Solution Anti-fungal treatment (R software)

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1 Contents Solution Anti-fungal treatment (R software) Question 1: Data import 2 Question 2: Compliance with the timetable 4 Question 3: population average model 5 Question 4: continuous time model 9 Question 5: conditional odds ratios 11 Question 6: glmer model 12 Question 7: with a random slope 14 Appendix A: Graphical display 16 Question

2 First, load the necessary packages library(lme4) library(geepack) library(doby) # esticon library(lattice) Question 1: Data import df.onych <- read.table(" + header = TRUE, na.strings = ".") Re-order the levels of the qualitative variables: names(df.onych) <- gsub(pattern = "response", replacement = "response.", + x = names(df.onych), fixed = TRUE) names(df.onych) <- gsub(pattern = "time", replacement = "time.", + x = names(df.onych), fixed = TRUE) df.onych$treatment <- factor(df.onych$treatment, levels = 0:1, + labels = c("200mg", "250mg")) df.onych$id <- factor(df.onych$id) Reshape the dataset: varying_columns <- c(paste0("response.",1:7), paste0("time.",1:7)) dfl.onych <- reshape(df.onych, + varying = which(names(df.onych) %in% varying_columns), + sep = ".", idvar = c(" id"), v.names = c("symptoms","time"), + direction = "long", timevar = "visitnb") dfl.onych$visitnb.factor <- factor(dfl.onych$visitnb, + levels = 1:7, labels = paste0("visit",1:7)) dfl.onych$timeweeks.planned <- factor(dfl.onych$visitnb, + levels = 1:7, + labels = c(0,4,8,12,24,36,48)) dfl.onych$timeweeks.planned <- as.numeric(as.character(dfl.onych$timeweeks.planned)) dfl.onych$timeweeks <- dfl.onych$time*52/12 2

3 Compute the prevalence: aggregate(symptoms ~ visitnb + treatment, + data = dfl.onych, + FUN = function(x){ + c(n = length(x), sum = sum(x), mean = mean(x), variance = var(x)) + } + ) visitnb treatment symptoms.n symptoms.sum symptoms.mean symptoms.variance mg mg mg mg mg mg mg mg mg mg mg mg mg mg

4 Question 2: Compliance with the timetable aggregate(timeweeks ~ timeweeks.planned + treatment, + data = dfl.onych, + FUN = function(x){ + c(median = median(x), min = min(x), max = max(x)) + } + ) timeweeks.planned treatment timeweeks.median timeweeks.min timeweeks.max mg mg mg mg mg mg mg mg mg mg mg mg mg mg # see appendix A for a graphical display 4

5 Question 3: population average model Baseline adjustement: dfl.onych$treatment_adj <- dfl.onych$treatment dfl.onych$treatment_adj[dfl.onych$visitnb.factor=="visit1"] <- "200mg" dfl.onych$treatadj_x_visit <- paste(dfl.onych$visitnb.factor, + dfl.onych$treatment_adj, sep =" ") table(dfl.onych$visitnb.factor,dfl.onych$treatment_adj) 200mg 250mg visit visit visit visit visit visit visit #### NOTE: remember to reorder by id otherwise gee do not fit correctly dfl.onych <- dfl.onych[order(dfl.onych$id),] Estimate the model gee.binun <- geeglm(symptoms ~ treatadj_x_visit -1, + id = id, data = dfl.onych, + family = binomial(link = "logit"), corstr = "unstructured") summary(gee.binun)$coefficient Estimate Std.err Wald Pr( W ) treatadj_x_visitvisit1 200mg e-06 treatadj_x_visitvisit2 200mg e-06 treatadj_x_visitvisit2 250mg e-07 treatadj_x_visitvisit3 200mg e-07 treatadj_x_visitvisit3 250mg e-09 treatadj_x_visitvisit4 200mg e-11 treatadj_x_visitvisit4 250mg e-12 treatadj_x_visitvisit5 200mg e-13 treatadj_x_visitvisit5 250mg e-15 treatadj_x_visitvisit6 200mg e-14 treatadj_x_visitvisit6 250mg e-12 treatadj_x_visitvisit7 200mg e-14 treatadj_x_visitvisit7 250mg e-12 5

6 Working correlation matrix n.time <- length(unique(dfl.onych$timeweeks.planned)) corm <- matrix(na, nrow = n.time, ncol = n.time) corm[lower.tri(corm)] <- gee.binun$geese$alpha corm [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] NA NA NA NA NA NA NA [2,] NA NA NA NA NA NA [3,] NA NA NA NA NA [4,] NA NA NA NA [5,] NA NA NA [6,] NA NA [7,] NA Odd ratios: # contrast matrix n.coef <- length(coef(gee.binun)) Contrast <- matrix(0, nrow = 3, ncol = n.coef) colnames(contrast) <- names(coef(gee.binun)) Contrast[1,c("treatadj_X_visitvisit1 200mg","treatadj_X_visitvisit7 200mg")] <- c(-1,1) Contrast[2,c("treatadj_X_visitvisit1 200mg","treatadj_X_visitvisit7 250mg")] <- c(-1,1) Contrast[3,c("treatadj_X_visitvisit7 200mg","treatadj_X_visitvisit7 250mg")] <- c(-1,1) # on the working scale resc <- esticon(gee.binun, cm = Contrast, conf.int = TRUE, joint.test = FALSE) # odd ratio cbind(estimate = exp(resc$estimate), + CIinf = exp(resc$estimate-1.96*resc$std.error), + CIsup = exp(resc$estimate+1.96*resc$std.error)) estimate CIinf CIsup [1,] [2,] [3,]

7 Predicted prevalences: sum(is.na(dfl.onych)) [1] 450 length(gee.binun$fitted.values) [1] 1908 NROW(dfL.onych[!is.na(dfL.onych$symptoms),]) [1] 1908 df.pred <- cbind(dfl.onych[!is.na(dfl.onych$symptoms),], + predicted.gee_un = gee.binun$fitted.values) df.pred <- df.pred[order(df.pred$visitnb),] xyplot(predicted.gee_un ~ visitnb, group = id, + data = df.pred[df.pred$id%in%c("1","3"),], + type = "l") 0.3 predicted.gee_un visitnb 7

8 # if add patient with missing data # R will connect non-consecutive points for those patients # leading to a wrong representation xyplot(log(predicted.gee_un/(1-predicted.gee_un)) ~ visitnb, group = id, + data = df.pred[df.pred$id%in%c("1","3"),], + type = "l") log(predicted.gee_un/(1 predicted.gee_un)) visitnb 8

9 Question 4: continuous time model Estimate the model gee.binctun <- geeglm(symptoms ~ time:treatment, + id = id, + data = dfl.onych, + subset = dfl.onych$visitnb < 6, + family = binomial(link = "logit"), corstr = "unstructured") summary(gee.binctun) Call: geeglm(formula = symptoms ~ time:treatment, family = binomial(link = "logit"), data = dfl.onych, subset = dfl.onych$visitnb < 6, id = id, corstr = "unstructured") Coefficients: Estimate Std.err Wald Pr( W ) (Intercept) e-07 *** time:treatment200mg e-08 *** time:treatment250mg e-09 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Estimated Scale Parameters: Estimate Std.err (Intercept) Correlation: Structure = unstructured Link = identity Estimated Correlation Parameters: Estimate Std.err alpha.1: alpha.1: alpha.1: alpha.1: alpha.2: alpha.2: alpha.2: alpha.3: alpha.3: alpha.4: Number of clusters: 294 Maximum cluster size: 5 9

10 Compute the odd ratios # contrast matrix n.coef <- length(coef(gee.binctun)) Contrast <- matrix(0, nrow = 3, ncol = n.coef) colnames(contrast) <- names(coef(gee.binctun)) Contrast[1,c("time:treatment200mg")] <- 1 Contrast[2,c("time:treatment250mg")] <- 1 Contrast[3,c("time:treatment200mg","time:treatment250mg")] <- c(1,-1) # on the working scale resc <- esticon(gee.binctun, cm = Contrast, conf.int = TRUE, joint.test = FALSE) # odd ratio cbind(estimate = exp(resc$estimate), + CIinf = exp(resc$estimate-1.96*resc$std.error), + CIsup = exp(resc$estimate+1.96*resc$std.error)) estimate CIinf CIsup [1,] [2,] [3,]

11 Question 5: conditional odds ratios 11

12 Question 6: glmer model Fit the model: glmer.bintime <- glmer(formula = symptoms ~ time:treatment + (1 id), + data = dfl.onych, + subset = dfl.onych$visitnb<6, + family = binomial(link = "logit")) summary(glmer.bintime) Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmermod] Family: binomial ( logit ) Formula: symptoms ~ time:treatment + (1 id) Data: dfl.onych Subset: dfl.onych$visitnb < 6 AIC BIC loglik deviance df.resid Scaled residuals: Min 1Q Median 3Q Max Random effects: Groups Name Variance Std.Dev. id (Intercept) Number of obs: 1400, groups: id, 294 Fixed effects: Estimate Std. Error z value Pr( z ) (Intercept) < 2e-16 *** time:treatment200mg e-12 *** time:treatment250mg e-14 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Correlation of Fixed Effects: (Intr) tm:200 tm:trtmn tm:trtmn VarCorr(glmer.BinTime) Groups Name Std.Dev. id (Intercept)

13 Compute the odd ratios: n.coef <- length(fixef(glmer.bintime)) Contrast <- matrix(0, nrow = 3, ncol = n.coef) colnames(contrast) <- names(fixef(glmer.bintime)) Contrast[1,c("time:treatment200mg")] <- 1 Contrast[2,c("time:treatment250mg")] <- 1 Contrast[3,c("time:treatment200mg","time:treatment250mg")] <- c(1,-1) # on the working scale # one should use confint(glmer.bintime) # but to save computation time we use another function instead resc <- esticon(glmer.bintime, cm = Contrast, conf.int = TRUE, joint.test = FALSE) # odd ratio cbind(estimate = exp(resc$estimate), + CIinf = exp(resc$estimate-1.96*resc$std.error), + CIsup = exp(resc$estimate+1.96*resc$std.error)) estimate CIinf CIsup [1,] [2,] [3,]

14 Question 7: with a random slope Fit the model: system.time( + glmer.binslope <- glmer(formula = symptoms ~ time:treatment + (time id), + data = dfl.onych, + subset = dfl.onych$visitnb<6, + family = binomial(link = "logit")) + ) user system elapsed summary(glmer.binslope) Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmermod] Family: binomial ( logit ) Formula: symptoms ~ time:treatment + (time id) Data: dfl.onych Subset: dfl.onych$visitnb < 6 AIC BIC loglik deviance df.resid Scaled residuals: Min 1Q Median 3Q Max Random effects: Groups Name Variance Std.Dev. Corr id (Intercept) time Number of obs: 1400, groups: id, 294 Fixed effects: Estimate Std. Error z value Pr( z ) (Intercept) < 2e-16 *** time:treatment200mg e-12 *** time:treatment250mg e-15 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Correlation of Fixed Effects: (Intr) tm:200 tm:trtmn tm:trtmn

15 Compute the odd ratios: n.coef <- length(fixef(glmer.binslope)) Contrast <- matrix(0, nrow = 3, ncol = n.coef) colnames(contrast) <- names(fixef(glmer.binslope)) Contrast[1,c("time:treatment200mg")] <- 1 Contrast[2,c("time:treatment250mg")] <- 1 Contrast[3,c("time:treatment200mg","time:treatment250mg")] <- c(1,-1) # on the working scale # one should use confint(glmer.binslope) instead resc <- esticon(glmer.binslope, cm = Contrast, conf.int = TRUE, joint.test = FALSE) # odd ratio cbind(estimate = exp(resc$estimate), + CIinf = exp(resc$estimate-1.96*resc$std.error), + CIsup = exp(resc$estimate+1.96*resc$std.error)) estimate CIinf CIsup [1,] 5.475e e e-04 [2,] 2.696e e e-04 [3,] 2.030e e e+01 15

16 Appendix A: Graphical display Question 2 Graphical display library(ggplot2, quietly = TRUE) gg.base <- ggplot(dfl.onych, aes(x = visitnb.factor, y = time, + color = factor(symptoms))) gg.base + geom_boxplot() + scale_colour_discrete(name = "symptoms") Warning: Removed 150 rows containing non-finite values (stat_boxplot). 15 time 10 symptoms visit1 visit2 visit3 visit4 visit5 visit6 visit7 visitnb.factor gg.base <- ggplot(dfl.onych, aes(x = timeweeks.planned, y = timeweeks, + group = id, color = factor(symptoms))) gg.base + geom_line() + scale_colour_discrete(name = "symptoms") + geom_abline(intercept = 0, slope Warning: Removed 101 rows containing missing values (geom_path). 16

17 80 60 timeweeks 40 symptoms 0 1 NA timeweeks.planned 17

Solution: anti-fungal treatment exercise

Solution: anti-fungal treatment exercise Course repeated measurements - R exercise class 5 December 5, 2017 Contents 1 Question 1: Import data 2 1.1 Data management.....................................