Concept: Full Time Equivalent (FTE) Physicians - Calculations
Last Updated: 2000-03-06
Let us have three regions with the same output.
Area A is served exclusively by a large number of physicians with small practices (typical of remote regions).
Area B is served exclusively by "typical" full time physicians (FTE=1).
Area C is served by one physician with a very large practice.
Let us also assume that the lower benchmark=40 and the upper=60.
For illustrative purposes, there is a one to one relationship between payments and output.
Table 1: FTE Calculations with Variability
Area A Area B Area C output FTE output FTE output FTE 30 0.75 (30/40) 40 1.0 100 1.51 (1+ln(100/600)) 35 0.875 (35/40) 60 1.0 - - 35 0.875 (35/40) - - - - 100 2.50 100 2.0 100 1.51 While the three areas have the same output of 100, the workloads (output/total FTE) are 40, 50 and 66 respectively.
Should the areas not have had a "bias" distribution, that is, a relatively similar proportion of physicians by practice size, the workload would have been similar.
The full potential of the national F.T.E (or any other for that matter) cannot be realized if the investigator does not fully understand the premises behind the algorithm:
Homogeneity
Are we sure that the practices' profile and fee structure are similar for the groups under consideration? Only the yes answer will validate using payments as a proxy for workload.
Distribution
A perfect normal distribution is the ideal situation. Badly skewed distributions are the norm. The distribution underlying the national algorithm is skewed towards lower values. (recall the 4 quarters rule in the benchmark calculation).
A Bimodal distribution, two groups gravitating around two central values, is a good indication of poor homogeneity. That was the case with Internists and Pediatricians. In fact, in the case of pediatricians, there were two distinct groups: a) the GFTs, working for the University and b) the generalists working in the community. The payments captured for the former group was extremely low as their earnings are mostly salaried/teaching. A mechanical application of the algorithm produces nonsensical results.Benchmark Stability
The larger the number of observations the more stable the benchmarks. This has to do with the "positional" nature of the benchmarks. Unlike the mean or the standard deviation, which describes certain attributes of the distribution as a whole, the nth percentile is simply the value below which n/100% of the observations are found. Benchmark stability has to do with the difference between ordered values, or the magnitude of the change if the benchmark were defined to be the value at the nth+1 percentile instead of the nth.
Table 2: Difference Between Ordered Values
position nth-3 nth-2 nth-1 nth nth+1 nth+2 nth+3
value group 1 10 10.2 10.4 10.5 10.5 10.6 10.7
value group 2 10 15 25 40 50 55 60
The benchmark defined by nth percentile is much more stable for group1. It makes little difference whether the benchmark happened to be defined by the nth, nth+1...nth+n, or by nth, nth-1...nth-n percentile. In turn, the magnitude of the difference between nth and nth+1 observation is influenced by the number of physicians in the distribution. The larger the number of observations, the more stable the percentiles, the benchmarks, and hence the more consistent the FTE counts. In fact, for the year 1994, the number of GP claiming in each of the quarters was 821, and the average percentage change from the Nth to Nth+1 position was .009%. In contrast, for specialists the number of mds ranged from 71 to 199, depending upon the specialty, the average percentage change was from 6 to 10%.Consistency and Changes Over Time
While the issues of homogeneity, nature of the distribution and benchmark stability will define the "true" picture, a good understanding of changes over time will ensure a consistent count of physician supply throughout the years.
In Manitoba, since 1991, there has been a steady decline in Physician's earnings, that is, the income that we are able to capture from the database. (for many reasons). Does the decline on payments, the variable at the algorithm's core, change the FTE calculation...? The short answer is a qualified no, this is because the income decline happened to be across the board, random, and it introduced no bias.
The following example illustrates a situation where income in year 2 increased across the board, twice as much relative to year 1.
Table 3: FTE Calculations
year p10 p20 p30 p40 p50 p60 p70 p80 p90 p100 total 1$
FTE
1
0.25
2
0.50
3
0.75
4
1
5
1
6
1
7
1.15
8
1.29
9
1.41
10
1.51
55 income
9.86 f.t.e.2$
FTE
2
0.25
4
0.50
6
0.75
8
1
10
1
12
1
14
1.15
16
1.29
18
1.41
20
1.51
110 income
9.86 f.t.e.Obviously, the income increase does not alter any of the elements underlying the distribution, that is, the number of observations, and the relative evaluation of an individual relative to everybody else. Notice that the increase (decrease) of income would have a different meaning if it were due to increases (decreases) on prices or quantity alone. In the former case (prices), the same number of physicians would be operating at a constant workload but at different price levels. There would be no changes in FTE nor in workload. In the latter case (quantity) the same number of physicians would operate at a constant price but at different workload levels. No changes in FTE but the workload would be twice as much as the first year.
For completeness sake, let us examine the case where everybody gets a constant increase (decrease) in income. In the following example, income in year 2 increases by a constant of, let us say, $2.
Table 4: FTE Calculations Constant Increase
year p10 p20 p30 p40 p50 p60 p70 p80 p90 p100 total 1$
FTE1
0.252
0.503
0.754
15
16
17
1.158
1.299
1.4110
1.5155 income
9.86 f.t.e.2$
FTE3
0.504
0.665
0.836
117
18
19
1.1110
1.2211
1.3112
1.4075 income
10.03 f.t.e.
The increase from 9.86 to 10.03 FTE cannot be validated. If we assume that the $2 increase in income is due to prices alone, then in year #2, we would expect the same number of physicians working at the same workload level of year #1.
The discussion above shows the need for a comprehensive understanding of the factors determining the FTE final count, as well as the need for testing for significant changes in the distribution before changes of FTE over time can be validated.
Changes FTE=f(x) changes (heads, income (prices, quantity))
Changes in heads (number of observations) affects the final FTE counts in following ways:
new benchmark = ((income at p40) + (income at p40+1))/2
fiscal year | income (millions) | FTE (n=742) |
91/92 | 90.26 | 684.50 |
92/93 | 91.06 | 680.95 |
93/94 | 88.25 | 685.52 |
94/95 | 83.08 | 675.35 |
If the income fluctuation is the same across the board, then we should expect the benchmark to behave similarly.
Table 6: Benchmark
fiscal year | income (millions) | lower benchmark (thousand) | upper benchmark (thousand) |
91/92 | 90.26 | 97.5 | 138.0 |
92/93 | 91.06 | 100.2 +3 | 141.0 +3 |
93/94 | 88.25 | 95.6 -5 | 136.0 -5 |
94/95 | 83.08 | 87.6 -8 | 130.0 -6 |
Example: Lower income
It was already suggested that the decrease from 685 to 675 FTE in 1994 relative to 1993, was largely due to changes in the low income distribution. Given the fact that the lower income part of the algorithm is a linear relation (sum of FTE=sum of (income/lower benchmark)), in a "perfect" income distribution, we should expect the average FTE to be =0.50.
The following table shows the behaviour of the low income group.
Table 7: FTE Low Income
year heads FTE average FTE over heads average months active per year 91 296 144 0.487 9.69 92 296 144 0.506 10.48 93 296 151 0.511 10.64 94 296 138 0.465 9.74 Clearly, the decrease in 1994, from 151 to 138 FTE, is due to a drastic shift of the distribution towards lower income (quantity) values ... Similarly, the increase in 1992 from 144 to 150 FTE is due to a shift towards higher income (quantity) values. In the latter case, the increase (1992) represents the "full year" work of those who started their practice in 1991. In the former case, the decrease represents the "part year" work of those who close their practice down in 1994. Whether they were a newcomer in 1991, or whether they departed in 1994, the lower FTE reflects their "part year" practices. Still, the extreme low average FTE value for 1994 suggests an overall decrease in quantity. If we break up the 1994 FTE of those who departed and those who stayed, we would be able to fully account and explain the changes of 1994 relative to 1993.
Table 8: Departing and Full Year FTE
year heads FTE average FTE over heads average months active 93 296 151 0.511 10.64 departing 94 31 9 0.286 5.25 full year 94 265 129 0.486 10.24
The decrease of 13 (151-138) FTE in 1994, is due to 9 FTE who retired sometime in 1994. We can predict that an extra 4 FTE departed as well but have not formalized status with Manitoba Health (i.e.: number still active). The decrease in the average number of months active reinforces the argument for the relationship FTE-quantity.
We have proved for the lower income segment of the algorithm the following:
- The income fluctuations do not alter the algorithm's consistency and hence comparisons over time are sound.
- When heads are held constant, changes in FTE are function of changes in income (quantity).
Example: Upper Income (non linear relationship)
The logarithmic nature of the function makes comparison over time misleading and difficult to interpret. By definition, the marginal increase of log(y) is decremental.
Table 9: Upper Income Non-Linear Relationship
Y % change FTE 1+ln(y) % change ln(y) 2 - 1+ 0.69 - 3 1.5 1+ 1.09 1.23 5 1.6 1+ 1.61 1.25 9 1.8 1+ 1.20 1.22 11 1.2 1+ 2.34 1.04 30 12.93 The practical implication is that, keeping quantity (Y) constant, the sum of ln(Y) (FTE) will depend of the "shape" of the distribution.
If we re-arrange the above distribution into one which less skewed...
Table 10: Less Skewed Distribution
Y FTE 1+ln(y) 4 1+1.39 5 1+1.61 5 1+1.61 8 1+2.08 8 1+2.08 30 13.77
The increase from 12.93 to 13.77 FTE is a non-sensical result since, as shown, changes of FTE is a f(x) of income (quantity) and, in this case income (Y) is constant.Changes in FTE
The following table illustrates changes in FTE from 1993 to 1994.
Table 11: Changes in FTE
year heads FTE number of claims highest income 93 296 384 3086 789673 94 296 388 3085 636065
The increase of 4 FTE cannot be validated. The number of claims (mostly ambulatory visits) for all practical purposes is the same. Notice, however, the huge decrease in the most extreme income value. Clearly, the distribution in 1994 shifted away from extreme values and the increase in FTE is just a "numerical" reflection of the logarithmic nature of the algorithm.
parent group | specialties | heads | FTE |
General Practitioners |
Urban Gps Rural Gps Emergency * - |
706 349 7 1062 |
498.535 305.577 4.303 808.415 |
Psychiatry | - | 133 | 111.049 |
Pediatrics |
specialists generalists ** - |
38 68 106 |
38.000 55.689 93.689 |
Obstetrics | - | 63 | 58.145 |
Medical |
internal specialists generalists ** neurology geriatrics * rheumatology dermatology - |
159 24 21 3 8 13 228 |
127.568 16.219 16.576 0.556 5.294 14.532 180.745 |
General Surgery | - | 81 | 67.454 |
Surgery |
thoracic plastic urology orthopedic neurology EENT (eyes) EENT (otorhino) EENT * (out prov) - |
10 12 17 32 5 35 23 4 138 |
10.23 12.21 17.05 28.57 3.68 33.19 14.34 0.02 119.28 |
Grand Total | - | 1811 | 1438.78 |
* mostly salaried (ie: we do not capture activity very well) |
** Internist and pediatrics generalist/specialists... see discussion on (f). |
1). Generalist
Internist Generalists:
first criteria----> mdcbloc '01' internal medicine. drcoke definition the most reliable of all external sources. (short list and no human error) Wpg specialist list and G.F.Ts lists least reliable: hundreds of numbers and several levels of errors. (names->numbers->fake numbers->typing.)
Most freq tariff----> office visits likely generalists. consults and specifics tariffs (ie:electros,lung function,etc) likely specialists.
Defining generalists:
first level---->if mdcbloc='01' & drcoke= no label or General and most freq tariff=office visits.
second level----> From D.r Coke list I know, for example, that Gastro has Office visits as the most frequent tariff... From the first level generalist definition I look for gastro in the gft or wpg or also certified list... if found I reclassify this physician from generalist to specialist. note: "Interested in" does not qualify for specialist.2) Pediatrics
Defining generalist:
first stage--> from the G.F.T list those without specialty (blank) or community, ambulatory or emergency are generalists.
second stage----> from "also certified" those with OTHER than blank or community are converted to specialists.
third stage---> those with most freq tariff OTHER than Office visits are converted to specialists.
fourth stage----> those with consult gt than 0 and ratio consult/amb ge 30% are converted to specialists. note: "also interested in" does not qualify
fifth stage----> phynos 1052, 1688, 2348, 2936 converted to specialists (dr brian postl' list)