Estimating the long-term functional burden of osteoporosis-related fractures

We include only cases where the Medicare fracture date of service was prior to the HRS interview date.

See http://​hrsonline.​isr.​umich.​edu/​sitedocs/​userg/​dr-008.​pdf for a detailed list of the questions used from year to year. Generally, the questions are framed as “Because of a health problem, do you have any difficulty…” The specific difficulties for questions used in the mobility index are: (1) “with walking one block,” (2) “with walking several blocks,” (3) “with walking across a room,” (4) “climbing one flight of stairs without resting,” and (5) “climbing several flights of stairs without resting.”

See http://​hrsonline.​isr.​umich.​edu/​sitedocs/​userg/​dr-008.​pdf for a detailed list of the questions used from year to year. Generally, the questions are framed as “Because of a health problem, do you have any difficulty…” The specific difficulties for questions used in the gross motor skills index are: (1) “with walking one block,” (2) “with walking across a room,” (3) “climbing one flight of stairs without resting,” (4) “getting in or out of bed,” and (5) “bathing or showering.”

See http://​hrsonline.​isr.​umich.​edu/​sitedocs/​userg/​dr-008.​pdf for a detailed list of the questions used from year to year. Generally, the questions are framed as “Because of a health problem, do you have any difficulty…” The specific difficulties for questions used in the fine motor skills index are: (1) “with picking up a dime from a table,” (2) “with eating, such as cutting up your food,” and (3) “with dressing, including putting on shoes and socks.”

For the 1996 match, we dropped 127 comparison cases that were not within the common support (out of 3737 possible comparison cases). All 91 fracture cases in 1996 were within the common support. For the 1998 match, we dropped 263 comparison cases that were not within the common support (out of 3237 possible comparison cases). We dropped one fracture case in 1998 that was not within the common support (out of 114 fracture cases). For the 2000 match, we dropped 415 comparison cases that were not within the common support (out of 4454 possible comparison cases). All 85 fracture cases in 2000 were within the common support. For the 2002 match, we dropped 305 comparison cases that were not within the common support (out of 4654 possible comparison cases). All 100 fracture cases in 2002 were within the common support. For the 2004 match, we dropped 158 comparison cases that were not within the common support (out of 4568 possible comparison cases). All 82 fracture cases in 2004 were within the common support. For the 2006 match, we dropped 434 comparison cases that were not within the common support (out of 4229 possible comparison cases). All 91 fracture cases in 2006 were within the common support. For the 2008 match, we dropped 363 comparison cases that were not within the common support (out of 4032 possible comparison cases). All 88 fracture cases in 2008 were within the common support. For the 2010 match, we dropped 339 comparison cases that were not within the common support (out of 3910 possible comparison cases). All 97 fracture cases in 2010 were within the common support.

We explored using additional baseline covariates for propensity score matching, including whether individuals smoked (ever smoked), drank alcoholic beverages (measured as counts or whether respondent had 3+ per day), and engaged in 3+ hours of vigorous physical activities per week. These covariates were all statistically insignificant in predicting a fracture and did not affect the matching. Therefore, we chose the more parsimonious model with fewer covariates.

Here is a simplified version of the regression-adjusted DD model:

where \( \hat{\beta_1} \) is our estimated difference-in-difference; post = 1 in the period after the fracture and 0 in the pre-period; fracture = 1 for fracture cases and 0 for comparison cases; X is a vector of individual level (time-invariant controls). It does not matter which time-invariant covariates are included in X (or not included), because they are differenced out. To see this, consider what \( \hat{Y_{\mathrm{i}}} \) is for both fracture and comparison cases in the pre- and post-periods; then examine the first differences (last column) where we look at the change in Y for each group.