# Uses of Screener Estimates in the Cancer Control Supplement

- Introduction
- Variance-Adjustment Factor
- Attenuation of Regression Parameters Using Screener Estimates
- References

## Introduction

Dietary intake estimates derived from the Five-Factor Screener are rough estimates of usual intake of fruits and vegetables, fiber, calcium, servings of dairy, and added sugar. These estimates are not as accurate as those from more detailed methods (e.g., 24-hour recalls). However, validation research suggests that the estimates may be useful to characterize a population's median intakes, to discriminate among individuals or populations with regard to higher vs. lower intakes, to track dietary changes in individuals or populations over time, and to allow examination of interrelationships between diet and other variables. In addition, diet estimates from the Cancer Control Supplement (CCS) could be used as benchmark national data for smaller surveys, for example, in a particular state.

## Variance-Adjustment Factor

### What is the variance adjustment estimate and why do we need it?

Data from the Five-Factor Screener are individuals' reports about their intake and, like all self-reports, contain some error. The algorithms we use to estimate servings of fruits and vegetables, grams of fiber, mg of calcium, servings of dairy, and teaspoons of added sugar calibrate the data to 24-hour recalls. The screener estimate of intake represents what we expect the person would have reported on his 24-hour recall, given what he reported on the individual items in the screener. As a result, the mean of the screener estimate of intake should equal the mean of the 24-hour recall estimate of intake in the population. (It would also equal the mean of true intake in the population if the 24-hour recalls were unbiased. However, there are many studies suggesting that recalls underestimate individuals' true intakes).

When describing a population's distribution of dietary intakes, the parameters needed are an estimate of central tendency (i.e. mean or median) and an estimate of spread (variance). The variance of the screener, however, is expected to be smaller than the variance of true intake, since the screener prediction formula estimates the conditional expectation of true intake given the screener responses, and in general the variance of a conditional expectation of a variableis smaller than the variance ofitself. As a result, the screener estimates of intake cannot be used to estimate quantiles (other than median) or prevalence estimates of true intake without an adjustment. Procedures have been developed to estimate the variance of true intake using data from 24-hour recalls, by taking into consideration within person variability^{1,2}. We extended these procedures to allow estimation of the variance of true intake using data from the screener. The resulting variance adjustment factor adjusts the screener variance to approximate the variance of true intake in the population.

### How did we estimate the variance adjustment factors?

We have estimated the adjustment factors in the two external validation datasets available to us: the Observing Protein and Energy Nutrition Study (OPEN) and the Eating at America's Table Study (EATS). The results indicate that the adjustment factors differ by gender and dietary variable. Under the assumption that the variance adjustment factors appropriate to the 2005 National Health Interview Study (NHIS) are similar to those in these two external datasets, the variance-adjusted screener estimate of intake should have variance closer to the estimated variance of true intake that would have been obtained from repeat 24-hour recalls.

Nutrient | Gender | Variance Adjustment Factor |
---|---|---|

Total Fruit & Vegetable Intake | Male | 1.2 |

Female | 1.0 | |

Fruit & Vegetable Intake (excluding fried potatoes) |
Male | 1.2 |

Female | 1.0 | |

Fiber Intake | Male | 1.4 |

Female | 1.2 | |

Calcium Intake | Male | 1.0 |

Female | 0.9 | |

Dairy Intake | Male | 1.1 |

Female | 1.1 | |

Added Sugar Intake | Male | 1.5 |

Female | 1.3 |

### How do you use the variance adjustment estimates?

To estimate quantile values or prevalence estimates for an exposure, you should first adjust the screener so that it has approximately the same variance as true intake.

Adjust the screener estimate of intake by:

- multiplying intake by an adjustment factor (an estimate of the ratio of the standard deviation of true intake to the standard deviation of screener intake); and
- adding a constant so that the overall mean is unchanged.

The formula for the variance-adjusted screener is:

variance-adjusted screener = (variance adjustment factor) * (unadjusted screener - mean_{unadj scr.}) + mean_{unadj scr.}

This procedure is performed on the normally distributed version of the variable (i.e., Pyramid servings of fruits and vegetables is square-rooted; fiber is cube rooted; calcium is quarter-rooted; dairy is square-rooted; and added sugar is cube rooted). The results can then be back-transformed (e.g. cubed, squared, etc.) to obtain estimates in the original units.

The variance adjustment procedure is used to estimate prevalence of obtaining recommended intakes for the 2000 NHIS in:

Thompson FE, Midthune D, Subar AF, McNeel T, Berrigan D, Kipnis V. Dietary intake estimates in the National Health Interview Survey, 2000: methodology, results, and interpretation.J Am Diet Assoc2005 Mar;105(3):352-63; quiz 487. [View Abstract]

### When do you use variance adjustment estimates?

The appropriate use of the screener information depends on the analytical objective. Following is a characterization of suggested procedures for various analytical objectives.

Analytical Objective | Procedure |
---|---|

Estimate mean or median intake in the population or within subpopulations. | First, transform the variable to normalized version. Then, use the unadjusted screener estimate of intake. |

Estimate quantiles (other than median) of the distribution of intake in the population; estimate prevalence of attaining certain levels of dietary intake. | Use the variance-adjusted screener estimate. |

Classify individuals into exposure categories (e.g., meeting recommended intake vs. not meeting recommended intake) for later use in a regression model. | Use the variance-adjusted screener estimates to determine appropriate classification into categories. |

Use the screener estimate as a continuous covariate in a multivariate regression model. | First, transform the variable to normalized version. Then, use the unadjusted screener estimate. |

## Attenuation of Regression Parameters Using Screener Estimates

When the screener estimate of dietary intake is used as a continuous covariate in a multivariate regression, the estimated regression coefficient will typically be attenuated (biased toward zero) due to measurement error in the screener. The "attenuation factor"^{3} can be estimated in a calibration study and used to deattenuate the estimated regression coefficient (by dividing the estimated regression coefficient by the attenuation factor).
We estimated attenuation factors in the OPEN and EATS studies (see below). If you use these factors to deattenuate estimated regression coefficients, note that the data come from relatively small studies that consist of fairly homogeneous samples (primarily white, well-educated individuals).

Gender | Square-Root Fruit & Veg | Square-Root Fruit & Veg (excluding French Fries) | Cube-Root Fiber | Quarter-Root Calcium | Square-Root Dairy | Cube Root Added Sugar |
---|---|---|---|---|---|---|

Men | 0.75 | 0.79 | 0.75 | 0.57 | 0.80 | 0.93 |

Women | 0.64 | 0.66 | 0.67 | 0.45 | 0.73 | 0.88 |

If you categorize the screener values into quantiles and use the resulting categorical variable in a linear or logistic regression, the bias (due to misclassification) is more complicated because the categorization can lead to differential misclassification in the screener^{4}. Although methods may be available to correct for this^{5,6}, it is not simple, nor are we comfortable suggesting how to do it at this time.

Even though the estimated regression coefficients are biased (due to measurement error in the screener or misclassification in the categorized screener), tests of whether the regression coefficient is different from zero are still valid. For example, if one used the SUDAAN REGRESS procedure with fruit and vegetable intake (estimated by the screener) as a covariate in the model, one could use the Waldstatistic provided by SUDAAN to test whether the regression coefficient were statistically significantly different from zero. This assumes that there is only one covariate in the model measured with error; when there are multiple covariates measured with error, the Waldtest that a single regression coefficient is zero may not be valid, although the test that the regression coefficients for all covariates measured with error are zero is still valid.

## References

- National Research Council. Nutrient Adequacy: Assessment Using Food Consumption Surveys. Washington, DC: National Academy Press, 1986.
- Institute of Medicine. Dietary Reference Intakes: Applications in Dietary Assessment. Washington, DC: National Academy Press, 2000.
- Rosner B, Willett WC, Spiegelman D.
Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error.
*Stat Med*1989 Sep;8(9):1051-69; discussion 1071-3. - Flegal KM, Keyl PM, Nieto FJ.
Differential misclassification arising from nondifferential errors in exposure measurement.
*Am J Epidemiol*1991 Nov 15;134(10):1233-44. - Flegal KM, Brownie C, Haas JD.
The effects of exposure misclassification on estimates of relative risk.
*Am J Epidemiol*1986 Apr;123(4):736-51. - Morrissey MJ, Spiegelman D.
Matrix methods for estimating odds ratios with misclassified exposure data: extensions and comparisons.
*Biometrics*1999 Jun;55(2):338-44.

Last Modified: 11 Apr 2014