the United States. Prevalence is 1% to 2% at age 65 years, but increases markedly to 35% or greater by age 85. Because of a demographic shift toward a more aged population, the percentage of affected individuals is rapidly increasing. This trend is expected to continue for the foreseeable future. Therefore, accurate and timely diagnosis and effective treatments are critical to optimal outcomes over the 8- to 10-year course of the illness [Traditionally, a probable diagnosis of AD was accomplished by history, clinical examination, neuroimaging, and neuropsychological and laboratory testing to rule out treatable causes for the patient's symptoms and to differentiate AD from other possible causes of dementia ,3. Much Currently, predominant symptoms of dementia are treated primarily with second-generation cholinesterase (ChE) inhibitors. These drugs have demonstrated efficacy, as measured by cognitive, behavioral, and functional outcomes, in randomized, placebo-controlled clinical trials, the majority of which have been of 6 months' duration -6. In anRivastigmine's approval by the FDA in 2000 was supported by several pivotal trials, including a randomized US trial (ENA 713 B352). In thisMuch work remains to be done to more definitively answer questions about when to start therapy, which patients are most likely to benefit, what constitutes clinically relevant beneficial effects over the longer term, and when these drugs are no longer clinically effective. Consideration should also be given to withdrawal of therapy. Findings presented in this article will add to the current limited dataset for long-term efficacy and outcomes with cholinesterase inhibitor therapy for persons with probable AD.This report describes our experience in following the cohort of patients at our center with AD treated with the ChE inhibitor rivastigmine (a medication that inhibits both butyl- and acetylcholinesterase) as part of the ENA 713 B352 pivotal trial for a period up to 5 years.Data in this analysis came from a subgroup of 37 patients with originally mild- to moderate-stage  AD followed at a large Mid-Western university site in a 26-week, prospective, randomized, double-blind, placebo-controlled, parallel-group study of rivastigmine as therapy for AD conducted at 22 research sites across the United States (ENA713, B352 Study Group, 1998) [Patients were enrolled according to previously described inclusion criteria . Of noteImmediately following the double-blind phase of the study, open-label rivastigmine was flexibly titrated over a 12-week time period to a maximum tolerated dosage of up to 6 mg BID. By the end of the 12 week titration 25 participants were on 4–6 mg. of rivastigmine and 11 participants had dropped from the study. One participant remained on a 2 mg. dose and dropped from the study between weeks 52 and 78.Outcomes measures included the Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-cog) and the Clinician's Interview-Based Impression of Change, with caregiver input (CIBIC-Plus). Ability to carry out activities of daily living (ADL) was assessed by the Progressive Deterioration Scale (PDS). Disease-staging measures included the Geriatric Deterioration Scale (GDS) and the MMSE. In the open-label phase of the study, efficacy evaluations were performed every 6 to 8 weeks for titration and early maintenance, and every 26 weeks for the next 5 to 6 years.These data are predominantly descriptive, with analyses including Kaplan- Meier survival plots when appropriate. All statistical analyses on our single center extension were performed at our center using SPSS. Subgroup analyses by initial treatment randomization were also performed.Twenty-one Caucasian women and 11 Caucasian men participated in the open label extension of this pivotal study. Twenty-two participants reported a family history of AD. Selected demographic and baseline characteristics of the subsample are presented in Table A total of 25 patients during the 5-year term eventually withdrew from the study. Reasons for termination, stratified by original group during the double-blind phase, are summarized in Figure Of the 4 patients who withdrew from the study due to disease progression, 3 were men between the ages of 57 and 64 years. The 57-year-old man was in the original high-dose group, with a baseline MMSE score of 16 and an MMSE score of 0 at the 234-week data collection. The other two male participants were aged 62 and 64 years with baseline MMSE scores of 22 and 20, respectively. The 62-year-old man in the original low-dose group withdrew at week 104 with an MMSE score of 9; the 64-year old man in the original high-dose group withdrew at week 156 with an MMSE score of 11. Interestingly, the 76-year-old woman in the original low-dose group, with a baseline MMSE score of 22, withdrew after the 26-week data collection (MMSE = 21).The Kaplan-Meier survival analysis, shown in Figure Of the subjects starting open-label rivastigmine, 25% were still participating at week 234. Of the 8 subjects still participating, 5 were female and only 1 reported a family history of AD. Interestingly, this group was characterized by a broad age range (57–85 years), a broad range of baseline MMSE scores (15–26), and by the fact that 5 of the 8 remaining participants at week 234 were in the original high-dose rivastigmine group.For the end point defined as a 5-point drop from the baseline MMSE score, the group mean was 94 weeks. However, an age-related observation was noted such that the mean time to a 5-point drop from baseline MMSE for the ≤ 70 age group was 67 weeks as compared with 122 weeks for the >70 years age group. A similar trend was observed for scores on the ADAS-cog. For the group as a whole, mean time to a 4-point deterioration on the ADAS-cog was 84 weeks; with a mean of 70 weeks for the younger group and 104 weeks for the older group. [In the original study, mean age across the 22 research sites was 74.5 years; mean age for participants in this report was 71.8 years]Figures When evaluating qualitative data, it is important to examine particular patients in terms of the data collected and treatment response at end of study. Data for the youngest man and the elderly woman, considered side-by-side, seem counterintuitive. Part of the explanation, however, may rest with the caregivers' experiences with and beliefs about the patients. This information can be accessed by reviewing the "symptoms most troubling" item from the CIBIC-Plus. This item asks, "With respect to the above symptoms, which are the biggest problems for you and/or other caregivers?" The spouse of the 57-year-old man reported that the "symptoms most troubling" for her were the patient's "selective difficulties and his attitude problem" (week 104, MMSE = 11) and that the patient "doesn't try" (week 130, MMSE = 7). These comments suggest a lack of acceptance of the patient's diagnosis and a lack of belief regarding the patient's documented decline that could explain continued clinic visits until, at week 234, the patient's MMSE score was 0. In contrast, the caregiver for the 76-year-old woman cited the fact that the patient "doesn't want to leave the house" (week 12) and the patient's anxiety about coming to clinic appointments (week 26) as the "most troubling" symptoms. These comments suggest that the caregiver was encountering patient resistance and observing patient distress, which were exacerbated by efforts to participate in the study. Therefore, further clinic visits were declined. Retrospectively, it is impossible to determine how the caregiver's beliefs and experience with the patient affect perceptions about disease status, treatment response, and decisions to continue or terminate treatment. These are interesting hypothesis-generating observations that should be explored in future investigations.Limited data are available on the tolerability and effectiveness of cholinesterase inhibitor therapy for periods up to 3 years -7, but nOf note, approximately two thirds of the participants still enrolled at week 234 were in the original high-dose rivastigmine group during the double-blind phase; this finding suggests that early therapy with rivastigmine may confer some benefit in delaying long-term progression of symptoms, as has been previously suggested by analysis of the combined 26 weeks of double-blind and first 26 weeks of open-label data from the B352 US trial . ThroughIn summary, long-term therapy with the ChE inhibitor rivastigmine was well tolerated with no dropouts due to adverse effects past the first 9 months of the open-label extension. In contrast to the generally reported community experience of relatively brief duration of therapy with ChE inhibitors in AD, 25% of patients in this study were still taking rivastigmine by the end of 5 years. Of interest is the multifactorial nature of reasons for treatment discontinuation. Only 1 of these patients withdrew from the study because of perceived treatment failure over the 5-year period. Disease progression accounted for the withdrawal of 4 patients.These results are informative both for the duration of treatment, and because the majority of the patients who continued treatment during this 5 year period were from the group originally titrated up to a high dose during the initial double-blind phase. Given that the sample size prohibits significance testing, these data suggest that rivastigmine therapy may be sustained over long periods of time in a significant percentage of patients with AD, and that high-dose therapy, particularly when begun early, may have an advantage in delaying the progression of the illness.MRF has received grant support and has served as consultant and received honoraria from Novartis Pharmaceuticals Corporation. MLL has no financial interest to declare.MF carried out the original clinical trial, conceived of the design for the observational study, and participated in the drafting and revisions of the manuscript. ML participated in the design of the observational study, performed statistical analysis, and participated in the drafting and revisions of the manuscript. Both authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here: