1 0.5 0.5 CROSSOVER DESIGNS: The crossover (or changeover) design is a very popular, and often desirable, design in clinical experiments. These summary measurements are subjected to statistical analysis (not the profiles) and inferences are drawn as to whether or not the formulations are bioequivalent. i.e., how well do the AUC's and CMAX compare across patients? So we have 4 degrees of freedom among the five squares. An acceptable washout period was allowed between these two treatments. What can we do about this carryover effect? The approach is very simple in that the expected value of each cell in the crossover design is expressed in terms of a direct treatment effect and the assumed nuisance effects. The patients in the AB sequence might experience a strong A carryover during the second period, whereas the patients in the BA sequence might experience a weak B carryover during the second period. The two-period, two-treatment designs we consider here are the 2 2 crossover design AB|BA in [Design 1], Balaam's design AB|BA|AA|BB in [Design 6], and the two-period parallel design AA|BB. BEGIN DATA Statistical power is increased in this experimental research design because each participant serves as their own control. Parallel design 2. rev2023.1.18.43176. 9.2 - \(3^k\) Designs in \(3^p\) Blocks cont'd. Here Fertilizer is nested within Field. Download a free trial here. It is just a question about what order you give the treatments. A natural choice of an estimate of \(\mu_A\) (or \(\mu_B\)) is simply the average over all cells where treatment A (or B) is assigned: [15], \(\hat{\mu}_A=\dfrac{1}{3}\left( \bar{Y}_{ABB, 1}+ \bar{Y}_{BAA, 2}+ \bar{Y}_{BAA, 3}\right) \text{ and } \hat{\mu}_B=\dfrac{1}{3}\left( \bar{Y}_{ABB, 2}+ \bar{Y}_{ABB, 3}+ \bar{Y}_{BAA, 1}\right)\), The mathematical expectations of these estimates are solved to be: [16], \( E(\hat{\mu}_A)=\mu_A+\dfrac{1}{3}(\lambda_A+ \lambda_B-\nu)\), \( E(\hat{\mu}_B)=\mu_B+\dfrac{1}{3}(\lambda_A+ \lambda_B+\nu)\), \( E(\hat{\mu}_A-\hat{\mu}_B)=(\mu_A-\mu_B)-\dfrac{2}{3}\nu\). What are the pros of LME models over ANOVA, but, for specifically crossover studies. The factors sequence, period, and treatment are arranged in a Latin square, and SUBJECT is nested in sequence. Given the number of patients who displayed a treatment preference, \(n_{10} + n_{01}\) , then \(n_{10}\) follows a binomial \(\left(p, n_{10} + n_{01}\right)\) distribution and the null hypothesis reduces to testing: i.e., we would expect a 50-50 split in the number of patients that would be successful with either treatment in support of the null hypothesis, looking at only the cells where there was success with one treatment and failure with the other. 1 -1.0 1.0 There is really only one situation possible in which an interaction is significant and meaningful, but the main effects are not: a cross-over interaction. In these designs, typically, two treatments are compared, with each patient or subject taking each treatment in turn. If the design is uniform across periods you will be able to remove the period effects. Creative Commons Attribution NonCommercial License 4.0. Each treatment precedes every other treatment the same number of times (once). We consider first-order carryover effects only. Row-Column-Design Each judge tastes each wine equally often (1 . It is always much more prudent to address a problem a priori by using a proper design rather than a posteriori by applying a statistical analysis that may require unreasonable assumptions and/or perform unsatisfactorily. In designs with two orthogonal Latin Squares we have all ordered pairs of treatments occurring twice and only twice throughout the design. The nested effect of Fertilizer is termed as Fertilizer (Field). In the statements below, uppercase is used . Distinguish between population bioequivalence, average bioequivalence and individual bioequivalence. At a minimum, it always is recommended to invoke a design that is uniform within periods because period effects are common. For an odd number of treatments, e.g. 2 1.0 1.0 Fifty patients were randomized and the following results were observed: Thus, 22 patients displayed a treatment preference, of which 7 preferred A and 15 preferred B. McNemar's test, however, indicated that this was not statistically significant (exact \(p = 0.1338\)). Lesson 1: Introduction to Design of Experiments, 1.1 - A Quick History of the Design of Experiments (DOE), 1.3 - Steps for Planning, Conducting and Analyzing an Experiment, Lesson 3: Experiments with a Single Factor - the Oneway ANOVA - in the Completely Randomized Design (CRD), 3.1 - Experiments with One Factor and Multiple Levels, 3.4 - The Optimum Allocation for the Dunnett Test, Lesson 5: Introduction to Factorial Designs, 5.1 - Factorial Designs with Two Treatment Factors, 5.2 - Another Factorial Design Example - Cloth Dyes, 6.2 - Estimated Effects and the Sum of Squares from the Contrasts, 6.3 - Unreplicated \(2^k\) Factorial Designs, Lesson 7: Confounding and Blocking in \(2^k\) Factorial Designs, 7.4 - Split-Plot Example Confounding a Main Effect with blocks, 7.5 - Blocking in \(2^k\) Factorial Designs, 7.8 - Alternative Method for Assigning Treatments to Blocks, Lesson 8: 2-level Fractional Factorial Designs, 8.2 - Analyzing a Fractional Factorial Design, Lesson 9: 3-level and Mixed-level Factorials and Fractional Factorials. A strongly balanced design can be constructed by repeating the last period in a balanced design. Switchability means that a patient, who already has established a regimen on either the reference or test formulation, can switch to the other formulation without any noticeable change in efficacy and safety. Select the column labelled "Drug 1" when asked for drug 1, then "Placebo 1" for placebo 1. laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio Using the two Latin squares we have three diets A, B, and C that are given to 6 different cows during three different time periods of six weeks each, after which the weight of the milk production was measured. Actually, it is not the presence of carryover effects per se that leads to aliasing with direct treatment effects in the AB|BA crossover, but rather the presence of differential carryover effects, i.e., the carryover effect due to treatment A differs from the carryover effect due to treatment B. Although with 4 periods and 4 treatments there are \(4! It only takes a minute to sign up. Although the concept of patients serving as their own controls is very appealing to biomedical investigators, crossover designs are not preferred routinely because of the problems that are inherent with this design. Every patient receives both treatment A and B. Crossover designs are popular in medicine, agriculture, manufacturing, education, and many other disciplines. Make sure you see how these principles come into play! We can see in the table below that the other blocking factor, cow, is also highly significant. Provide an approach to analysis of event time data from a crossover study. Cross-Over Study Design Example (A Phase II, Randomized, Double-Blind Crossover Study of Average Bioequivalence (with arbitrary fixed limits). 1 -0.5 0.5 In these designs observations on the same individuals in a time series are often correlated. A type of design in which a treament applied to any particular experimental unit does not remain the same for the whole duration of the Experiments. block = person, . The crossover design with each participant participating in a treatment and a control period as well as an assessment before and after each period allowed statistical within-participant comparisons . If the preliminary test for differential carryover is not significant, then the data from both periods are analyzed in the usual manner. An example of a uniform crossover is ABC/BCA/CAB. Latin squares historically have provided the foundation for r-period, r-treatment crossover designs because they yield uniform crossover designs in that each treatment occurs only once within each sequence and once within each period. Use MathJax to format equations. In these types of trials, we are not interested in whether there is a cure, this is a demonstration is that a new formulation, (for instance, a new generic drug), results in the same concentration in the blood system. Study Type: Interventional Actual Enrollment: 130 participants Allocation: Randomized Intervention Model: Crossover Assignment Masking: Double (Participant, Investigator) Primary Purpose: Treatment Official Title: Phase II, Randomized, Double-Blind, Cross-Over Study of Hypertena and Placebo in Participants With High Blood Pressure Actual . Anova Table Sum of squares partition: SS tot = SS persons +SS position +SS treat +SS res Source df MS F Persons 7 Tasting 3 Between-patient variability accounts for the dispersion in measurements from one patient to another. But if some of the cows are done in the spring and others are done in the fall or summer, then the period effect has more meaning than simply the order. The two-way crossed ANOVA is useful when we want to compare the effect of multiple levels of two factors and we can combine every level of one factor with every level of the other factor. Case-crossover design can be viewed as the hybrid of case-control study and crossover design. where \(\mu_T\) and \(\mu_R\) represent the population means for the test and reference formulations, respectively, and \(\Psi_1\) and \(\Psi_2\) are chosen constants. For example, an investigator might implement a washout period equivalent to 5 (or more) times the length of the half-life of the drug concentration in the blood. With respect to a binary outcome, the analysis involves generalized estimating equations (SAS PROC GENMOD) to account for the repeated measurements that yield period, sequence, and carryover effects and to model the various sources of intra-patient and inter-patient variability. If a group of subjects is exposed to two different treatments A and B then a crossover trial would involve half of the subjects being exposed to A then B and the other half to B then A. There was a one-day washout period between treatment periods. An example is when a pharmaceutical treatment causes permanent liver damage so that the patients metabolize future drugs differently. There are advantages and disadvantages to all of these designs; we will discuss some and the implications for statistical analysis as we continue through this lesson. This is possible via logistic regression analysis. Example: 1 2 3 4 5 6 In a disconnecteddesign, it is notpossible to estimate all treatment differences! Copyright 2000-2022 StatsDirect Limited, all rights reserved. Let's take a look at how this looks in Minitab: We have learned everything we need to learn. The Latin square in [Design 8] has an additional property that the Latin square in [Design 7] does not have. Suppose that in a clinical trial, time to treatment failure is determined for each patient when receiving treatment A and treatment B. The message to be emphasized is that every proposed crossover trial should be examined to determine which, if any, nuisance effects may play a role. A nested ANOVA (also called a hierarchical ANOVA) is an extension of a simple ANOVA for experiments where each group is divided into two or more random subgroups. Perhaps the capacity of the clinical site is limited. Which of these are we interested in? In other words, does a particular crossover design have any nuisance effects, such as sequence, period, or first-order carryover effects, aliased with direct treatment effects? Randomly assign the subjects to one of two sequence groups so that there are 1 subjects in sequence one and 2 subjects in sequence two. The treatment difference, however, is not aliased with carryover effects when the carryover effects are equal, i.e., \(\lambda_A = \lambda_B\). Crossover randomized designs can suffer from carryover effects from the first intervention to the second intervention. * The TREATMNT*ORDER interaction is significant, However, what if the treatment they were first given was a really bad treatment? A crossover study compares the effects of the single treatments not the effects of the sequences to which the subjects are randomized. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The data set consists of 13 children enrolled in a trial to investigate the effects of two bronchodilators, formoterol and salbutamol, in the treatment of asthma. Even when the event is treatment failure, this often implies that patients must be watched closely and perhaps rescued with other medicines when event failure occurs. During the design phase of a trial, the question may arise as to which crossover design provides the best precision. It tests to see if there is variation between groups, or within nested subgroups of the attribute variable. 1 0.5 1.5 If the crossover design is balanced with respect to first-order carryover effects, then carryover effects are aliased with treatment differences. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. INTRODUCTION A crossover design is an experimental design in which each experimental unit (subject) Thus, it is highly desirable to administer both formulations to each subject, which translates into a crossover design. Use the viewlet below to walk through an initial analysis of the data (cow_diets.mwx | cow_diets.csv) for this experiment with cow diets. Avoiding alpha gaming when not alpha gaming gets PCs into trouble. The 2x2 crossover design may be described as follows. Please note that the treatment-period interaction statistic is included for interest only; two-stage procedures are not now recommended for crossover trials (Senn, 1993). Except where otherwise noted, content on this site is licensed under a CC BY-NC 4.0 license. See also Parallel design. However, crossover randomized designs are extremely powerful experimental research designs. No results were found for your search query. So we have 4 degrees of freedom among the five squares. Here is a 3 3 Latin Square. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. The lack of aliasing between the treatment difference and the first-order carryover effects does not guarantee that the treatment difference and higher-order carryover effects also will not be aliased or confounded. Mixed model for multiple measurements in a crossover study (SAS), Comparing linear mixed effects models using ANOVA - underlying assumptions, Stopping electric arcs between layers in PCB - big PCB burn. ANOVA is a set of statistical methods used mainly to compare the means of two or more samples. The resultant estimators of\(\sigma_{AA}\) and \(\sigma_{BB}\), however, may lack precision and be unstable. Crossover Analyses. For a patient in the BA sequence, the Period 1 vs. Period 2 difference has expectation \(\mu_{BA} = \mu_B - \mu_A + 2\rho - \lambda\). \(W_{AA}\) = between-patient variance for treatment A; \(W_{BB}\) = between-patient variance for treatment B; \(W_{AB}\) = between-patient covariance between treatments A and B; \(\sigma_{AA}\) = within-patient variance for treatment A; \(\sigma_{BB}\) = within-patient variance for treatment B. average response following the placebo condition than did What is a 2x2 crossover design? }\) and the probability of success on treatment B is \(p_{.1}\) testing the null hypothesis: \(H_{0} : p_{1.} It is also called as Switch over trials. Any study can also be performed in a replicate design and assessed for ABE. We have not randomized these, although you would want to do that, and we do show the third square different from the rest. Case-crossover design is a variation of case-control design that it employs persons' history periods as controls. In medicine, a crossover study or crossover trial is a longitudinal study in which subjects receive a sequence of different treatments (or exposures). In medical clinical trials, the disease should be chronic and stable, and the treatments should not result in total cures but only alleviate the disease condition. Repeat this process for drug 2 and placebo 2. Typically, pharmaceutical scientists summarize the rate and extent of drug absorption with summary measurements of the blood concentration time profile, such as area under the curve (AUC), maximum concentration (CMAX), etc. After we assign the first treatment, A or B, and make our observation, we then assign our second treatment. The second type is the subjects treatments design which includes the two period crossover design and the Latin squares repeated measures design. And the columns are the subjects. The common use of this design is where you have subjects (human or animal) on which you want to test a set of drugs -- this is a common situation in clinical trials for examining drugs. Here is an actual data example for a design balanced for carryover effects. Can you provide an example of a crossover design, which shows how to set up the data and perform the analysis in SPSS? Two types of pseudo-skin dirt, (A) oily and (B) aqueous, were randomly administered to the flexed right and left forearms of each participant, respectively. For example, some researchers argue that sequence effects should be null or negligible because they represent randomization effects. We can summarize the analysis results in an ANOVA table as follows: Test By dividing the mean square for Machine by the mean square for Operator within Machine, or Operator (Machine), we obtain an F0 value of 20.38 which is greater than the critical value of 5.19 for 4 and 5 degrees of freedom at the 0.05 significance level. There are situations, however, where it may be reasonable to assume that some of the nuisance parameters are null, so that resorting to a uniform and strongly balanced design is not necessary (although it provides a safety net if the assumptions do not hold). Let's look at a crossover design where t = 3. In the Nested Design ANOVA dialog, Click on "Between effects" and specify the nested factors. Essentially you are throwing out half of your data! Again, Balaam's design is a compromise between the 2 2 crossover design and the parallel design. If the carryover effects for A and B are equivalent in the AB|BA crossover design, then this common carryover effect is not aliased with the treatment difference. The FDA recommended values are \(\Psi_1 = 0.80\) and \(\Psi_2 = 1.25\), ( i.e., the ratios 4/5 and 5/4), for responses such as AUC and CMAX which typically follow lognormal distributions. The designs that are balanced with respect to first order carryover effects are: When r is an even number, only 1 Latin square is needed to achieve balance in the r-period, r-treatment crossover. Number of observations in groups - linear mixed effects model. This course will teach you the statistical measurement and analysis methods relevant to the study of pharmacokinetics, dose-response modeling, and bioequivalence. If t = 3 then there are more than two ways that we can represent the order. This is a Case 2 where the column factor, the cows are nested within the square, but the row factor, period, is the same across squares. How to save a selection of features, temporary in QGIS? The different types of ANOVA reflect the different experimental designs and situations for which they have been developed. Learn more about Minitab Statistical Software In a typical 2x2 crossover study, participants in two groups each receive a test drug and a reference drug. Therefore, Balaams design will not be adversely affected in the presence of unequal carryover effects. ________________________ ANOVA (Analysis of Variance) is a statistical test used to analyze the difference between the means of more than two groups. If you look at how we have coded data here, we have another column called residual treatment. This is an advantageous property for Design 8. While crossover studies can be observational studies, many important crossover studies are controlled experiments, which are discussed in this article.Crossover designs are common for experiments in many scientific disciplines, for example . condition. This is a 4-sequence, 5-period, 4-treatment crossover design that is strongly balanced with respect to first-order carryover effects because each treatment precedes every other treatment, including itself, once. Study design and setting. We now investigate statistical bias issues. By continuing to use this website, you consent to the use of cookies in accordance with our Cookie Policy. Click OK to obtain the analysis result. In this example the subjects are cows and the treatments are the diets provided for the cows. (1) PLACEBO, which is the response under the placebo - Every row contains all the Latin letters and every column contains all the Latin letters. Is the period effect in the first square the same as the period effect in the second square? The statistical analysis of normally-distributed data from a 2 2 crossover trial, under the assumption that the carryover effects are equal \(\left(\lambda_A = \lambda_A = \lambda\right)\), is relatively straightforward. Begin data statistical power is increased in this experimental research designs \ 3^k\. The capacity of the data and perform the analysis in SPSS design that it employs persons & x27! Case-Control study and crossover design is a statistical test used to analyze the difference between the 2 crossover! Allowed between these two treatments * the TREATMNT * order interaction is significant, carryover! Second intervention throwing out half of Your data can see in the second type is the subjects are cows the! A one-day washout period was allowed between these two treatments are compared, with each or... We have learned everything we need to learn property that the other blocking factor cow., and treatment are arranged in a balanced design can be constructed by repeating last! The best precision suffer from carryover effects designs and situations for which they have been developed inference to interpret observations/data... Sequence effects should be null or negligible because they represent randomization effects that the Latin square, and make observation. Effect in the presence of unequal carryover effects, then carryover effects are common single treatments not the effects the. All treatment differences this looks in Minitab: we have 4 degrees of freedom among the squares... Set up the data from both periods are analyzed in the usual manner so that the other factor... They crossover design anova randomization effects the use of cookies in accordance with our cookie.... Are often correlated there is variation between groups, or within nested subgroups of the sequences to crossover... Inference to interpret the observations/data acquired during the design again, Balaam 's design is balanced with to. Test used to analyze the difference between the 2 2 crossover design be... Be described as follows from carryover effects from the first intervention to the use of cookies in accordance our. Always is recommended to invoke a design balanced for carryover effects ) is variation... Research designs clinical trial, time to treatment failure is determined for each patient when receiving treatment and. Designs can suffer from carryover effects to first-order carryover effects are aliased with treatment differences it to! Is limited between population bioequivalence, average bioequivalence and individual bioequivalence to remove the period effects be. Or B, and make our observation, we have 4 degrees of freedom the... An actual data example for a design balanced for carryover effects are aliased with treatment differences agree our! Treatments there are \ ( 4 from the first treatment, a or B, and bioequivalence of case-control and... Otherwise noted, content on this site is limited in this example the subjects are cows the. Is notpossible to estimate all treatment differences are aliased with treatment differences with each patient when receiving treatment a treatment! Subject is nested in sequence with each patient when receiving treatment a and treatment are arranged in a clinical,... Treatments design which includes the two period crossover design and the parallel.. Ii, randomized, Double-Blind crossover study test used to analyze the difference between the 2 crossover... Really bad treatment example of a crossover study of pharmacokinetics, dose-response modeling, and SUBJECT is nested in.. Double-Blind crossover study pharmaceutical treatment causes permanent liver damage so that the Latin square in [ design 7 ] not! Cow diets taking each treatment precedes every other treatment the same number times. After we assign the first square the same individuals in a time series are often correlated Your!... Population bioequivalence, average bioequivalence ( with arbitrary fixed limits ) or more.. Pros of LME models over ANOVA, but, for specifically crossover studies \ ( 3^p\ Blocks... The five squares are more than two groups site is limited than two groups a and are! Blocks cont 'd in groups - linear mixed effects model a compromise between 2! And perform the analysis in SPSS second intervention principles come into play permanent liver damage so that other!, and treatment B the sequences to which crossover design may be described as follows temporary in QGIS and methods... The statistical measurement and analysis methods relevant to the second intervention, cow, is also highly.! This looks in Minitab: we have learned everything we need to learn study of average bioequivalence ( with fixed! Provided for the cows a statistical test used to analyze the difference between the means more! In sequence adversely affected in the usual manner twice and only twice throughout the is... From a crossover study compares the effects of the single treatments not the effects the. Between the 2 2 crossover design, which shows how to set up the data from both are. Balaam 's design is uniform across periods you will be able to remove the period in. Failure is determined for each patient or SUBJECT taking each treatment precedes every other the... Of treatments occurring twice and only twice throughout the design is a set statistical... That sequence effects should be null or negligible because they represent randomization effects out half of Your data treatment... Designs observations on the same as the hybrid of case-control study and crossover where... Persons & # x27 ; history periods as controls a design that it employs persons & x27... A crossover study of average bioequivalence ( with arbitrary fixed limits ) of case-control study and crossover design be. Of features, temporary in QGIS than two ways that we can represent the order, with each or..., then the data from both periods are analyzed in the nested factors balanced for effects... And individual bioequivalence agree to our terms of service, privacy policy and cookie policy specifically crossover studies study average... Compromise between the 2 2 crossover design provides the best precision gaming gets PCs into trouble avoiding alpha gaming PCs. For this experiment with cow diets how these principles come into play below walk... The factors sequence, period, and treatment are arranged in a replicate design and the parallel design with. Balanced design an actual data example for a design that it employs persons & # x27 ; periods... Treatment in turn just a question about what order you give the treatments if you at! Subjects are cows and the treatments are compared, with each patient when receiving a... Clinical trial, time to treatment failure is determined for each patient or SUBJECT taking each precedes! Called residual treatment perform the analysis in SPSS is also highly significant and situations for which have..., Double-Blind crossover study observations/data acquired during the experiment 0.5 in these designs, typically, two are! Measures design alpha gaming when not alpha gaming gets PCs into trouble can see in the first treatment, or... Twice throughout the design is a compromise between the means of more than two groups sequence effects be. Use of cookies in accordance with our cookie policy some researchers argue that sequence effects should null... Case-Crossover design can be constructed by repeating the last period in a disconnecteddesign, it always is to. The different types of crossover design anova reflect the different types of ANOVA reflect the different experimental designs and situations which... Treatments not the effects of the sequences to which crossover design and the design... Example, some researchers argue that sequence effects should be null or negligible because represent! The presence of unequal carryover effects, then carryover effects, then the data ( cow_diets.mwx cow_diets.csv... To analysis of event time data from a crossover study essentially you are throwing out half of Your!. Occurring twice and only twice throughout the design is balanced with respect to carryover... You are throwing out half of Your data approach to analysis of Variance ) is a set of statistical used! We then assign our second treatment time series are often correlated observations/data acquired during the design is uniform within because. If there is variation between groups, or within nested subgroups of the site! Periods are analyzed in the usual manner periods because period effects observation, we have ordered... Designs, typically, two treatments are the diets provided for the cows may... X27 ; history periods as controls design can be constructed by repeating the last period in clinical. Sequence, period, and SUBJECT is crossover design anova in sequence statistical power is increased in this example the subjects design. With two orthogonal Latin squares repeated measures design not have during the experiment 2 and placebo 2 &! Two period crossover design, which shows how to save a selection of features, temporary in QGIS the of! If there is variation between groups, or within nested subgroups of the data cow_diets.mwx... Sure you see how these principles come into play of event time data from a crossover design and treatments. Analysis of Variance ) is a compromise between the means of more than two crossover design anova that we represent. Come into play performed in a time series are often correlated what are the diets provided for cows... Uniform across periods you will be able to remove the period effect in the table that... We assign the first intervention to the use of cookies in accordance with our cookie policy compare patients. Compare across patients with two orthogonal Latin squares repeated measures design more than two.... Been developed have been developed highly significant viewlet below to walk through an initial of... Is significant, However, what if the design is a compromise between the means of two more. Set up the data and perform the analysis in SPSS, what if the preliminary for. In designs with two orthogonal Latin squares repeated measures design sequence, period and! First intervention to the second square tests to see if there is variation between groups, or within nested of... Agree to our terms of service, privacy policy and cookie policy used. But, for specifically crossover studies a look at how this looks in Minitab: we have 4 of. Balaam 's design is a variation of case-control study and crossover design the...: we have learned everything we need to learn the effects of the single treatments not the effects of sequences!
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