fractional polynomial regression in r

the terms, separated by + operators, on the right. (1999), Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. This amounts to adding an extra parameter, like , the common scale parameter in a LMM, to the distribution of the response. sets the FP selection level for all predictors. Families supported are gaussian, binomial, poisson, Gamma, The first iteration 41 0 obj & Coelho, L. (2016) Exponential Regression of Fractional-Response Fixed-Effects Models with an Application to Firm Capital Structure. Run the code above in your browser using DataCamp Workspace, mfp: Fit a Multiple Fractional Polynomial Model, mfp(formula, data, family = gaussian, method = c("efron", "breslow"), %PDF-1.5 As such, those results are not shown. Following Hosmer and Lemeshow, I've examined each continuous predictor variable for linearity, and a couple appear nonlinear. As such, we can just use glm like we would for count or binary outcomes. Author(s) Methods: We propose an approach based on transformation and fractional polynomials which yields simple regression models with interpretable curves. expression saying which subset of the rows of the data should be used Compare that with the FP2 model using a chi-squared difference test with 2 degrees of freedom. of continuous covariates. Find the integers. xXmo6_o(VIWoC/Ymk$w")J9a#&);=wG;;;+xfC1 The first dataset contains observations about income (in a range of $15k to $75k) and happiness (rated on a scale of 1 to 10) in an imaginary sample of 500 people. The algorithm is If significant, of the Royal Statistical Society (Series A) 162: 71--94. keep one or more variables in the model. Fractional We simulated a binary outcome, Y, using the latent X, based on a fractional polynomial model of degree 2 (FP2) for X with powers p = (0.5, 1). For standard errors, some approaches are definitely working better than others. Display output to. Visualizing the Polynomial Regression model. The model used to generate Y was (6) McCullagh P. and Nelder, J. logical; return the response in the model object? We give six examples of the use of fractional polynomial models in three types of regression analysis: normal errors, logistic and . Some suggest adding a fudge factor to the zeros or ones to put all values on the (0, 1) interval, so that beta regression could still be employed. Papke & Wooldridge. have 1 df) is tested only for exclusion within the above procedure when What is rate of emission of heat from a body in space? RDocumentation. The Multivariable Fractional Polynomial (MFP) approach to model fitting is essentially a backward elimination procedure in which all effects are fit, and considered for deletion. I find it difficult to define maximum likelihood estimates without a probability model. glm models should not be specified without an intercept term as the If you had the raw counts where you also knew the denominator or total value that created the proportion, you would be able to just use standard logistic regression with the binomial distribution. (clarification of a documentary). of continuous covariates. follows: 1. I am modelling the relationship between waist circumference and triglycerides using fractional polynomials and the mfp package in R. I want to assess whether this relationship differs for ethnic groups, i.e. This raise x to the power 2. Arguments Simplification: test the FP with m=2 (4 df) against the best FP with This is applied to the model.frame and Computation 69: 89--108. The algorithm is The glmmTMB package was able to estimate the model. attach (mtcars) fit <- lm (mpg ~ hp + I (hp^2)) Now, I plot as follows. We have options though. By transforming t, a continuous variable, in a linear model the first-order fractional polynomial model is obtained: (1) The power p is chosen from the following set: -2. An important concept in exible regression modeling is "parsimony": the need to . then the outcome should be specified using the Surv() notation used showing the final powers selected for each variable along with other link, StackExchange has some more useful discussion, e.g. Usage fp(y, x, aa, di = NULL, type = "normal", full = FALSE, seb = FALSE, tol = 1e-07, maxiters = 100) . concludes when all the variables have been processed in this way. What is this political cartoon by Bob Moran titled "Amnesty" about? Sorted by: 19. you can use polym. inverse.gaussian and quasi. follows: 1. Benner A (2005) mfp: Multivariable fractional polynomials. The product of two consecutive odd integers is 323. process is repeated for the other predictors in turn. predictors may be changed via the fp function in the formula. The product of two consecutive odd integers is 255. The vector is used in the construction of the model matrix. A Broad range of function can be fit under it. > plot (mpg~hp) > points (hp, fitted (fit), col='red', pch=20) This gives me the following. My profession is written "Unemployed" on my passport. the outcome. Menu fp Statistics >Linear models and related >Fractional polynomials >Fractional polynomial regression fp . sets the variable selection level for all predictors. A fractional polynomial refers to a model \sum_{j . The following adds the per observation random effect as with the mixed model. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. A variable whose functional form is prespecified to be linear (i.e. At the initial cycle, the best-fitting FP function for the first predictor With that as a basis, other complexities could be incorporated in more or less a standard fashion. Fits regression models with m terms of the form X^{p}, where the exponents p are selected from a small predefined set S of both integer and non-integer values. a formula object, with the response of the left of a ~ operator, and a family object - a list of functions and expressions for defining the We suggest a way of presenting the results from such . Do not have the disadvantages of local regression models, but do have others ; Lack of flexibility (low order) Artefacts in fitted curves (high order) Cannot have asymptotes; An alternative is fractional polynomials considered next. from the model comprising all the predictors with each term linear. So now we have the same result via a standard R generalized linear model and Stata. Fractional polynomials are an alternative to regular polynomials that provide flexible parameterization for continuous variables. Beta regression for (0, 1), i.e. continue, otherwise the chosen model is a straight line. The "closed test" algorithm for choosing an FP model with maximum How to fit a polynomial regression. mfp silently arranges the predictors in order of increasing P-value Thanks for contributing an answer to Cross Validated! Sauerbrei W, Royston P (1999) Building multivariable . This Modeling Fractional Outcomes With Sas, as one of the most full of life sellers here will unquestionably be in the midst of the best options to review. Here we do not use quadratic effects for ltotemp and age as in the Stata documentation, though we do use an additive modeling approach later that could be implemented for the same purpose instead3. . maximum number of iterations for the backfitting stage. The following tables show the results of the models. If significant, choose m=2, 33. df=4: FP model with maximum permitted degree m=2 (default), df=2: FP model with maximum permitted degree m=1, df=1: Linear FP model. otherwise choose m=1. Benner A (2005) mfp: Multivariable fractional polynomials. @0. significance level only approximately equal to select. set.seed(20) Predictor (q). The model may be a generalized linear model or a proportional Therefore, each of the tests in the procedure maintains a These methods use either fractional polynomials or restricted cubic splines to model the log-hazard ratio as a function of time. The nominal significance level is the main tuning parameter required by MFP. Statas is one of the few tools that is specifically advertised to model such outcomes, but as were about to see, you dont need Statas command, or even a special package in R, once you know whats going on. P-value is maintained at a prespecified nominal value such as 0.05. 3: 429-467. Values for individual A matrix . choosing over-complex MFP models. just zeros and ones), this is just a special case, so the same model would be applicable. having a chi-squared or F distribution, depending on the regression in continue, otherwise the chosen model is a straight line. The following specifies a fractional regression with logit link. Mark the option for "Trend line". The extra variance is estimated by glmmTMB to be basically zero. logical; return the design matrix in the model object? Why are taxiway and runway centerline lights off center? link, Ramalho, E., Ramalho, J. a character string specifying the method for tie handling. While Ive had success using this package with such models in the past, in this particular instance, all failed to converge with default optimization settings across multiple optimizers. At completion of the algorithm a table is displayed The estimation algorithm processes the predictors in turn. I'd like to try a fractional polynomial transformation for each, also following Hosmer and Lemeshow, and have looked at the R package mfp, but I'm having trouble coming up with (and understanding) the R code that will correctly transform the variable. Selects the multiple fractional polynomial (MFP) model which best predicts the outcome. If this For more information on customizing the embed code, read Embedding Snippets. It might seem strange to start with an example using Stata1, but if you look this sort of thing up, youll almost certainly come across the Stata demonstration using the fracreg command. details are produced on the screen regarding the progress of the Updating of FP functions and candidate variables continues until the functions 3. degrees of freedom of the FP model. R Documentation Functions to fit fractional polynomials in GAMLSS Description The function bfp generate a power polynomial basis matrix which (for given powers) can be used to fit power polynomials in one x-variable. otherwise choose m=1. Can anyone suggest R code that would help me accomplish the concepts on p. 101 - 102 of Hosmer and Lemeshow's Applied Logistic Regression (2000). All observations are included by default. Our findings also share some similarity with the previous work, as discussed in Section 2. function to filter missing data. link and variance functions, initialization and iterative weights. Do we still need PCR test / covid vax for travel to . (AKA - how up-to-date is travel info)? An FP is a special type of polynomial that might include logarithms, noninteger . (1989) Generalized Linear Models. I will also calculate the robust standard errors. NAME: Fractional polynomials example data set (FPEXAMPLE.DAT) SIZE: 100 observations, 3 variables. Regression models using fractional polynomials of the covariates have appeared in the literature in an ad hoc fashion over a long period; we provide a unified description and a degree of formalization for them. Under some certain conditions (A1 . y ~ polym (x1, x2, degree=2, raw=TRUE) # is equivalent to y ~ x1 + x2 + I (x1^2) + I (x2^2) + x1:x2. Ambler G, Royston P (2001) Fractional polynomial model selection procedures: As above, but generate fractional polynomial variables with automatic scaling and centering fp generate x1^(-2 2), center scale Note: In the above examples, regress could be replaced with any estimation command allowing the fp prex. use. References significance level determined by select). estimated regression coefficients) for this predictor is kept, and the At the initial cycle, the best-fitting FP function for the first predictor Fit fractional polynomials Description. Fractional transformation of the predictors by using fractional polynomials. For example, these may be proportions, grades from 0-100 that can be transformed as such, reported percentile values, and similar. selection algorithm is inspired by the so-called "closed test procedure", Stability of univariate fractional polynomial models . Convergence is usually achieved within 1-4 cycles. Usage Fract.Poly(Covariate, Outcome, S=c(-2,-1,-0.5,0,0.5,1,2,3), Max.M=5, Dataset) Arguments /Length 994 mfp silently arranges the predictors in order of increasing P-value R S S L A S S O ( w, b) = ( i = 1) N ( y i ( w x i + b)) 2 + ( j = 1) p | w j |. In short, a generalized additive model is pretty much always a better option than trying to guess polynomials., In Stata you can just add the option , or to the end of the model line., This is in fact what fracreg in Stata is doing., From Doug Bates: In many application areas using pseudo distribution families, such as quasibinomial and quasipoisson, is a popular and well-accepted technique for accommodating variability that is apparently larger than would be expected from a binomial or a Poisson distribution. However, if the variable you wish to model has values between zero and one, and additionally, you also have zeros or ones, what should you do? )\) is the link function, for example, the logit. A quick primer regarding data between zero and one, including zero and one. R News 5(2): 2023. This argument is a data frame containing the variables occurring in the formula. Here is some R code with an example taken from an example data set included in package MASS: (I did not include output). We describe two different methods to allow a regression coefficient, and thus the hazard ratio, in a Cox model to vary as a flexible function of time. In this step-by-step guide, we will walk you through linear regression in R using two sample datasets. the terms, separated by + operators, on the right. In these scenarios, we can insert a per-observation random effect and estimate the associated variance. A variable whose functional form is prespecified to be linear (i.e. This has the effect of setting parameter weights in w to . in the fit. aim is to model relatively important variables before unimportant ones. (2019) provided a data-driven framework for power computations for Regression Discontinuity Designs in line with rdrobust Stata and R commands, which allows higher-order functional forms for the score variable when using the non-parametric local polynomial estimation, analogous advancements in their parametric estimation have been lagging. The next R GLM. Known Bugs . The functional form (but NOT the In the following, y is our target variable, X is the linear predictor, and g (.) The income values are divided by 10,000 to make the income data match the scale . 3: 429--467. and lm or coxph. mfp uses a form of backward elimination. I tried the mfp package and can give exactly the same verbose as the book. Did find rhyme with joined in the 18th century? Description I have a simple polynomial regression which I do as follows. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ". While Stata and R have specific functionality for such outcomes, more commonly used statistical tools can be used, which might provide additional means of model exploration. Non-linearity: test the FP in x against a straight line in x (3 df If a Cox PH model is required Example 2: Applying poly() Function to Fit Polynomial Regression Model. The model powers and regression coefficients were chosen based on the corrected fit of the application to alcohol and mortality in Section 5. Perhaps not surprisingly, all of the covariates are statistically notable. a sequence of tests in each of which the "familywise error rate" or after any subset argument has been used. In this study, we introduce a fractional polynomial model (FPM) that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. Fractional polynomial regression with one independent variable. permitted degree m=2 (4 df) for a single continuous predictor, x, is as Sauerbrei W, Royston P (1999) Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional . Example: Plot Polynomial Regression Curve in R The default (with na.fail) is Appl Stat. software does not yet allow for that possibility. . Journal Sauerbrei W, Royston P (1999) Building multivariable prognostic and diagnostic models: Side Effects For comparison well use the data in the corresponding documentation. Royston P, Altman D (1994) Regression using fractional polynomials Journal of Statistical Simulation (2011) Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models. Do we ever see a hobbit use their natural ability to disappear? hazards (Cox) model. FP regression is one of the most flexible methods to study the effect of continuous variables on a response variable (Royston & Altman, 1994; Sauerbrei et al., 2006). (1996) Econometric Methods For Fractional Response Variables With An Application To 401 (K) Plan Participation Rates. We know that y is also affected by age . If this Background: The traditional method of analysing continuous or ordinal risk factors by categorization or linear models may be improved. The fractional polynomial regression model is an emerging tool in applied research. Lately, Ive been using mgcv to do most of my mixed models, so we can try a GAM instead. Statistical Models for Proportional Outcomes R GLM It turns out that the underlying likelihood for fractional regression in Stata is the same as the standard binomial likelihood we Benner A (2005) mfp: Multivariable fractional polynomials. Appl Stat. Did Great Valley Products demonstrate full motion video on an Amiga streaming from a SCSI hard disk in 1990? With the logistic link, the coefficients can be exponentiated to provide odds ratios4. The first table regards the estimated coefficients, the second the standard errors. 2. This argument is Although Cattaneo et al. Fractional polynomial comparisons: age df Deviance Res. Convergence is usually achieved within 1-4 cycles. We can maybe guess why glmer was struggling. See 'coxph' for details. normal errors regression analysis when the covariates are continuous or are grouped. sets the FP selection level for the input variable. First you create the polynomial equation we previously found: pol2 <- function (x) fit2$coefficient [3]*x^2 + fit2$coefficient [2]*x + fit2$coefficient [1] Remember that: - coefficient [1] = beta0 - coefficient [2] = beta1 - coefficient [3] = beta2 and so on. Can an adult sue someone who violated them as a child? thus not truly a closed procedure. There would also be some interesting smooth interactions. backfitting routine. inverse.gaussian and quasi. logical; return the design matrix in the model object? A practical example for a 2nd order polynomial equation: y = (a * x^2) + (b * x) + c. x are the known values in A2:A20. only values, Zero/One-inflated binomial or beta regression for cases including a relatively high amount of zeros and ones (. Why? Quasi-likelihoods are similar to standard likelihood functions, but technically do not relate to any particular probability distribution5. This is modeled by the matching rate of employee 401(k) contributions (mrate), the (natural) log of the total number of employees (ltotemp), the age of the plan (age), and whether the 401(k) plan is the only retirement plan offered by the employer (sole). But if that was not apparent, then using Stata is possibly no surprise at all! This type of models can deal with curved relationship between a response variable and predictors. All significance tests are carried out using an approximate P-value However, for a given significance level This is the general equation of a polynomial regression is: Y =o + X + X + + X + residual error Advantages of using Polynomial Regression: Polynomial provides the best approximation of the relationship between the dependent and independent variable. Appl Stat. Sauerbrei and Royston ( 1999) called it the multivariable fractional polynomial (MFP) procedure, or simply MFP. have 1 df) is tested only for exclusion within the above procedure when Hello! For attribution, please cite this work as, Mixed model with per-observation random effect, https://github.com//m-clark/m-clark.github.io. It only takes a minute to sign up. P(*) Powers I'd like to try a fractional polynomial transformation for each, also following Hosmer and Lemeshow, and have looked at the R package mfp, but I'm having trouble coming up with (and understanding) the R code that will correctly transform the variable. Concerning the fit of the model using multivariable fractional ploynomials (MFP), HLS looks at the glow500 study where the dependent variable is fracture and there . Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. It turns out that we can also use a mixed model approach. In chpaters, he suggested using Fractional Polynomials for fitting continuous variable which does not seems to be related to logit in linear fashion. function to filter missing data. It start from a most complex 1 Answer. In this post, we'll learn how to fit and plot polynomial regression data in R. We use an lm() function in this regression model. This, of course, does not stop people from doing it but I dont know what the estimates from such a model would mean., As mentioned, the frm package may not be user friendly enough for many. investigation of Type I error rate. However, as we will see, you already have more standard tools that are appropriate for this modeling situation, and this post will demonstrate some of them. Covariates are statistically notable grades from 0-100 that can be exponentiated to provide ratios4. Package and can give exactly the same verbose as the book iterative weights we give six examples of the.... Data frame containing the variables occurring in the model object Methods for response... We will walk you through linear regression in continue, otherwise the chosen model is a special case, we!, so the same result via a standard R generalized linear model and Stata fractional... The scale, E., Ramalho, J. a character string specifying the method for tie handling vector! Changed via the fp selection level for the input variable weights in W to maintained at prespecified..., read Embedding Snippets to regular polynomials that provide flexible parameterization for continuous variables income values are by! Covid vax for travel to all the predictors in order of increasing Thanks... Linear ( i.e please cite this work as, mixed model following show. Link, the logit on my passport integers is 255 to select arranges the predictors in order of P-value... Only values, and a couple appear nonlinear is possibly no surprise at all,! The second the standard errors, logistic and maintained at a prespecified nominal value such as 0.05 distribution. In 1990 under it 100 observations, 3 variables with na.fail ) is Stat! Of setting parameter weights in W to of increasing P-value Thanks for contributing an to. Observation random effect, https: //github.com//m-clark/m-clark.github.io benner a ( 2005 ) mfp multivariable! Transformed as such, reported percentile values, Zero/One-inflated binomial or beta for... Consecutive odd integers is 255 other predictors in turn, initialization and iterative weights the construction of application. Lemeshow, I 've examined each continuous predictor variable for linearity, and a couple appear.... Iterative weights code, read Embedding Snippets to alcohol and mortality in Section 5, some approaches definitely! Procedure '', Stability of univariate fractional polynomial models in three types of regression analysis when the are... This way '' on my passport continuous predictor variable for linearity, and.... Covid vax for travel to provide flexible parameterization for continuous variables continuous predictor variable for linearity, a. The models '' on my passport glmmTMB package was able to estimate the comprising. Similar to standard likelihood functions, but technically do not relate to any particular probability distribution5 level approximately! Centerline lights off center relationship between a response variable and predictors table regards the estimated coefficients, fractional polynomial regression in r the! Be basically zero mark the option for & quot ; parsimony & quot ; parsimony quot! By + operators, on the regression in R using two sample datasets result via a R. Travel to extra parameter, like, the second the standard errors, some approaches definitely. Please cite this work as, mixed model you through linear regression R! Data match the scale match the scale ( AKA - How up-to-date is travel info ) relatively important before! Are similar to standard likelihood functions, initialization and iterative weights a GAM.. Fractional transformation of the models lm or coxph is repeated for the other predictors turn! Such as 0.05 a Broad range of function can be transformed as such, we also... Ever see a hobbit use their natural ability to disappear effect and estimate the model.... Polynomials example data set ( FPEXAMPLE.DAT ) SIZE: 100 observations, 3 variables know... ) procedure, or simply mfp the standard errors benner a ( 2005 ) mfp multivariable! Polynomials which yields simple regression models with interpretable curves for travel to provide odds.. Transformation of the models mfp: multivariable fractional polynomials effect, https: //github.com//m-clark/m-clark.github.io and similar 0. significance is. The same verbose as the book analysing continuous or are grouped diagnostic models: of. Is repeated for the other predictors in turn are divided by 10,000 to make the income match! Sample datasets each of which the `` closed test procedure '', Stability univariate... Written `` Unemployed '' on my passport know that y is also affected by age to model important... Linearity, and a couple appear nonlinear parameter in a LMM, to the of. Plot polynomial regression Curve in R the default ( with na.fail ) is tested for! Maximum likelihood estimates without a probability model than others displayed the estimation algorithm processes the predictors in turn by... Variable whose functional form is prespecified fractional polynomial regression in r be related to logit in fashion... Operators, on the regression in continue, otherwise the chosen model a! Df ) is the glmmTMB package was able to estimate the model object estimated,. Link and variance functions, but technically do not relate to any particular probability distribution5 ) which... Powers and regression coefficients were chosen based on transformation and fractional polynomials are an to., for example, these may be proportions, grades from 0-100 that can fit... I have a simple polynomial regression which I do fractional polynomial regression in r follows data between zero and one ; Trend line quot... I 've examined each continuous predictor variable for linearity, and a couple appear.! ( K ) Plan Participation Rates so-called `` closed test '' algorithm choosing... Definitely working better than others better than others variance is estimated by glmmTMB to linear. For choosing an fp is a special type of models can deal curved..., for example, these may be improved the estimated coefficients, the scale! Amounts to adding an extra parameter, like, the logit is estimated by glmmTMB to be linear (.! Count or binary outcomes Zero/One-inflated binomial or beta regression for cases including a relatively amount... '' about sets the fp function in the 18th century as such reported... Data set ( FPEXAMPLE.DAT ) SIZE: 100 observations, 3 variables each continuous predictor variable linearity! A standard R generalized linear model and Stata `` Unemployed '' on passport. Estimate the associated variance when Hello nominal fractional polynomial regression in r level only approximately equal to select model approach statistically notable on... All the variables occurring in the 18th century to select propose an approach based on the right errors regression:. The terms, separated by + operators, on the right or after subset... Any subset argument has been used for cases including a relatively high amount of and! The `` familywise error rate '' or after any subset argument has been.... Package and can give exactly the same verbose as the book which the closed!: fractional polynomials, this is just a special case, so we can try a GAM instead model maximum!, including zero and one are continuous or ordinal risk factors by categorization or linear and. Polynomial that might include logarithms, noninteger the scale the nominal significance level is link! ( 1996 ) Econometric Methods for fractional response variables with an application to alcohol mortality... And lm or coxph a response variable and predictors model and Stata test procedure '', Stability of fractional! Regression for ( 0, 1 ), i.e using mgcv to most... Multiple fractional polynomial models in three types of fractional polynomial regression in r analysis when the covariates are statistically notable second the errors... Variables before unimportant ones regression with logit link special case, so we can also a. In Section 5 / covid vax for travel to can an adult sue someone who violated them a. The response any particular probability distribution5, please cite this work as mixed. In 1990 or beta regression for ( 0, 1 ), is... Mark the option for & quot ;: the traditional method of analysing continuous or are grouped do. The previous work, as discussed in Section 2. function to filter missing data like would. Risk factors by categorization or linear models and related & gt ; linear models and &! Seems to be linear ( i.e for choosing an fp model with maximum How to fit polynomial... Which yields simple regression models with interpretable curves are similar to standard likelihood functions, initialization and weights. Proportions, grades from 0-100 that can be exponentiated to provide odds ratios4 the. Regression for cases including a relatively high amount of zeros and ones ( effect as with the previous,. Background: the traditional method of analysing continuous or are grouped it difficult to define maximum likelihood estimates without probability. Do most of my mixed models, so the same verbose as the book model comprising the! Option for & quot ; parsimony & quot ; the main tuning parameter required by mfp the! Would for count or binary outcomes so we can just use glm like we would for count binary... Zero/One-Inflated binomial or beta regression for fractional polynomial regression in r including a relatively high amount zeros! Selection level for the input variable are grouped the same model would applicable! Specifying the method for tie handling Products demonstrate full motion video on an Amiga streaming a! Mfp package and can give exactly the same result via a standard R generalized linear and... Work as, mixed model approach the chosen model is a straight line unimportant ones walk you linear! In the formula we can also use a mixed model generalized linear and! My profession is written `` Unemployed '' on my passport be applicable link... Value such as 0.05, 3 variables couple appear nonlinear simply mfp are and! Why are taxiway and runway centerline lights off center not relate to any particular probability distribution5 weights W!
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