Inspection paradox and performance indicators

[Clive Downs]

Hi everyone,

Is the example data listed below a variant of the inspection paradox?

1. patients have to undergo reviews on a specified schedule - first at 4
weeks after admission, next after 3 months, then at 6-month intervals.

2. there is a performance indicator based on patients' active participation
in reviews:  in the data, the 'pfail' variable =  0 for participation, 1
for failed to participate. The indicator is defined on the percent of
patients participating in *all* the reviews carried out over the period (ie
they must have participated in all reviews to count in the denominator of
the indicator. (denominator is count of patients who participated in all
reviews, numerator is all patients in the dataset)

3. usually the indicator is measured over a full year; the example data
covers the part year from 1 April 08 to end November. When aggregated by id
the indicator is 153/178 = 86%.

4. when the indicator is measured for one month only, (eg November) the
result is a higher value for the indicator (eg for November it is 40/41 =
97.6%. (leaving aside for the moment that it is not good to calculate
percentages with fewer than 100 cases.).

5. it is possible that whenever this is calculated for a month, the result
will tend to underestimate the 'regular' (ie calculated over one year)
value.

Intuitively, if one examines patient reviews over a short period, relative
to the review schedule, each patient will have less opportunity to fail.
Just as in the inspection paradox, if you wait for a bus, it is likely you
will have to wait longer than the listed frequency suggests.

Thanks,

Clive.

* set up data - 318 records for reviews from 1 Apr 2008 to 30 Nov. 2008.
*--------------------------------------------------------------------.

DATA LIST FREE/  id(A6)  revdate(ADATE)  Pfail.
BEGIN DATA

445 6/23/2008 0
5358 5/16/2008 0
5358 11/27/2008 0
30961 6/16/2008 0
30961 9/15/2008 0
60956 5/2/2008 0
60956 9/22/2008 0
86190 8/13/2008 0
86193 6/12/2008 0
89551 6/9/2008 0
89551 11/13/2008 0
89772 4/24/2008 0
89772 9/15/2008 0
89775 9/11/2008 0
90478 6/20/2008 0
90478 7/30/2008 0
90478 9/18/2008 0
92485 7/18/2008 0
92485 11/5/2008 0
110695 6/2/2008 0
110695 8/11/2008 0
110815 5/19/2008 0
111688 5/6/2008 0
111688 10/8/2008 0
118660 5/6/2008 0
118660 7/29/2008 0
118660 10/13/2008 0
118663 7/16/2008 0
119467 4/24/2008 0
119467 8/19/2008 0
119467 11/4/2008 0
124210 4/10/2008 0
124210 7/2/2008 0
124210 9/26/2008 0
125980 6/5/2008 0
130518 9/24/2008 0
130779 9/1/2008 0
131208 4/29/2008 0
142853 9/8/2008 0
156439 4/1/2008 0
156439 9/23/2008 0
156628 9/3/2008 0
156817 5/14/2008 0
156817 11/12/2008 0
159777 4/10/2008 0
159777 5/13/2008 0
160857 8/7/2008 0
167217 7/15/2008 0
167678 4/18/2008 0
167678 5/19/2008 0
167678 7/24/2008 0
167678 10/21/2008 0
172389 4/7/2008 0
172389 10/2/2008 1
174980 4/21/2008 0
174980 10/6/2008 0
178877 6/2/2008 0
178877 11/19/2008 0
180194 9/22/2008 0
181113 5/9/2008 0
181113 7/9/2008 0
181113 9/19/2008 1
181113 11/3/2008 1
181114 5/14/2008 0
181114 7/9/2008 0
182509 5/19/2008 0
182509 7/22/2008 0
182509 10/14/2008 0
182509 11/21/2008 0
183448 7/24/2008 1
184748 8/7/2008 0
193292 4/30/2008 0
193292 7/8/2008 0
193982 6/4/2008 0
193982 11/10/2008 0
195649 4/8/2008 1
195649 4/8/2008 0
195649 7/9/2008 0
198226 7/9/2008 0
198226 7/9/2008 0
198267 4/25/2008 0
198267 10/1/2008 0
201079 5/22/2008 0
201079 11/4/2008 0
203133 6/12/2008 0
203539 6/24/2008 0
203539 9/19/2008 0
205446 8/13/2008 0
205446 9/22/2008 0
205446 11/17/2008 0
207033 4/1/2008 0
207033 9/23/2008 0
207383 7/21/2008 0
207384 9/4/2008 0
207385 7/2/2008 0
207385 11/13/2008 0
207386 7/30/2008 0
210501 6/30/2008 0
212203 11/21/2008 0
215423 7/19/2008 0
215423 8/18/2008 0
215900 6/18/2008 0
215900 11/24/2008 0
220365 9/1/2008 0
220374 9/1/2008 0
220408 6/25/2008 0
220408 11/11/2008 0
221105 5/2/2008 0
221105 7/25/2008 0
221462 4/7/2008 0
221462 10/2/2008 0
223348 5/6/2008 0
223348 7/21/2008 0
223513 8/7/2008 0
225061 7/9/2008 1
225086 5/6/2008 1
225086 11/5/2008 0
225520 7/11/2008 0
225520 8/29/2008 0
225520 11/20/2008 0
225841 6/4/2008 1
225841 11/19/2008 0
225907 6/16/2008 0
225907 6/16/2008 0
225907 10/20/2008 0
226645 6/26/2008 0
226645 11/10/2008 0
226646 4/3/2008 0
226646 9/22/2008 0
226646 11/24/2008 0
226990 4/14/2008 0
226990 6/27/2008 0
226990 10/10/2008 0
226990 11/27/2008 0
227257 6/20/2008 0
227257 11/25/2008 0
227303 7/25/2008 0
228188 7/15/2008 0
228188 10/6/2008 0
228283 4/3/2008 0
228283 9/22/2008 0
228283 11/24/2008 0
228394 6/5/2008 0
228395 6/5/2008 0
228396 4/23/2008 0
228396 10/16/2008 0
228816 4/1/2008 0
228816 9/25/2008 0
229930 6/3/2008 0
230060 8/6/2008 0
230060 10/9/2008 0
230827 7/8/2008 0
230858 7/14/2008 0
230971 5/19/2008 0
231103 4/7/2008 0
231103 6/19/2008 0
231103 9/9/2008 0
231106 5/1/2008 0
231106 9/22/2008 0
231207 6/17/2008 0
231208 6/17/2008 0
231208 11/25/2008 0
232317 6/9/2008 0
232317 10/20/2008 0
232335 5/14/2008 0
232335 7/3/2008 0
232662 5/19/2008 0
232662 10/22/2008 0
233065 9/22/2008 0
233096 5/19/2008 0
234221 4/18/2008 1
234221 10/1/2008 1
234367 4/4/2008 0
234367 9/29/2008 0
234833 4/3/2008 0
234833 9/22/2008 0
234833 11/24/2008 0
234856 5/6/2008 0
234856 7/21/2008 0
235564 9/9/2008 1
236678 6/5/2008 1
236678 7/15/2008 1
236678 10/2/2008 0
237692 5/7/2008 0
237692 7/8/2008 0
237692 10/10/2008 0
237693 7/25/2008 0
237774 6/25/2008 0
237774 11/11/2008 0
239979 9/22/2008 0
239981 9/22/2008 0
241125 7/30/2008 0
241126 8/19/2008 0
241127 7/29/2008 0
241291 4/1/2008 0
241291 6/27/2008 0
241291 9/10/2008 0
241416 5/23/2008 0
242336 5/27/2008 0
243205 6/18/2008 0
243205 11/24/2008 0
243664 5/9/2008 0
243664 8/22/2008 0
243664 11/14/2008 0
243980 4/3/2008 0
243980 9/30/2008 0
244371 6/2/2008 0
244383 6/26/2008 0
244383 9/25/2008 0
244840 4/15/2008 1
244840 6/25/2008 0
245168 5/20/2008 0
245168 10/20/2008 0
246481 5/12/2008 1
246780 5/19/2008 0
247225 6/16/2008 0
247225 11/12/2008 0
250164 7/8/2008 0
250971 6/11/2008 1
250971 11/4/2008 0
252333 5/20/2008 0
252333 10/20/2008 0
252468 6/16/2008 0
252468 11/3/2008 0
252470 6/16/2008 1
252470 10/31/2008 0
252614 7/7/2008 0
252614 10/28/2008 0
255645 4/23/2008 0
255645 7/14/2008 0
255846 5/9/2008 1
255846 10/1/2008 0
255868 5/21/2008 1
256204 9/17/2008 0
256204 9/17/2008 0
256816 6/19/2008 1
256816 8/6/2008 1
256816 11/5/2008 0
257389 8/19/2008 1
258147 6/3/2008 1
258175 7/2/2008 0
258175 9/29/2008 0
258640 7/15/2008 1
258640 10/6/2008 0
258642 4/24/2008 0
258642 10/23/2008 0
258642 11/12/2008 0
258899 10/23/2008 0
259102 7/1/2008 0
259102 11/27/2008 0
259103 7/1/2008 0
259103 11/27/2008 0
259104 7/1/2008 0
259104 11/27/2008 0
259187 6/30/2008 0
259187 9/17/2008 0
260086 6/6/2008 1
260882 7/28/2008 0
262147 6/10/2008 0
262147 10/20/2008 0
264116 4/30/2008 1
264116 7/17/2008 1
264549 6/9/2008 0
264549 11/12/2008 0
500227 7/18/2008 1
500227 9/26/2008 1
501041 10/28/2008 0
501535 5/2/2008 1
501535 7/28/2008 1
502500 6/4/2008 1
502500 7/4/2008 0
503269 5/30/2008 0
504135 4/9/2008 0
504135 4/16/2008 0
504135 9/1/2008 0
504817 5/15/2008 0
504923 4/16/2008 0
504923 9/3/2008 0
509280 4/15/2008 0
509280 10/8/2008 0
509473 7/2/2008 0
509603 4/2/2008 0
509603 7/7/2008 0
511094 4/28/2008 0
511094 10/15/2008 0
511511 4/22/2008 0
511511 7/22/2008 0
512096 5/21/2008 0
512096 9/9/2008 0
514882 7/17/2008 0
514882 10/1/2008 0
516350 4/11/2008 0
516350 9/25/2008 0
516353 4/11/2008 0
516353 9/26/2008 0
516943 4/22/2008 0
516943 7/17/2008 0
519869 5/15/2008 0
520351 7/14/2008 0
520746 8/29/2008 0
520961 7/9/2008 0
521735 6/11/2008 0
521735 11/20/2008 0
522052 6/9/2008 0
522052 11/24/2008 0
522499 5/28/2008 0
522499 9/25/2008 0
522504 5/28/2008 0
522504 9/25/2008 0
523821 5/1/2008 0
523821 7/16/2008 0
524308 6/3/2008 0
524308 8/28/2008 0
525410 7/31/2008 0
525410 10/20/2008 0
526750 10/2/2008 0
526750 11/17/2008 0
527832 11/20/2008 0
END DATA.

* work out failures for year to end Nov. aggregated by id.
*--------------------------------------------------------.
DATASET DECLARE aggfail_year.
AGGREGATE
  /OUTFILE='aggfail_year'
  /BREAK=id
  /failures = MAX(Pfail).

* work out failures for November only.
*----------------------------------------------------.

* select if review date is in November.
USE ALL.
COMPUTE filter_$=(revdate > DATE.DMY(01,11,2008)).
FORMAT filter_$ (f1.0).
FILTER BY filter_$.
EXECUTE .
* frequencies (percentage of) for failures.
FREQUENCIES
  VARIABLES=Pfail
  /ORDER=  ANALYSIS .

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