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Unformatted text preview: PubH 7405: REGRESSION ANALYSIS LR: BIOMEDICAL APPLICATIONS In applications, sometimes data are classified into groups, and within each group a separate regression model of Y on X may be postulated . For example, the regression of forced expiratory volume (Y) on age (X) may be considered separately for men in different occupational groups because different occupations may have different effects on the lung health of workers . Differences between the regression lines, especially the slopes , are our primary interest. AN EXAMPLE Suppose we study vital capacity among men working in the cadmium industry; the main purpose of the study was to see whether exposure to fumes was associated with a change in respiratory function . However, we must take into account the effect of age because respiratory performance declines with age . The men in the sample were divided into three groups : (1) those who were exposed for at least 10 years , (2) those who were exposed for less than 10 years , and (3) Control group consisted of men not exposed to fumes . We then consider three regression lines : Y = Vital Capacities (liters) versus X = Age It is wellknown that respiratory test performance declines with age. But the question is whether being exposed to fume in the cadmium industry would accelerate the declining process . That is to focus on the difference of slopes . We could consider to merge groups 1 and 2 then compare to group 3; however, the result would be masked by a phenomenon called healthy worker effects (healthier people are more likely to choose more dangerous occupations). The main focus could be placed on the comparison of group 1 versus group 2 by showing an attenuation of health worker effects : the decline is steeper in group 1 ( longer exposure ) than in group 2 ( shorter exposure ). hen possible differences between the regression lines, for example the slopes, are of interest, there are two possibilities: (1) If the slopes clearly differ , from one group to another, then we have no choice but to draw separate groupspecific inferences . (2) If the slopes do not differ , the lines are parallel with a common slope; that common slope can and should be estimated using combined data from all groups. GROUPSPECIFIC RESULTS Suppose there are k groups with n i pairs of observations (i.e. correlation data) in the i th group; a regression line is fitted with the following results for the slope: i i i i x x MSE b s b 2 _ 1 2 1 ) ( ) ( slope Estimated GENERAL METHODOLOGY Let w i be the inverse of the variance of the i th slope; under the null hypothesis that the true slopes of the k groups are all equal , the following statistic G follows approximately a Chisquare distribution with (k1) degrees of freedom : 2 ~ 1i i ) b (b w G 1 1 1 ~ 1 2 ) ( 1 i i i i i w b w b b s w Similar to ANOVA Weighted average The use of this G statistic is similar to the F statistic in oneway ANOVA: Deviations...
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This note was uploaded on 11/21/2011 for the course PUBH 7405 taught by Professor Staff during the Fall '08 term at Minnesota.
 Fall '08
 Staff

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