improve confidence interval estimation for population mean cosinor

DESCRIPTION

@@ -2,12 +2,12 @@ Package: card
 Type: Package
 Title: Cardiovascular Applications in Research Data
 Version: 0.1.0.9000
-Authors@R: c(
-			person("Anish S. Shah", 
-			email = "ashah282@uic.edu", 
-			role = c("aut", "cre", "cph"),
-			comment = c(ORCID = "0000-0002-9729-1558"))
-		)
+Authors@R: 
+    person(given = "Anish S.",
+           family = "Shah",
+           role = c("aut", "cre", "cph"),
+           email = "shah.in.boots@gmail.com",
+           comment = c(ORCID = "0000-0002-9729-1558"))
 Description: A collection of cardiovascular research datasets and analytical
 		tools, including methods for cardiovascular procedural data, such as 
 		electrocardiography, echocardiography, and catheterization data. Additional
@@ -17,7 +17,7 @@ URL: https://cran.r-project.org/package=card
 BugReports: https://github.com/shah-in-boots/card/issues
 Encoding: UTF-8
 LazyData: true
-RoxygenNote: 7.3.1
+RoxygenNote: 7.3.2
 Roxygen: list(markdown = TRUE)
 Depends:
 		R (>= 4.1),

R/cosinor-constructor.R

@@ -7,8 +7,8 @@
 #'   linearization of the parameters to assess their statistics and
 #'   distribution.
 #'
-#' @param t Represents the _ordered_ time indices that provide the positions for the
-#'   cosine wave. Depending on the context:
+#' @param t Represents the _ordered_ time indices that provide the positions for
+#'   the cosine wave. Depending on the context:
 #'
 #'   - A `data frame` of a time-based predictor/index.
 #'

R/cosinor-fit.R

@@ -165,7 +165,7 @@ cosinor_pop_impl <- function(predictors, outcomes, tau, population) {
 
   # Remove patients with only p observations (will cause a det ~ 0 error)
   counts <- by(df, df[, "population"], nrow)
-  lowCounts <- as.numeric(names(counts[counts <= 2*p + 1]))
+  lowCounts <- as.numeric(names(counts[counts <= 2 * p + 1]))
   df <- subset(df, !(population %in% lowCounts))
 
   # Message about population count removal
@@ -315,71 +315,159 @@ confint.cosinor <- function(object, parm, level = 0.95, ...) {
 	}
 
 	switch(
-	  object$type,
-	  Population = {
-  		# Message
-  		message("Confidence intervals for amplitude and acrophase for population-mean cosinor use the methods described by Fernando et al 2004, which may not be applicable to multiple-components.")
-
-  		# Freedom by number of individuals
-  		k <- nrow(object$xmat)
-
-  		# Standard errors
-  	  SE_mesor <- sd(xmat[, "mesor"]) / sqrt(k)
-  		for(i in 1:p) {
-  		  assign(paste0("SE_amp", i), (sd(xmat[, paste0("amp", i)]) / sqrt(k)))
-  		  assign(paste0("SE_phi", i), (sd(xmat[, paste0("phi", i)]) / sqrt(k)))
-  		  assign(paste0("SE_beta", i), (sd(xmat[, paste0("beta", i)]) / sqrt(k)))
-  		  assign(paste0("SE_gamma", i), (sd(xmat[, paste0("gamma", i)]) / sqrt(k)))
-  		}
+		object$type,
+		Population = {
+			# Message
+			message("Confidence intervals for amplitude and acrophase for population-mean cosinor use the methods described by Fernández et al. 2004.")
 
-  	  # Save SE
-  	  se <- list()
-      for(i in 1:p) {
-        se[[i]] <- c(
-          paste0("SE_amp", i),
-          paste0("SE_phi", i),
-          paste0("SE_beta", i),
-          paste0("SE_gamma", i)
-        )
-      }
-  	  se <- c(SE_mesor, unlist(mget(unlist(se))))
-  	  names(se)[1] <- "SE_mesor"
-  	  names(se) <- gsub("SE_", "", names(se))
+			# Number of individuals
+			k <- nrow(xmat)
 
-  	  # Confidence intervals
-  	  tdist <- stats::qt(1 - a/2, df = n - k)
-  	  confints <- list()
-  	  for(i in 1:p) {
-  	    confints[[i]] <-
-  	      c(
-  	        # Amp
-    	      get(paste0("amp", i)) - tdist * get(paste0("SE_amp", i)),
-    	      get(paste0("amp", i)) + tdist * get(paste0("SE_amp", i)),
-    	      # Phi
-    	      get(paste0("phi", i)) - tdist * get(paste0("SE_phi", i)),
-    	      get(paste0("phi", i)) + tdist * get(paste0("SE_phi", i))
-  	    )
-  	  }
+			# Extract parameters from xmat
+			params <- as.data.frame(xmat)
 
-      df <- rbind(
-        c(mesor - tdist*SE_mesor, mesor + tdist*SE_mesor),
-        matrix(unlist(confints), ncol = 2, byrow = TRUE)
-      )
-      rnames <- list()
-      for(i in 1:p) {
-        rnames[[i]] <- c(paste0("amp", i), paste0("phi", i))
-      }
-      rownames(df) <- c("mesor", unlist(rnames))
-      colnames(df) <- c(paste0(100*(a/2),"%"), paste0(100*(1-a/2), "%"))
+			# Convert column names to lowercase
+			colnames(params) <- tolower(colnames(params))
 
-  	  # Returned
-      estimates <- list(
-        ci = df,
-        se = se
-      )
-      return(estimates)
+			popParams <- colMeans(params)
+			varCovMat <- cov(params)
+
+			# Degrees of freedom
+			df <- k - 1
 
-	  },
+			# Critical value from chi-squared distribution
+			cValue <- qchisq(level, df = 2)
+
+			# Initialize data structures for output
+			ciMatrix <- matrix(nrow = 0, ncol = 2)
+			colnames(ciMatrix) <- c(
+				sprintf("%.1f%%", a / 2 * 100),
+				sprintf("%.1f%%", (1 - a / 2) * 100)
+			)
+
+			seVector <- numeric()
+			names(seVector) <- character()
+
+			# MESOR confidence interval
+			seMesor <- sqrt(varCovMat["mesor", "mesor"] / k)
+			tValue <- qt(1 - a / 2, df)
+			ciMesor <- c(
+				popParams["mesor"] - tValue * seMesor,
+				popParams["mesor"] + tValue * seMesor
+			)
+
+			# Add MESOR to outputs
+			ciMatrix <- rbind(ciMatrix, ciMesor)
+			rownames(ciMatrix)[nrow(ciMatrix)] <- "mesor"
+
+			seVector <- c(seVector, seMesor)
+			names(seVector)[length(seVector)] <- "mesor"
+
+			# For each component
+			for (i in 1:p) {
+				# Get beta and gamma parameter names
+				betaName <- paste0("beta", i)
+				gammaName <- paste0("gamma", i)
+
+				# Extract individual estimates
+				beta_i <- params[[betaName]]
+				gamma_i <- params[[gammaName]]
+
+				# Compute sample means
+				betaBar <- mean(beta_i)
+				gammaBar <- mean(gamma_i)
+
+				# Compute covariance matrix for beta and gamma
+				covMat <- cov(cbind(beta_i, gamma_i))
+
+				# Eigen decomposition of covariance matrix
+				eig <- stats::eigen(covMat)
+				V <- eig$vectors
+				D <- diag(eig$values)
+
+				# Square root of covariance matrix
+				rootCov <- V %*% sqrt(D) %*% t(V)
+
+				# Generate ellipse points
+				thetaSeq <- seq(0, 2 * pi, length.out = 1000)
+				ellipsePoints <- sqrt(cValue) * (rootCov %*% rbind(cos(thetaSeq), sin(thetaSeq)))
+
+				betaTheta <- betaBar + ellipsePoints[1, ]
+				gammaTheta <- gammaBar + ellipsePoints[2, ]
+
+				# Compute amplitude and acrophase
+				# Make sure acrophase is within the unit circle
+				amplitudeTheta <- sqrt(betaTheta^2 + gammaTheta^2)
+				acrophaseTheta <- atan2(-gammaTheta, betaTheta)
+				acrophaseTheta <- (acrophaseTheta + pi) %% (2 * pi) - pi
+
+				# Compute confidence intervals for amplitude and acrophase
+				ampLower <- min(amplitudeTheta)
+				ampUpper <- max(amplitudeTheta)
+
+				phiLower <- min(acrophaseTheta)
+				phiUpper <- max(acrophaseTheta)
+
+				# Compute standard errors for beta and gamma
+				seBeta <- sqrt(var(beta_i) / k)
+				seGamma <- sqrt(var(gamma_i) / k)
+
+				# Compute t-value for beta and gamma
+				tValueBetaGamma <- qt(1 - alpha / 2, df)
+
+				# Confidence intervals for beta and gamma
+				betaLower <- betaBar - tValueBetaGamma * seBeta
+				betaUpper <- betaBar + tValueBetaGamma * seBeta
+
+				gammaLower <- gammaBar - tValueBetaGamma * seGamma
+				gammaUpper <- gammaBar + tValueBetaGamma * seGamma
+
+				# Add beta to outputs
+				ciMatrix <- rbind(ciMatrix, c(betaLower, betaUpper))
+				rownames(ciMatrix)[nrow(ciMatrix)] <- paste0("beta", i)
+
+				seVector <- c(seVector, seBeta)
+				names(seVector)[length(seVector)] <- paste0("beta", i)
+
+				# Add gamma to outputs
+				ciMatrix <- rbind(ciMatrix, c(gammaLower, gammaUpper))
+				rownames(ciMatrix)[nrow(ciMatrix)] <- paste0("gamma", i)
+
+				seVector <- c(seVector, seGamma)
+				names(seVector)[length(seVector)] <- paste0("gamma", i)
+
+				# Add amplitude to outputs
+				ciMatrix <- rbind(ciMatrix, c(ampLower, ampUpper))
+				rownames(ciMatrix)[nrow(ciMatrix)] <- paste0("amplitude", i)
+
+				# Standard error for amplitude
+				amplitude_i <- sqrt(beta_i^2 + gamma_i^2)
+				seAmplitude <- sqrt(var(amplitude_i) / k)
+				seVector <- c(seVector, seAmplitude)
+				names(seVector)[length(seVector)] <- paste0("amplitude", i)
+
+				# Add acrophase to outputs
+				ciMatrix <- rbind(ciMatrix, c(phiLower, phiUpper))
+				rownames(ciMatrix)[nrow(ciMatrix)] <- paste0("acrophase", i)
+
+				# Standard error for acrophase
+				acrophase_i <- atan2(-gamma_i, beta_i)
+				acrophase_i <- (acrophase_i + pi) %% (2 * pi) - pi
+				# Compute angular standard deviation
+				seAcrophase <- sqrt(-2 * log(abs(mean(exp(1i * acrophase_i)))))
+				seVector <- c(seVector, seAcrophase)
+				names(seVector)[length(seVector)] <- paste0("acrophase", i)
+			}
+
+			# Name the columns of ciMatrix according to confidence levels
+			colnames(ciMatrix) <- c(
+				sprintf("%.1f%%", a / 2 * 100),
+				sprintf("%.1f%%", (1 - a / 2) * 100)
+			)
+
+			# Return the output as a list
+			return(list(ci = ciMatrix, se = seVector))
+		},
 	  Individual = {
 
   		# Nummber of parameters
@@ -467,6 +555,9 @@ confint.cosinor <- function(object, parm, level = 0.95, ...) {
 
 }
 
+
+
+
 ## Zero Amplitude Test
 
 #' @title Zero Amplitude Test

tests/testthat/test-cosinor-fit.R

@@ -13,18 +13,19 @@ test_that("models can be generally fit", {
 	# Harmonic checks
 	expect_gt(length(mcos$tau), 1)
 	expect_equal(max(mcos$tau) %% min(mcos$tau), 0)
-	expect_message(cosinor_features(mcos))
+	expect_warning(cosinor_features(mcos))
 
 	# Confidence intervals
 	expect_type(confint(scos), "list")
 })
 
 test_that("population cosinors can be fit", {
 
+	# Single population cosinor
 	f <- sDYX ~ hour
 	data <- twins
 	population = "patid"
-	cosinor(formula = f, data = data, tau = 24, population = population)
+	m <- cosinor(formula = f, data = data, tau = 24, population = population)
 
 
 })

tests/testthat/test-cosinor-plots.R

@@ -2,7 +2,7 @@ test_that("ggcosinor makes a ggplot", {
 	data("twins")
 	scos <- cosinor(rDYX ~ hour, twins, 24)
 	mcos <- cosinor(rDYX ~ hour, twins, c(24, 12))
-	pcos <- cosinor(rDYX ~ hour, twins, 24, "patid")
-	g <- ggcosinor(mcos)
+	pcos <- expect_message(cosinor(rDYX ~ hour, twins, 24, "patid"))
+	g <- expect_warning(ggcosinor(mcos))
 	expect_s3_class(g, "ggplot")
-})
+})