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TABLE 6-Expected Change In Cohort Distribution from 1970
to 1974 with Varying Treatment Programs
1974 Ablily Gfoup
I 1I IMI tV V VI D
1970 .- --
Athlly 1 oliil
Group Pahlenis 89 72 95 133 1 18 .I- bO
í 221 73 46 46 27 11 0 18
II 112 12 16 26 27 19 3 9
111 114 4 9 18 34 32 8 9
IV 96 0 1 3 30 36 18 8
V 52 0 0 2 14 18 14 4
Vl 20 0 0 0 1 y 15 2
O 0 0 0 0 0 0 0 0
tion he will have in any future year he desires frtom which he
1may dctcrminuie whal resotirces he will neeccl to service those
patientis ofl' ourse. distaiit protjeclions haive .ess reilialbilily
than near projections.
Table 6 was generated. specifically for the 197(1 cohort
shown. fronm ai fiur-yeair probability matrix sintilar- o tilhat of
'I';ablc 5. Th'le next tIluce sets of' s .lupplcntli y inl'ornillion
are all shown in Tahblc 7. This table lisls the nimlber ol' years
a patient is expected to spend in each of the groips belfore
either dying or being placed in a community loster home (limited
to Grotip VI as per T'l'ihe 5) li'r the firsl time. 'The total
cost the patient is expecled to incur lip to itis eveni is also
shown and was derived hy multiplying the yeairs spent in
each group by the Unnual cost ol' the prograin selecied lfor
that group (from Table 5). L.;istly. the table gives the probability
of each of the outcomnes occurriíng lirsl.
Table 7 shows. for example. that a patient in the lowest
ability group (I) is expected to spend 4.4 years in thai group.
including time spent there due to regressing from higher
groups. abhot two and one-hall' year.s in Groups II aund 111
each, and about lfoutr and one-half yeai;s il Grotups IV ;and V
each before he either dies or is placed in a l'oster home. for a
total of 18.3 years spent in the hospital at a total cost of alnmost
$18)0.Wf. 'T'he likceilhood is ;ianlosl Iwicc as gilc;al ilitla Iic
will be placed in a foster home ralther than dying first. a very
positive prognosis for a patient in this group.
TABLE 7-Expected Stay Times in Years with Varying Treatment
Programs Until Either First Placement or
Death
Outcome
Abilily Group Total Probability
1970 . .........-
Ability Place-
Group 11 il IV V Years Cost (S/Pat) ment Death
I 4.4 2.2 2.8 4.6 4.5 18.3 179.500 .64 .36
II 1.1 2.8 2.6 4.9 4.8 16.2 166,400 .68 .32
111 0.4 0.9 3.2 5.1 5.1 14.6 155,400 .71 .29
IV 0.1 0.2 0.6 5.6 5.4 11.9 130,900 .76 .24
V 0.1 0.2 0.6 3.9 5.8 10.5 113,000 .79 .21
AJPH November, 1976, Vol. 66, No. 11
- 120 -
EVALUATION TECHNIQUES IN HEALTH SERVICES
Lastly. the Maitkova molel is not limit to ti ealinlgíed e'aitli;iiing only
Ihose progranms ' ith which ain ;igenc\ h;, erperience. For
insl;ince. il' ; ne%' moule ' opel';ran c'onditioning hecome%
av:d"l;¿lt oruh ;t a llotili;ítiil lo ;ill e\ ninI lllg pr'gra;l i' con-
Ceílípliatcd. stlbjcctivc etli; iate', ofl the t'rlnmsition probahililíes
coulltd CqUlly %%t l ¡le ued' iii l tihe lI';tií,i¿ito prolablilty
m;itrix. 'i'hc eiffect otl'tlihe neA o modiied i prog'ailln coild ihen
I, lc .' i '.itiiii c t ill at iil tllf Nilli ;it i ¡'la';,I es I ;ia ld 7. ''hli,
woutld also give thc eIl'eet oin the total coNt t ttihe hospilal antl
tiltis asclrie ;an equivllentl wsorth to the progra;in.
Disc'..ss.ion
Although the Markov model and the Halpern and BIin-
¡ner nilldel Irc.ilirel ;, Cnllsidetrail;ae aimnilUSt of' ell'aortl io Ise.
evenl more el'ort is requictd Ilo provide aleculrlic. Inc;lninigltll
iiiput daia l'for t¡le niodels. Clc'ily. the st;tirticmal ni:;miptil.'tion
of inacctirate daita¡ is % 'orse thani useleC -il may veil he
mi:slalding. Tlhus. to ¡ise these imotels for tile pu'pose they
were intended ieqtii'¢cs ami ciis.II'mots O ;illl¡tiilt tf sstmk re'l'tll
ascertaining the reliability andt validity ol'f the rawv dtta. In ¡tddition.
an appropriate scoring aníd recoe'ding sy>stem must be
designed. monitore(d. and properiy titilized. And finally. the
rcstulis of ithe ilodel ;,, ;ailyacs i¡lil Isc iierprei.ted ;antd very
carel'tilly expl;ined IeNs ineoire.1le inl'eirences he dtirir n.
Ftl'hernmore. l*iy ev;.ll;ion model is onlly one lootl in
the total program evaitiation process. ''hc M;uiinko mnudel
;aiid tlíe Il;pilcpiin ;and li inlsicr modeili l ;icl'cr;l' It' e es¡pci;allv
useli.l inii this regai'd. U nodouitedly . moex ;ilitíivíon ilmdetJls
for the hcalilh services swill he dcv eloped and i.come ;v;,ilable
as time progr'esses buit hliing lihc interinm the [v.t nmodels
described here appear' to prose,,,, the moni genieral applicaibility
Cfor qua;italivic plrogratil xi uatltioi. \\'hen ti.ed in
conjunction with additionail quatli;iltiye intirmnaition and real
world constraints these models should prove ecxtremely helpful
to Ihe cliniciains and health atdlminiNitratir'n lced wJith the
task'ol' progri'am evaltition.
REFERENCES
1. Weikel. K. Evatliuation of naiional hellh progranis. Am. J. Public
Health 61:1801. 1971.
2. Levey. S. and Loonmh;a. N. P. Healih Care Admninisilalion. p.
421. I.ippincoll Co.. 1973.
3. Scriven. M. Goal-iree evaluation. Evaui;atlio 1:b62. 1973.
4. Halpern. J, and Binner. P. R. A model for a¡n ouipUt valuc anatlysis
of inmenlul health programs. Administra;tion in Mental Health
1:40-51. 1972.
5. I:yniain. R. K.. T;arj;iil. G.. and McGlmnige. I). The Mitrktov
Ch.i¡in as ;, Ilctilhod kt, eví.Islitiíg s.hotols ¡for ihe mlenal;lily re.
atl. edAm. A . Menial I)cliciicny 72:435-144. 1967.
6. LEyrií;ma. 1. iK.. Iaiij;an. C;.. ialnd CaIsady l. NI. N;ailurail hIisitary fl
aícquisition of basic skills bh hospila;lize reitrided palienls. Am.
J. Mental Deficiency 75: 120-129. 1970.
7. Meredith. J. A M:ikwia .il5na'!is i ot ai ge;.Jitiic %ya;rd. M;anagenient
Science 19:(1( 4-612. 1973.
8. Meredilh. J. Prograni evalualtioun in a htopit;ll for ¡ihe ment;all relarded.
Am. J. Menitl Deficiencv 781:471-48I1. 1974.
9. Kemeny. J. C. and Snell. J. 1.. Finile Miarkov Chaiins. D. Van
Noslitrnd. 1960.