USING THE WEIGHTED INTERVAL MIDPOINT ESTIMATOR (WIME) TO ESTIMATE A POPULATION MEAN FROM INTERVAL DATA
Author(s)
Magyar AF*1;Wang B1, Furnback WE2 1Alliance Life Sciences, Somerset, NJ, USA, 2Alliance Life Sciences Consulting Group, Jersey City, NJ, USA
OBJECTIVES: In survey questions where the variable of interest is quantitative, responses often involve selecting one of several mutually exclusive intervals in which the variable lies within (denoted interval data). This precludes one from using many of the popularly reported measures of center (mean, median, mode, etc.). To this end, a simple estimator is proposed to estimate the population mean, µ, when the data are intervaled and its properties are studied. METHODS: For estimation of µ given intervaled data, we propose the Weighted Interval Midpoint Estimator (WIME). Expressions for its expected value and variance are derived. These are then calculated for normal distributions and a χ2distribution on 1 degree of freedom using various interval configurations. Bootstrapping methods are then proposed to obtain estimates of the sampling distribution of the WIME as well as the sample mean given the interval counts. RESULTS: In general, the WIME is a biased estimator of µ; this bias is the same for all sample sizes. Simple bounds for the bias can derived. Both the bias and variance of the estimator depend on the choice of intervals. In the case of the normal distribution, equal-length intervals produce estimates with seemingly no bias and variance slightly above that of the sample mean as opposed to a non-equal-length configuration, even if the intervals are not symmetric about µ. For the χ2distribution on 1 degree of freedom, using equal-length intervals produces estimates with less bias and variance than when using non-equal-length intervals. CONCLUSIONS: While the WIME is a quick and easy method to estimate µ, its performance depends on the intervals chosen. Thus prudence must be taken when selecting them. In the event no prior information exists to guide the process, equal-length intervals seem to be a safe fallback.
Conference/Value in Health Info
2013-05, ISPOR 2013, New Orleans, LA, USA
Value in Health, Vol. 16, No. 3 (May 2013)
Code
PRM200
Topic
Methodological & Statistical Research
Topic Subcategory
Confounding, Selection Bias Correction, Causal Inference
Disease
Multiple Diseases