Statistical Issues in Analyzing 24-Hour Dietary Recall and 24-Hour Urine Collection Data for Sodium and Potassium Intakes

Mark A. Espeland1,2, Shiriki Kumanyika3,4, Alan C. Wilson5, David M. Reboussin1, Linda Easter6, Mary Self6, Julia Robertson1, W. Mark Brown1 and Mary McFarlane1

1 Section on Biostatistics, Wake Forest University School of Medicine, Winston-Salem, NC.
2 Medical Statistics Unit, London School of Hygiene and Tropical Medicine, London WC1E 7HT, United Kingdom.
3 Center for Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA.
4 Department of Human Nutrition and Dietetics, University of Illinois at Chicago, Chicago, IL.
5 Department of Medicine, Robert Wood Johnson Medical School, University of Medicine and Dentistry of New Jersey, New Brunswick, NJ.
6 Section on Epidemiology, Wake Forest University School of Medicine, Winston-Salem, NC.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
Dietary recalls and urine assays provide different metrics for assessing sodium and potassium intakes. Means, variances, and correlations of data obtained from these two modes of measurement differ. Pooling of these data is not straightforward, and results from studies employing the different modes may not be comparable. To explore differences between these metrics, the authors used data from the Trial of Nonpharmacologic Intervention in the Elderly (TONE), which included repeated standardized 24-hour dietary recalls and 24-hour urine collections administered over 3 years of follow-up, to estimate sodium and potassium intakes. The authors examined data from 341 control participants assigned to usual care that were collected between August 1992 and December 1995. Dietary recalls yielded estimates of sodium intake that averaged 22% less than those from urine assays and estimates of potassium intake that averaged 16% greater than those from urine assays. Sodium intake estimates were less repeatable (r = 0.22 for diet; r = 0.30 for urine) than potassium intake estimates (r = 0.49 for diet; r = 0.50 for urine), making relations with outcomes more difficult to characterize. Overall, the performance of the two measurement modes was fairly similar across demographic subgroups. Errors in separate estimations of long term sodium and potassium intakes using short term data were strongly correlated, more strongly than the underlying long term intakes of these electrolytes. Because of the correlated measurement error, estimated regression coefficients for linear models including both electrolytes as predictors may be confounded such that the separate relations between these nutrients and outcomes such as blood pressure cannot be reliably estimated by common analytical strategies.

clinical trials; epidemiologic methods; measurement error; nutrition assessment; potassium; sodium

Abbreviations: CI, credible interval; TONE, Trial of Nonpharmacologic Intervention in the Elderly


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
The characteristic nutrient intake of an individual over the span of time typical of epidemiologic cohort studies or clinical trials is a construct that generally cannot be measured precisely. Short term reports or assays provide different perspectives on this construct but are biased relative to each other and vary in their reliability. By using more than one measurement mode, investigators may develop pooled estimates that are more stable. By repeating measures across time, they may reduce the influence of random variation. However, significant imprecision often remains that saps statistical power and biases observed relations.

When panels of nutrients are measured, the measurement errors of individual nutrients relative to long term intakes may be correlated, which may induce or inflate observed correlations and make characterization of multivariate relations difficult. This is relevant to understanding the interrelations of sodium and potassium intakes with hypertension. Increased sodium intake is associated with increased blood pressure, whereas increased potassium intake may reduce blood pressure (1GoGoGoGo–5Go). Estimating the effect of long term consumption of either nutrient on blood pressure requires separating these opposing effects and controlling error.

The Trial of Nonpharmacologic Intervention in the Elderly (TONE) included repeated assessment of sodium and potassium intakes by 24-hour dietary recalls and assays of 24-hour urine samples. The systematic bias of these methods, i.e., the long term average differences between these measures and true intake, cannot be estimated. Instead, we can examine the relative bias of one mode versus the other. Relative biases may result from a number of factors—errors in self-reporting, inaccurate or incomplete food tables, missing data, varying metabolic processes, variable excretion rates, losses through other metabolic pathways such as sweat and feces, incomplete urine collection, differences between assay protocols, etc.—each of which may induce systematic relative bias across the cohort or across time. Similarly, there may exist systematic biases within subjects that are driven by many of the same factors; for example, some participants may be more forgetful or less compliant with protocols than others. Within each measurement mode, there may exist nonsystematic relative errors across the population related to variable recall, errors in collection, seasonal patterns, random fluctuations in metabolism, laboratory/processing errors, etc. There may exist short term systematic fluctuations across the population, e.g., secular trends or protocol changes. In this paper, we have pooled all of these factors and use the term "error" generally to address their composite influence on measurement.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
Detailed descriptions of TONE's design, methods, recruitment, and randomized cohort have appeared elsewhere (6GoGoGo–9Go). The study's principal aim was to assess whether interventions designed to reduce sodium intake and body weight, alone or in combination, could successfully substitute for pharmacologic treatment of hypertension. The TONE cohort was aged 60–79 years and had average systolic blood pressures less than 145 mmHg and average dia-stolic blood pressures less than 85 mmHg while being treated with a single antihypertensive medication at baseline. Individuals with body mass indices (weight (kg)/height (m)2) >=27.3 (females) or >=27.8 (males) were classified as obese by study criteria.

To avoid any influences of interventions on measurement, we restricted our analysis to the 341 participants in the TONE control group. These participants met approximately 1 month postrandomization and quarterly thereafter for educational sessions unrelated to nutrition and cardiovascular disease, which were expected to have little impact on reported and actual dietary intakes. Participant follow-up began in August 1992 and ended in December 1995, ranging from 16 months to 36 months.

By protocol, 24-hour dietary recalls were administered twice prior to randomization, at 9, 12, 18, 24, and 30 months postrandomization, and at exit from the study (if this did not coincide with other time points). Missed recalls were rare, averaging 4.2 percent among individuals who attended scheduled clinic examinations. Dietary recall data were collected during standardized, open-ended interviews using Minnesota Nutrition Data System software (10Go), a package selected for its accuracy, standardization, and comprehensive food and nutrient databases. The Nutrition Data System program automatically prompts interviewers to probe for complete food descriptions, variable recipe ingredients, and food preparation methods, including salt added during cooking. To enhance accuracy and ensure capture of discretionary salt use, prompts were added to cue interviewers to probe respondents regarding use of table salt. Nutrient calculations were performed using algorithms developed at the University of Minnesota (food database, version 6A; nutrient database, version 21) (10Go).

Split urine samples (day and night 12-hour periods) were collected according to the protocol of the Trial of Hypertension Prevention (11Go) twice prior to randomization, at 9, 18, and 30 months postrandomization, and at exit from the study. Collection rates exceeded 95 percent. Any missed voids or problems encountered during collection were recorded, and data from these 24-hour samples were not used in analyses. Collection times (times between morning voids on successive days) had to be 23–25 hours apart, and sample volume had to be >=500 ml. Samples were aliquoted, refrigerated at 0–4°C, and shipped refrigerated every 2 weeks for testing with a NOVA 1 + 1 sodium/potassium ion selective electrode instrument (Nova Biomedical, Waltham, Massachusetts) and reagents from Scientific Products (Baxter Healthcare Corporation, Edison, New Jersey). Coefficients of variation for the instrument were 1.1 percent for sodium and 0.8 percent for potassium. Total 24-hour excretion was calculated as concentration x volume x (24 hours/collection time).

Statistical methods
To simplify these analyses, we included only visits at which 50 or more participants provided sodium and potassium data from both 24-hour dietary recalls and urine collections: screening (n = 325), randomization (n = 320), 9 months (n = 283), 18 months (n = 255), and 30 months (n = 143). We examined pairwise correlations between dietary recall and urine measurements for visits for which the 24-hour collection periods overlapped versus those which did not overlap. While there was a slight decrease in correlation when collection periods did not overlap, we judged this to be minor. Cross-sectional correlations among electrolyte measures at each of the five visits were nearly identical, and correlations across time were fairly stable. Accordingly, we used models in which covariance matrices were constant over time.

We wished to distinguish the construct of an individual's long term intake of sodium and potassium from the imprecision of estimates of individual dietary recalls and urine collections. On the basis of univariate and multivariate plots, we determined that it was reasonable to assume that data were normally distributed. We fitted hierarchical linear models to the serial data with the following notation and structure (see Appendix). Vector Uij = [U(Na)ij, U (K)ij] denotes urinary sodium and potassium excretions from subject i and visit j. Vector Dij = [D(Na)ij, D (K)ij] denotes dietary recall sodium and potassium intakes from subject i and visit j. Vector was assumed to follow a multivariate normal distribution with subject-specific mean [µ(Na)i, µ(K)i] and covariance {sum}U. Vector Dij was assumed to follow a multivariate normal distribution with subject-specific mean [{delta}(Na)i, {delta}(K)i and covariance {sum}D. We used parameters {lambda}1 and {lambda}2 for the ratio of mean intake estimates of the measurement modes: {delta}(Na)i = {lambda}1 µ(Na)i and {delta}(K)i = {lambda}2 µ(K)i. These ratios express the population-based relative biases. In our primary model, we assumed that ratios were constant across individuals, intakes, and visits. In supporting analyses, we examined each of these assumptions by fitting more complex models. Letting {lambda}1 and {lambda}2 vary among individuals allowed us to characterize the extent to which systematic biases varied across the cohort. We set [µ(Na)i, µ(K)i = {gamma}0 + {gamma}i, where vector {gamma}i denoted the underlying population mean intakes (according to urine collection) of the two electrolytes and vector denoted the individual bivariate random effects. We assumed that these random effects followed a bivariate normal distribution with mean (0, 0) and covariance {sum}R. Matrix {sum}R denotes the covariance for the long term intakes among subjects, {sum}U denotes the intrasubject covariance associated with random variation and measurement error for urine, and {sum}D denotes the intrasubject covariance associated with random variation and measurement error for diet. We fitted additional models in which {lambda}1 and {lambda}2 were functions of intake {gamma}i. For example, we let {lambda}i1 = {omega}01 + {omega}11{gamma}i1 and {lambda}i2 = {omega}02 + {omega}12{gamma}i2, so that the relative bias was linearly related to an individual's long term intake.

Models were fitted with a Gibbs sampling algorithm (12Go, 13Go), programmed using BUGS software (14Go). Noninformative priors were assumed for parameters. After a "burn-in" phase during which 1,000 samples were discarded, the next 5,000 samples were used to estimate posterior distributions. We report medians of these posterior distributions as point estimates and 95 percent equal-tail credible intervals (approximately analogous to 95 percent confidence intervals). Analyses were rerun from several starting points; the congruence of these results and graphic inspection of sequential samples led us to conclude that the estimation process was stationary and that 5,000 samples were sufficient.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
Table 1 characterizes the cohort at baseline according to factors we thought might influence the accuracy/repeatability of dietary recall and/or urine collection. Table 2Go shows the distributions of the 1,381 dietary recalls and 1,335 urine collections across the five scheduled visits and the 1,326 visits for which both recalls and urine samples were available. Figures 1 and 2 portray the mean sodium and potassium levels measured at these visits. There were minor but statistically significant changes in the mean levels of measures across time (p = 0.01 for dietary sodium, p = 0.02 for dietary potassium, p < 0.001 for urinary sodium, and p < 0.0001 for urinary potassium). We treated these changes as if they were random and included them as components of error. Mean sodium intake estimated from urine exceeded that obtained from dietary recalls by 29.9 (standard error 1.4) mEq/24 hours (p < 0.001). Average potassium intake based on urine was lower than that for dietary recall by 10.0 (standard error 0.5) mEq/24 hours (p < 0.001).


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TABLE 1. Baseline characteristics of the 341 control participants randomized to usual care, Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995

 


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FIGURE 1. Average reported sodium consumption and urinary sodium excretion at baseline and across follow-up for 341 control participants randomized to usual care, Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995. Bars, standard error.

 


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FIGURE 2. Average reported potassium consumption and urinary potassium excretion at baseline and across follow-up for 341 control participants randomized to usual care, Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995. Bars, standard error.

 

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TABLE 2. Timing and frequency of 24-hour dietary recalls and 24-hour urine collections and percentages of recall/collection periods known to overlap on the same day, Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995

 
Table 3 presents observed correlations between measures (prior to factoring correlations attributable to measurement error). Measured sodium and potassium intakes were moderately correlated within each mode (r = 0.35 for both dietary recalls and urine collections). Between different modes, however, these correlations were much lower (r = 0.13 for dietary sodium vs. urinary potassium and r = 0.09 for dietary potassium vs. urinary sodium), reflecting the inflation of intramode correlations due to correlated measurement errors. The correlations between diet and urine measures were 0.30 for sodium and 0.43 for potassium.


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TABLE 3. Pearson correlation coefficients for cross-sectional associations between 24-hour sodium and potassium measures obtained from dietary recalls and urine collections, Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995

 
As estimated from our primary model, the long term population mean intakes of sodium and potassium ({gamma}0), scaled as if measured from urine, were 141.7 mEq/24 hours for sodium (95 percent credible interval (CI): 137.7, 145.5) and 56.6 mEq/24 hours for potassium (95 percent CI: 52.7, 60.3). The estimated ratios of dietary nutrient values to urinary nutrient values ({lambda}1 and {lambda}2) were different from each other and from 1.00: 0.78 (95 percent CI: 0.76, 0.81) for sodium and 1.16 (95 percent CI: 1.14, 1.19) for potassium. This led to estimated mean nutrient intakes, scaled as assessed by diet, of 110.5 mEq/24 hours (141.7 x 0.78) for sodium and 65.7 mEq/24 hours (56.6 x 1.16) for potassium.

The fitted variances for measurement error of sodium intakes exceeded the estimated variance in long term intakes among participants (table 4). The covariances between errors were marked and exceeded the estimated covariance between sodium and potassium intakes. As estimated from expressions given in the Appendix, the correlations between measurement errors for sodium and potassium were 0.30 (dietary recalls) and 0.38 (urine collections).


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TABLE 4. Fitted covariance matrices (mEq/24 hours)2: median values of posterior distributions from 5,000 sequential Gibbs samples,* Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995

 
The correlations between pooled long term intake and a single 24-hour dietary recall were 0.47 for sodium and 0.70 for potassium. Thus, the observed correlation between an outcome and sodium intake measured with a 24-hour recall would be expected to be only 47 percent as large as correlation between the outcome and long term intake. The correlations between long term intake and a single 24-hour urine sample were 0.55 for sodium and 0.71 for potassium.

We fitted additional models in which the ratios of dietary measures to urinary measures ({lambda}1 and {lambda}2) were allowed to vary with the participant's underlying intake (i.e., were functions of {gamma}i) and time. In the primary model, the absolute difference between dietary and urinary measures increased with intake (because their ratio is constant). This assumption appeared to represent the sodium data fairly well. For example, allowing {lambda}1 to change in a linear fashion with resulted in a fitted slope with a 95 percent credible interval that included 0. For potassium, however, the absolute difference did not appear to increase with intake but appeared to more closely follow an additive model. We also fitted models in which {lambda}1 and {lambda}2 were allowed to vary systematically among examinations, but we found only minor differences among fitted parameters. Finally, we expressed each ratio as a random effect from normal distributions with mean 0. The fitted standard deviations of these random effects distributions were small: 0.13 (95 percent CI: 0.09, 0.16) for sodium and 0.17 (95 percent CI: 0.15, 0.20) for potassium. We then reestimated the covariance matrices in table 4 with these three extensions to our primary model. The impact on fitted covariances was minor and had little overall effect on the correlations between nonsystematic errors.

We also explored whether it was feasible to assume that errors between dietary recalls and urinary assays are conditionally independent given long term intake (which is implicit in the parameterization that we adopted). We fitted a series of models in which a bivariate random effects term was used to express variation between examinations within an individual. The fitted estimates for this model were small and had little impact on the data in tables 4 and 5; therefore, we have not reported separately the results from this more complex model.


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TABLE 5. Fitted relative biases of dietary intake measures versus urinary intake measures (posterior median values and 95% credible intervals) and correlation coefficients for participant subgroups,* Trial of Nonpharmacologic Intervention in the Elderly, 1992–1995

 
The fitted correlation between sodium and potassium intakes from the primary model was rNaK = 0.26 (95 percent CI: 0.14, 0.38). As table 5 shows, the within-subject correlations of dietary recalls were rDNa = 0.22 (95 percent CI: 0.14, 0.38) for sodium and rDK = 0.49 (95 percent CI: 0.45, 0.53) for potassium. The within-subject correlations of measures from 24-hour urine samples were rUNa = 0.30 (95 percent CI: 0.25, 0.35) for sodium and rUK = 0.50 (95 percent CI: 0.46, 0.56) for potassium.

Age and gender did not appear to markedly affect either the relative biases of measures or the performance characteristics of measures. However, the relative bias of diet- versus urine-based sodium and potassium measures appeared to be greater among African Americans than among other participants. Interestingly, the estimated correlation between intakes of sodium and potassium in the diets of African Americans was nearly zero (r = 0.02) and the repeatability of both diet-based and urine-based measures was lower, although credible intervals for these estimates overlapped those for other participants.

Obesity was associated with greater relative measurement bias for sodium and slightly less bias for potassium. Overall, the within-subject correlation of measures was similar among obese and nonobese cohorts. The relative bias of diet- versus urine-based measures of sodium was lower among college-educated participants; however, the relative bias for potassium measures was higher. The within-subject correlation of dietary recall measures was slightly higher among college-educated participants; however, the repeatability of urine-based measures appeared not to be influenced by educational level. The within-subject correlation of sodium intake estimates appeared to vary among clinics.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
Dietary recalls and urine analyses are often the most feasible methods for estimating electrolyte intake. The two methods are imprecise, yet they provide complementary strategies for estimating long term intakes (4Go, 15GoGoGoGoGo–20Go). The TONE data allowed us to contrast directly the metrics these methods provide, both against each other and against the characterization of long term intake that is obtained by pooling the measurements across time. This approach helps one to avoid artificial and short term settings that comparisons based on controlled environments or more intrusive record-keeping require, and it is arguably more generalizable.

Relative bias of dietary recall versus urine collection
Several studies have examined the relative bias of dietary recall versus urinary assessments of electrolyte intake. In a study by Pietinen (16Go), 154 volunteers provided 4 days of consecutive food records and 3 days of consecutive 24-hour urine collections. Sodium intakes estimated from the urine collections were 7 percent lower than intakes estimated from food records. Potassium intakes estimated from urine were 8 percent lower than those obtained from food records. These results are in approximate accordance with those of other studies using food records (21GoGo–23Go). In contrast, we found that estimates of sodium intake from 24-hour dietary recalls were an average of 22 percent lower than those from 24-hour urine collection. Diet-based estimates of potassium intake exceeded those from urine assays by 16 percent overall, although our extended modeling indicated that this percentage may vary with intake.

Diet reports are particularly prone to underestimation of sodium intake because the databases used to assign nutrient values to foods included in dietary interviews often do not account for discretionary addition of salt (24Go, 25Go). Potassium intake may be lower than what is estimated from food tables because of losses during cooking. Daily intakes of sodium and potassium vary substantially. Ordinarily, more than 95 percent of ingested sodium is excreted in the urine (26Go). Urine is also the major route of potassium excretion, but urinary measurement tends to underestimate intake, since a larger proportion of potassium (e.g., 15 percent in populations with a Western diet) is lost in feces. Urine collections that are incomplete may underestimate electrolyte intakes.

The TONE study may have contained differential recall of sodium-rich food sources versus potassium-rich sources; however, the consistency of results across subgroups argues against this. There may have been differences in the relative influence of processing urine specimens on the measured sodium concentrations versus potassium concentrations; however, an internal reliability study in TONE found evidence of only small average changes (<5 percent) that might have been attributable to the freezing/thawing of urine samples (27Go). Relative errors in the laboratory methods may also have existed; however, the measurement assay was routinely calibrated against standards of known concentrations, so it must be presumed to have been relatively unbiased.

Correlation between long term sodium and potassium intakes
Some correlation between the underlying intakes of sodium and potassium is to be expected because of differences in overall food intakes: Individuals who consume larger amounts of food would generally be expected to have larger intakes of individual nutrients. In addition, many foods are relatively rich or poor sources of sodium and potassium. Overall, we found a modest correlation between intakes of sodium and potassium (r = 0.26). Thus, relations between outcomes and either of the nutrient intakes may be confounded unless both are included in regression models. Raw correlations of values from either measurement mode overestimated this correlation because of the strongly correlated measurement errors.

Repeatability of dietary and urinary measures
Sodium intakes based on dietary recall tended to have slightly less repeatability than those based on urine collections, as characterized by within-subject correlations for diet and urine (r = 0.22 (95 percent CI: 0.14, 0.38) for diet and r = 0.30 (95 percent CI: 0.25, 0.35) for urine). The repeat-ability of potassium assessments was higher than that for sodium: r = 0.49 (95 percent CI: 0.45, 0.53) for dietary recall and r = 0.50 (95 percent CI: 0.46, 0.56) for urine. Our estimates approximately agree with those observed in other studies but are slightly lower. For example, the reliability of 24-hour urine assessments reported in the INTERSALT Study, based on visits averaging 14 days apart, was 0.45 for sodium and 0.55 for potassium (28Go). For 24-hour urine samples in the Trials of Hypertension Prevention, the correlations across a similar period of time were 0.34 for sodium and 0.39 for potassium (4Go). It is to be expected that repeatability will decrease with longer intervals between repeated assessments.

Impact of correlated error
The TONE data confirm that measurement errors in assessing long term sodium and potassium intakes using short term data are strongly correlated for both dietary recall and urine collection. This finding has several important implications for the design and analysis of studies relating electrolyte intake to outcomes. The underlying relation between intakes of these two electrolytes cannot be determined from bivariate plots or correlations of cross-sectional measurements. Simple analytical strategies, such as jointly grouping individuals according to low-sodium and -potassium diets versus high-sodium and -potassium diets or creating ratios of sodium intakes to po-tassium intakes, may be misleading. Common approaches to repeated measurements do not avoid this problem: Because measurement errors are correlated, relations may not be resolved without more sophisticated modeling. Correlated measurement errors may disrupt multivariable prediction models. Simple linear, logistic, or proportional hazards regression models in which both measured sodium and measured potassium intakes are included as predictors may produce very biased regression coefficients such that the relative influences of the two electrolytes cannot be determined. Gleser (29Go) has described this phenomenon for least squares linear regression. The expected bias in regression coefficients in a model in which measured sodium and potassium intakes are jointly included as predictors can be computed from the covariances in table 4 or computed directly via Gibbs sampling (based on assumptions underlying our primary model). The reliability matrices {kappa}D = {sum}R[{sum}D + {sum}R]-1 and {kappa}U = {sum}R[{sum}U + {sum}R]-1 for diet and urine characterize these biases. Fitted regression coefficients for a multiple regression model, e.g., BD = [BDNa, BDK], are biased from the true regression parameters, e.g., ßD = [ßDNa, ßDK], according to the formula BD = {kappa}DßD. The relative magnitudes of the off-diagonal elements of matrices {kappa}D and {kappa}U express the confounding of the separate relations between the electrolytes and the dependent variable. For models in which dietary sodium and potassium measures are jointly used to predict blood pressure, the fitted least squares regression coefficient for sodium is approximately one third of the sum of 3 percent (95 percent CI: 0, 22) of the (negative) true coefficient with potassium and 97 percent of the (positive) true coefficient with sodium. Across the subgroups we examined, the expected contamination of slopes (due to this phenomenon) was estimated to be as large as 37 percent (although all 95 percent credible intervals included 0), and the estimated slopes were expected to be as low as one fifth of their true value. Thus, the correlated measurement error inherent in either measurement mode may preclude separately estimating the associations of individual nutrients using multiple regression. While these mathematical relations are not precise under some of the variations of our primary model, similar influences may be expected.

Consistency among subgroups
Kristal et al. (30Go) and Kipnis et al. (31Go) reported that the univariate performance of food frequency reports relative to food records may vary for some nutrients by ethnicity, education, clinic site, and individual, although neither group of investigators considered sodium or potassium. We found that relative measurement error and repeatability varied only modestly among demographic and clinical subgroups. The relative bias of dietary recall versus urine collection in estimating sodium intake appeared to be larger among African Americans and among persons who were not college graduates. Differences between estimates of potassium intake were not as marked. The repeatability of sodium intakes appeared to vary by clinic site, particularly for dietary recall. Overall, however, we were struck by the relative robustness of these methods across subgroups. In the absence of a gold standard, this robustness is relative to the two measurement modes and may not translate to accuracy in characterizing true long term intake. There was some variation in the underlying correlation between sodium and potassium intake; however, the 95 percent credible intervals overlapped for the subgroups we examined.


    Conclusions
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
Dietary recall and urine collection do not produce comparable estimates of sodium and potassium intakes. However, intakes estimated by these two modes have similar repeatability, such that the degradation of observed univariable relations due to measurement error is comparable. Sodium intake is less repeatable than potassium intake; observed relations with sodium will suffer greater biases due to measurement error, and less power will generally be available to detect them. Intakes of sodium and potassium are correlated, so it may be important to include both measures in regression models of outcomes they jointly influence. Yet because the measurement errors for the intakes of the two electrolytes are correlated, least squares estimates of regression parameters will be confounded. The separate contributions of intakes of these electrolytes to hypertension are difficult to characterize, and their contributions may not be accurately portrayed without more complex approaches. The performance of the methods used in the TONE study to estimate intakes may be influenced modestly by educational level, ethnicity, or clinic site, but overall results were similar across demographic subgroups.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 
This appendix provides additional detail on the notation we used and the distributions we assumed for the analyses. It also provides expressions for estimating reliability statistics from the fitted covariance expressions shown in table 4.

Let Xij denote the composite vector of dietary recall and urine collection data from participant i at visit j. Using notation from the Materials and Methods section (see text), Xij = [Dij, Uij, this vector is assumed to follow a conditional multivariate normal distribution with mean [{delta}(Na)i, {delta}(K)i, µ(Na)i, µ(K)i] = [{lambda}1µ(Na)i, {lambda}2µ(K)i, µ(Na)i, µ(K)i]. In our primary model, {lambda}1 and {lambda}2 are assumed to be constant across times, intakes, and individuals. We assume that µ(Na)i has underlying structure µ(Na)i = {gamma}0(1) + {gamma}i(1) and that µ(K)i has underlying structure µ(K)i = {gamma}0(2) + {gamma}i(2), in which {gamma}0 = [{gamma}0(1), {gamma}0(2)] denotes the underlying population mean sodium and potassium levels of excretion (scaled according to urine-based measurements) and {gamma}i = [{gamma}i(1), {gamma}i(2)] denotes the bivariate random effects for different intakes among participants. These bivariate random effects are assumed to follow a multivariate normal distribution with mean (0, 0) and 2 x 2 covariance {sum}R having elements {sigma}2R11, {sigma}R12, and {sigma}2R22.

We define {sum}D, with elements {sigma}2D11, {sigma}D12, and {sigma}2D22, as the covariance of measurement errors for sodium and potassium intakes based on dietary recall and {sigma}2U11, with elements {sigma}2U11, {sigma}U12, and {sigma}2U22, as the covariance of measurement errors for sodium and potassium intakes based on urine assays. Vector Xij has a 4 x 4 covariance matrix

The following correlation coefficients may be estimated from these matrices.

Correlation between measurement errors for sodium and potassium intakes:


Correlation between underlying intake and sodium and potassium measurements:




Underlying correlation between sodium and potassium:

Within-subject correlation between repeated measurements:




These parameters may be estimated directly by inserting estimates from fitted correlation matrices into expressions. Within the BUGS algorithm, the posterior distributions of estimates can be generated to yield posterior medians, modes, and credible intervals.


    ACKNOWLEDGMENTS
 
This research was supported by grants from the National Institute of Aging (R01 AG-09771, R01 AG-09773, R01 AG-09799, and P60AG-10484) and the National Heart, Lung, and Blood Institute (R01 HL-48642 and R03 HL-60197).


    NOTES
 
Reprint requests to Dr. Mark A. Espeland, Department of Public Health Sciences, Wake Forest University School of Medicine, Medical Center Boulevard, Winston-Salem, NC 27157 (e-mail: mespelan{at}wfubmc.edu).


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 Conclusions
 APPENDIX
 REFERENCES
 

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Received for publication September 8, 1999. Accepted for publication August 23, 2000.