Journal of Service Science and Management, 2011, 4, 491-498
doi:10.4236/jssm.2011.44056 Published Online December 2011 (http://www.SciRP.org/journal/jssm)
491
Stochastic Modeling on Drug Efficacy in Self Drug
Administration Health Problems
P. Tirupathi Rao1, M. Venkateswaran1, R. Vishnu Vardhan2
1Department of Statistics, S. V. University, Tirupati, India; 2Department of Statistics, Pondicherry University, Puducherry, India.
Received July 12th, 2011; revised September 3rd, 2011; accepted October 9th, 2011.
ABSTRACT
Evaluation of drug impact both on positive and negative sides is very important to monitor the drug administration
during the treatment. The effectiveness of drug is a variable due to various chance and assignable causes. Evaluation of
drug efficacy through conventional mathematical modeling is the existing practice. In this paper we proposed a Sto-
chastic model for measuring the drug efficacy for Non-Clinical and short term drug administration practices. Sensiti-
vity analysis is carried out to observe the model behavior. Development of computer software and desktop templates to
this model will provide effective decision support systems for health caretakers.
Keywords: Stochastic Model ing , Drug Efficacy, Self Drug Administration
1. Introduction
Treatment with drugs is one of the customary methods to
cure diseases. Drug administration on the disease control
in under developed and developing countries is mostly
on non-clinical environment, particularly for the short
term and seasonal related disease treatments like cold,
fever, influenza, cough etc. Major category/population of
the patients in India are getting the treatment through non
competent medical supervision. It leads to random pick-
ing of drug at the choice of either individual own behalf
or Medical Shop holders or Registered Medical Practi-
tioners etc. This sort of situation provokes non-assurance
of drug effectiveness on the control of the disease. Deci-
sion making on drug picking has to be made on various
parameters of drug administration like quantity of drug
per unit time, number of times (frequency) of drug ad-
ministration per unit time period and many other similar
factors. The health care taking must be supported by
competent screening procedures with proper health indi-
cators on the efficacy of drug under usage. Drug dosage
level less than the required and more than the sufficient
are unwanted as the farmer leads to the body drug resis-
tant and the later may cause hazards to general health of
the patient. Therefore the limits on size of the drug dose
are playing vital role in regulations of disease intensity.
Random and erratic usage of drug without scientific
approach will make drug administration more vulnerable.
It always act as double edged weapon through either
wanted or unwanted impact. Spontaneous selection of drug
based on purely chance manner requires due attention of
the researchers. Assessment on the levels of drug effect-
tiveness on the targeted disease control is the need of the
hour. Measuring the levels of both positive and negative
effectiveness is possible through the construction of a
relevant Mathematical model. Our study can measure the
net effectiveness of drug by considering the linear com-
bination of positive and negative influences of drug on
the disease control. This study will assist as the health
management tool for decision support system. It can as-
sess the influence of drug either of proper usage or of
abuse by obtaining various Statistical measures of lower
and higher order.
A suitable formulation of the bio-systems into mathe-
matical formulation and transforming classic mathema-
ticcal environment into statistical/empirical situations is
pivotal. There is much literature evidence on modeling the
drug efficiency in Deterministic environment. The work
so far carried out is mostly concentrated on drug admini-
stration for long term treatments. A few work is reported
in the literature on measuring the drug effectiveness on
the treatment of short term duration.
Drug administration on clinical environment can be
done in several different methods [1]. The model of drug
resistance from gene amplifications could be studied th-
rough the policies of optimal control [2]. Several asymp-
totic properties of infinite dimensional model drug resis-

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems
492
tance evolutions are available [3]. The phamalogemmics
can be studied through drug disposition, drug targets and
its side effects [4]. The Legand efficiency indices are con-
sidered as the guide spots in the discovery of drug effect-
tiveness [5]. Drug efficiency indices were also constru-
cted with structured based calculation [6]. The evaluation
of drug efficacy for long term Treatment problems can be
done through stochastic models. The environment of drug
administration with ‘r’ alternatives and each alternative is
of completely random is considered. The treatment is
administered for N days for which the effectiveness of
drug has varying chances. The selected drug for treating
the disease is correct with certainty for N1 days, the
choice of correct selection is equal to 1k for Nk days
where k = 1, 2, , r. Further the total period of treatment 
is . The model has applied to study the
1
k
i
i
NN


drug effectiveness for long term treatments like cancer,
T.B. and skin related diseases [7]. In this paper we have
developed a stochastic model for evaluating the effect-
tiveness of drug for the treatments of short durations.
This study has focused the attention on calculating the
drug efficacy when the choice of the drug is random and
having positive and negative impacts. The net effective-
ness of drug is a linear combination of both positive and
negative impacts with some weight coefficients.
2. Stochastic Model and Statistical Measures
In this study we develop a stochastic model for measure-
ing the effectiveness of the drug by considering the fol-
lowing assumptions based on the problems of the pa-
tients; Problems of Drug selection and Problems of Drug
administration.
 The patients may get ill health such as cold, sea-
sonal fever, headaches and similar non-chronic and
short term diseases at a random time.
 The patient is not having required knowledge on
the drug administration parameters such as (i) The
dosage level of drug; (ii) The frequency of drug
administration per unit time (iii) time between two
spells of drug administration; (iv) neither the pa-
tient nor healthcare taker on his behalf is aware on
the side effects of the drug.
 The patients may pick the drug either on his own
choice or from the suggestion of a medical shop-
keeper or from other similar people.
 He/She may initiate the usage of drugs with a group
of medicines initially but some medicines may be
missed during the administration period.
 There is every likely to skip some spells of taking
medicines during the course period of drug admini-
stration.
 The drug usage may be stopped abruptly at any
point of time on various reasons like he/she may get
relief from the problem, they may not enough stock
of drug to use for the required course period.
 Patient will select the drug of option among avai-
lable drugs.
 The usage of medicines may be either a single drug
or a group of drugs.
 He/She administered the drug one or more pills for
one time and more than one time in a day and more
than one day in over all administration.
This model can measure the drug effectiveness for in-
termediate evaluation during treatment period. Due to
various unexplained reasons and the varying levels of
health conditions of the patient during the course period,
the effectiveness of drug has to be considered as random
variable and it is obtained as measure of efficiency (e). It
is the ratio of the output achieved to the input used.
Acheived Ouput
eUsed Inputs 
Output can be obtained through various Statistical means
and parametric observations with pre and post-drug ad-
ministration datasets.
The model is constructed to obtain stochastic proc-
esses so as the behavior of a random variable Z can be
analyzed. It is the Net effectiveness of drug, expressed as
Z = a X + b Y; where a, b are the weight age coefficients
corresponding to X, Y respectively. They are obtained
through preparation of frequency tables and pattern iden-
tifications in the data.
X is a Bernoulli variable assuming values 1, 0 for the
drug impact when it has positive effect (1) and drug non
positive effect (0). “Positive effectiveness of drug” does
implies that the drug has perform its task on healing the
problem, what exactly it is meant for. “Non positive ef-
fectiveness of drug” does implies that the task of drug assi-
gnment may be un served as a neutral impact on overall
effectiveness in healing the problem.
Y is another Bernoulli variable assuming values 1, 0
for the drug impact has negative effect (1) and the drug
has non-negative effect (0). “Negative effectiveness of the
drug” does implies that usage of drug may cause some
loss to the general health due to side effects in mis-
matching of drug that is consumed and the health prob-
lem that is under study. “Non-negative effectiveness of
the drug” does mean that usage of drug may not harm the
overall health of the patient or there is a neutral negative
effectiveness.
Let p1 be the probability of positive impact and p2 be
the probability of non-positive impact. The probability
distribution for the same is P (X = i) = p1; for I = 1; P (X
= i) = p0; for I = 0; This probability distribution is ob-
tained from the stochastic process of an indicator varia-
ble {Xi; I = 0, 1}; further p1, p0 ≥ 0; p1 + p0 = 1. The rth

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems
493
order raw moment for the above probability distribution 1
22
2
10 10
11
.. ..
..
app bqq
ap bq





.
is


'
1r
X
p  .
Similarly, let q1 be the probability of Negative impact
and q2 be the probability of non negative impact. The
stochastic process of Y is {Yj; j = 0, 1} and the probabi-
lity distribution is
6) The 3rd Central Moment is:



32
31 11
32
11
..13. 2.
..13. 2.
app p
bqq q
 

1
P (Y = j) = q1; for j=1; P (Y = j) = q0; for j = 0; and q1 +
q0 = 1. q1, q0 ≥ 0 the kth order raw moments of the
7) The 4th Central Moment is:
distribution is .

'
1 kYq
 




42
41 111
42
1111
22
11 0111
..14.6.3.
.1 4.6.3.
6.... .
app pp
bqq qq
ab pqpqpq
 


3
3


The random variables X and Y are assumed to be in-
dependent as the occurrence of events say positive and
negative effective nesses are no way influenced by one
with the other so that bivariate stochastic process is {(Xi,
Yj); i, j = 0,1} and its probability function is P(X = i, Y = j)
= P(X = i). P(Y = j) for i, j = (0, 1) and the rth order raw 8) The coefficient of Skewness is:
moment of joint probability distribution is

'
11
,
r
X
Ypq  .



2
323
111111
13
22
10 10
..13.2.. 13.2.
.. ..
appp bqqq
app bqq

2


 



Z as combined random variable can measure the net
drug effectiveness by considering both positive and ne-
gative impacts together. Usually ‘b’ has a negative coef-
ficient so as Z value become Z = a X – b Y the study has
to be focused on Z variable as a mixture of X and Y
probability distribution. The Stochastic Process of Z is =
{Zk, k = 0, 1}where Zi,j = a Xi – b Yj the probability dis-
tribution is
9) The coefficient of Kurtosis is: (see Equation (9))
10) The Moment generating function of Z is:


11
00
manb t
zmn
mn
Mt pqe


11) Characteristic function of Z is:
 





11
11
;
,0,10Otherwise.
xy y
101 0
PZap pbqq
xy
xy

 

 
 



11 2
00
;1
manb it
zmn
mn
tpqefori 





12) Probability generating function of Z


11
00
ma nb
zmn
mn
PSpqS 


For all practical purposes we may consider b as (–1)
(b). The Statistical measures are obtained using relation Z
= aX + bY and b = (–1) b thus the results are: 3. Methodology
1) The rth order origin (raw) moment of Z is: The following methodology is considered for measuring
the drug efficacy. The usual practices that are happened
in clinical treatments are based on the readings of pre and
post tests. In general the diagnosis procedures at clinical
treatment are based on the screening tests. If we consider
an example of screening tests of fever, the intensity of
fever can be assessed with Temperature of the body,
Pulse rate of the nerve, no of breathes of the patient, skin
temperature, rectal temperature, etc.
 
'
11
0
1
rkr
rk
rk
Z
ap bq
k






.
By assuming r = 1, 2, 3, 4, we can obtain the first four
raw moments. With the help of these four, we can get
Mean, S. D., Variance, C. V. Coefficients of Skewness
and Kurtosis etc.
2) Average or Mean Effectiveness of Drug is: Fever may be caused due to so many reasons like in-
fections, inflammation, indigestion, insect bite, etc and
many unexplained also. Let us assume that a patient is
getting treatment for a fever. He has no idea about the
reason for getting fever. His objective is to get rid of fe-
ver by consuming some pills. In this context the drug may
give the effect on four fold namely:
11
. .ap bq.
3) Variability of Drug Effectiveness is:
22
10 10
.. ..app bqq .
4) Standard Deviation

1
22
2
10 10
app bqq.
5) Coefficient of Variation of Drug Effectiveness






42342322
1111111111 0111
22
22
10 10
.14.6.3..1 4.6.3.6.....
.. ..
a ppppbqqqqab pqpqpq
app bqq

 
 (9)

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems
494
1) Positive effect: The drug shall decrease the tempera-
ture through the means of suppressing the reasons of cau-
sing fever.
2) Non-Positive effect: The drug may not decrease the
temperature as it has no influence on suppression of the
fever causing factors.
3) Negative effect: The drug may give adverse effects
on general health of the patient causing unwanted side
effects.
4) Non-Negative effect: The drug may not give unwan-
ted side effects irrespective of its positive or non-positive
effects.
The concepts of Non-Positive and Non-negative ef-
fects of drug, though they appears to be same, we have
considered those two are significantly differed as the
impact factor of non-positive effect of the drug is not
equal to the impact factor of non-negative effect of drug.
The coefficient of positive effectiveness (a), may ob-
tained as influenced relation of many factors. It may other-
wise defined as 1
r
p
i
i
pe
ae r


;
p
i
eis the Positive
efficiency measure of ith factor; i = 1, 2, , r; As the
usual parameters of a disease like fevers are Body tem-
perature, Heartbeat/Pulse rate, number of breathes, skin
temperature etc.

Let us consider the first parameter namely temperature,
1
initial temperatureTemperature
beforeusing drugafter using drug
Quantity ofdrugused
ptb ta
eq






.
[Example: If tb = 103˚; ta = 102˚; q = 500 mg then
1
103 10210.20.002
500500 100
p
e ].
Let Heart beat count is the 2nd parameter, then
 
2
initial heartbeatHeartbeat count
b
efore using drugafterusing drug
quantity ofdrugused
p
e





HB preHB post
q


.
If number of breathes per unit time is the 3rd parameter
then
 
3
HB preHB post
quantityofdrug used
p
e .
In general sense,
p
revious readingpostreading
p
arameter parameter
useddrug quantity
i
th th
p
ii
e











 

reading ofpre testreading ofposttest
q
i
p
ii
e 
Combining all the above, 1
r
p
i
pi
e
ae r


, where ‘r’
is the total number of factors on which the positive effe-
cttiveness of drug is attained. Similarly the coefficient of
Negative effectiveness (b) may also be influenced by non
suitability or mismatching of drug to the disease under
treatment.
For example: usage of certain drug leads to increased
loss of albumin through urine.
 
1
Albumni lossAlbumni loss
b
eforedrug useafter drug use
quantityofdrug
el





Albpre testAlbposttest
q


,
el1 is the total negative effectiveness of drug. If there are
k types of factors that are making the drug negative ef-
fectiveness. Then the overall negative effectiveness is
obtained as
1
;
j
rl
l
j
e
be r



The coefficients of both po-
sitive effectiveness and negative effectiveness are inf-
luenced by all the relevant factors. This measure is statis-
tically valid as the readings are considered on various
parameters of the problem under study.
The chances of positive effectiveness ‘p1’, Non-posi-
tive effectiveness ‘p0’ are obtained as the proportions of
their impact on overall usage. These values are usually
obtained from the relative frequency distributions or
from some historical data. These observations may also
obtained from the pharmacology experimental studies.
Let a drug is applied on ‘m’ living beings and of which
‘x’ are having the positive result and the rest (m-x) are
not having the positive effectiveness. Then 1
x
pm

and
01
11
x
mx
ppmm

 .
The chances of negative impact can also be studied on
similar lines. Let a drug is applied on ‘n’ living beings of
which ‘y’ are having the negative impact and the remaining
n-y are not having negative results then the chances are

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems495
1
y
q and
n
01 11
ynx
qq   .
nn
4. Numerical Illustration and Sensitivity
In he insights of the drug efficiency, a data
that Average drug effi-
ci
efficiency is
an
fficiency is an in-
cr
ariability of drug efficiency is
an
of having Positive
Analysis
order to get t
is considered with inputs p1, q1, a and b. The outputs like
average drug effectiveness, variability in the drug effect-
tiveness, coefficient of variation, coefficient of Skewness,
coefficient of kurtosis, etc are calculated with software
MATHCAD. The numerical data is placed in Tables 1,
mean response and the variability of the drug impact are
analyzed. It is observed that Average drug efficiency is
an increasing function of p1, and it is negative when p1 <
q1, a < b where as Mean efficiency is an increasing func-
tion of p1, and it is positive when p1 > q1, a < b when
other parameters are constants. It is further observed that
Average drug efficiency is an increasing function of p1,
and it is negative when p1 < q1, a > b where as Mean effi-
ciency is an increasing function of p1, and it is positive
when p1 > q1, a > b when other parameters are constants.
It is observed that Average drug efficiency is a decreas-
ing function of q1, when p1 > q1, a < b where as Mean
efficiency is a decreasing function of q1, and it is negative
when p1 < q1, a < b when other parameters are constants.
It is further observed that Average drug efficiency is a
decreasing function of q1, and it is positive when p1 > q1,
a>b where as Mean efficiency is a decreasing function of
q1, and it is positive when p1 < q1, a > b when other pa-
rameters are constants.
It is observed from Figure 1
ency is an increasing function of p1, and it is negative
when p1 < q1, a < b, where as Mean efficiency is an in-
creasing function of p1, and it is positive when p1 > q1, a
< b when other parameters are constants. It is further
observed that Average drug efficiency is an increasing
function of p1, and it is negative when p1 < q1, a > b
where as Mean efficiency is an increasing function of p1,
and it is positive when p1 > q1, a > b when other parame-
ters are constants. It is observed that Average drug effi-
ciency is a decreasing function of q1, when p1 > q1, a < b
where as Mean efficiency is a decreasing function of q1,
and it is negative when p1 < q1, a < b when other pa-
rameters are constants. It is further observed that Avera-
ge drug efficiency is a decreasing function of q1, and it is
positive when p1 > q1, a > b where as Mean efficiency is
a decreasing function of q1, and it is positive when p1 < q1,
a > b when other parameters are constants.
It is observed that the variability of drug
increasing function of p1 when p1 < q1, a < b; it is de-
creasing function of p1 when p1 > q1, a < b; Further it is
observed that the variability of drug efficiency is a de-
creasing function of p1 when p1 < q1, a > b; it is decreas-
ing function of p1 when p1 > q1, a > b when other pa-
rameters are constants. It is observed that the variability
of drug efficiency is an increasing function of q1 when p1
> q1, a < b; it is decreasing function of q1 when p1 < q1, a
< b; Further it is observed that the variability of drug
efficiency is an increasing function of q1 when p1 < q1, a
> b; it is a decreasing function of q1 when p1 < q1, a > b
when other parameters are constants.
It is observed that Average drug e
easing function of a, it is negative when p1 < q1, a < b;
whereas Mean efficiency is an increasing function of a,
and it is positive when p1 < q1, a > b when other parame-
ters are constants. It is further observed that Average
drug efficiency is an increasing function of a, and it is
negative when p1 > q1, a < b where as Mean efficiency is
an increasing function of a, and it is positive when p1 > q1,
a > b when other parameters are constants. It is observed
that Average drug efficiency is a decreasing function of b,
it is negative when p1 < q1, a < b; whereas Mean effi-
ciency is a decreasing function of b, and it is positive
when p1 < q1, a < b when other parameters are constants.
It is further observed that Average drug efficiency is a
decreasing function of b, and it is negative when p1 > q1,
a < b where as Mean efficiency is a decreasing function
of b, and it is positive when p1 > q1, a > b when other
parameters are constants.
It is observed that the v
increasing function of a when p1 < q1, a < b; it is an
increasing function of a when p1 < q1, a > b; Further it is
observed that the variability of drug efficiency is an in-
creasing function of a when p1 > q1, a < b; it is an in-
creasing function of a when p1 > q1, a > b when other
parameters are constants. It is observed that the variabili-
ty of drug efficiency is an increasing function of b when
p1 < q1, a < b; it is an increasing function of b when p1 <
q1, a > b; Further it is observed that the variability of
drug efficiency is an increasing function of b when p1 >
q1, a < b; it is an increasing function of b when p1 > q1, a
> b when other parameters are constants.
5. Summary and Conclusions
Our study observed that the chance
impact of the drug is giving an increasing impact on its
average performance, decreasing impact on variability
when p1 > p0; increasing impact of variability when p1 <
p0. The coefficient of variation is a decreasing function of
performance of positive impact when p1 > q1. Consisten-
cy of drug performance may be increased by maintaining
more positive impact than negative impact. The chance
of having Negative impact of the drug is giving an de-
creasing impact on its average performance, increasing
impact in variability when p1 > p0. The coefficient of va-
riation is an increasing function of performance of

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems
496
ewness and kurtosis for varying values of p1, q1, a, b.
p1 β2
Table 1. Values of mean, variance, coefficients of sk
q1 A B Mean Variance C.V. β1
0.1 0.5 0.7 0.8 –0.33 0.204 – 0. 1.3690722.01
0.2 –0.26 0.238 –1.878 0.08 2.126
0.3 –0.19 0.263 –2.699 0.046 2.07
0.4 –0.12 0.278 –4.391 0.013 2.007
0.6 0
0
0
0
– 9
0. 0
0. 0
0. 0
0. 0 –
7
0. 0
0. 0
4
0. 0
0. 0
3
0.
3.
0. –
0.
0.3 0.1 0.055 2.349 0.099 2.261
.5 0.7 0.80.02 0.278 26.344 0.013 2.007
0.7 0.09 0.263 5.697 0.046 2.07
0.8 0.16 0.238 3.052 0.08 2.126
0.9 0.23 0.204 1.964 0.072 2.01
0.1 .5 0.8 0.7–0.27 0.18 –1.572 0.233 2.598
0.2 –0.19 0.225 –2.496 0.212 2.458
0.3 –0.11 0.257 –4.608 0.109 2.206
0.4 –0.03 0.276 –17.515 0.029 2.039
0.6 .5 0.8 0.70.13 0.276 4.042 0.029 2.039
0.7 0.21 0.257 2.414 0.109 2.206
0.8 0.29 0.225 1.635 0.212 0.212
0.9 0.37 0.18 1.147 0.233 2.598
0.6 .2 0.4 0.50.14 0.078 2
3.
0.471 2.625
0.3 0.09 0.091 350.245 2.26
0.4 0.04 0.098 7.842 0.086 2.039
0.5 –0.01 0.101 31.765 .19E-03 1.967
6 0.7 .4 0.5–0.11 0.091 –2.741 0.073 2.26
0.75 –0.135 0.085 –2.163 0.121 2.427
0.8 –0.16 0.078 –1.75 0.165 2.625
0.85 –0.185 0.07 –1.433 0.188 2.832
6 0.2 .6 0.3 0.3 0.101 1.058 0.164 1.658
0.3 0.27 0.105 1.202 0.137 1.726
0.4 0.24 0.108 1.369 0.108 1.753
0.5 0.21 0.109 1.571 0.083 1.761
6 0.7 .6 0.30.15 0.105 2.163 0.056 1.726
0.75 0.135 0.103 2.38 0.056 1.699
0.8 0.12 0.101
2.646 0.059 1.658
0.85 0.105 0.098 2.98 0.068 1.597
6 0.7 .1 0.5–0.29 0.055 0.808 0.66 1.864
0.2 –0.23 0.062 –1.083 0.427 2.071
0.3 –0.17 0.074 –1.601 0.208 2.223
0.4 –0.11 0.091 –2.741 .30E-022.26
6 0.7 0.6 .50.01 0.139 37.269 6.50E-06 2.114
0.7 0.07 0.17 5.892 7.23E-03 2.006
0.8 0.13 0.206 3.492 0.023 1.901
0.9 0.19 0.247 2.615 0.04 1.807
7 0.6 0.1 .5–0.23 0.062 –1.083 0.146 1.287
0.2 –0.16 0.068 –1.635 0.089 1.571
0.3 –0.09 0.079 –3.121 0.028 1.869
0.4 –0.02 0.094 –15.297 .75E-042.087
7 0.6 0.6 .50.12 0.136 3.069 0.059 2.256
0.7 0.19 0.163 2.124 0.12 2.257
0.8 0.26 0.194 1.696 0.186 2.234
0.9 0.33 0.23 1.454 0.25 2.199
6 0.7 0.4 .5–0.11 0.091 –2.741 0.073 2.26
0.6 –0.18 0.114 –1.876 0.153 2.247
0.7 –0.25 0.141 –1.504 0.235 2.208
0.8 –0.32 0.173 –1.299 .09E-012.16
6 0.7 0.4 0.15 0.135 0.043 1.538 0.097 1.532
0.2 0.1
0
0.047 2.163 0.056 1.726
0.25 .0650.052 3.492 0.023 1.901
0.3 0.03 0.057 7.979 44E-03 2.042
7 0.6 0.4 0.5 –0.02 0.094 15.297 4.75E-04 2.042
0.6 –0.08 0.12 –4.33 0.014 1.953
0.7 –0.14 0.151 –2.777 0.036 1.83
0.8 –0.2 0.187 –2.163 0.056 1.726
7 0.6 0.4 0.15 0.19 0.039 1.039 0.458 2.046
0.2 0.16 0.043 1.299 0.309 2.16
0.25 0.13 0.049 1.696 0.186 2.234

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems497
Figure 1. Graphical presentations of mean and variance effects of drug.

Stochastic Modeling on Drug Efficacy in Self Drug Administration Health Problems
498
Negative impact when p1 > q1. The chance of having
Positive impact of the drug is giving an increasing impact
on its average performance, increasing impact on varia-
bility when a > b. The coefficient of variation is a de-
creasing function of performance of positive impact of
drug when a > b. Consistency of drugs performance may
be increased by maintaining more positive impact than
negative impact. This model will help the individual pa-
tients in quantification of the problem severity with drug
abuse/misuse. Development of software to this model
will assist in the health monitoring of self health care
takers fort their decision support systems. The scope for
future work may be done with multinomial cases instead
of Bernoulli cases. This work may be extended to more
suitable contexts.
6. Acknowledgements
All the authors of the paper are very much greateful to
the editorial board, reviewers of the Paper, and Editors of
the Journal of Service Science and Management (JSSM)
for their valuable suggestion in improving the quality of
the paper.
REFERENCES
[1] S. H. Daukes, “A Consideration of the Various Methods
of Drug Administration,” Post Graduate Medical Journal,
Vol. 5, No. 49, 1929, pp. 1-7. doi:10.1136/pgmj.5.49.1
[2] J. Smieja, et al., “Optimal Control for the Model of Drug
Resistance Resulting from Gen Amplification,” Prepera-
tion of the 14th IFAC World Congress, Beijing, China,
Vol. 50, 1999, pp. 71-75.
[3] A. Swierniak et al., “Asymptotic Properties of Infinite Di-
mensional Model Drug Resistance Evolution,” Proceed-
ings of the European Control Conference (ECC), Brus-
sels, 1997.
[4] W. E. Evans and H. L. McLeod, “Pharmacogenomics—
drug disposition, drug targets, and side effects,” New
England Journal of Medicine, Vol. 348, No. 6, 2003, pp.
538-549. doi:10.1056/NEJMra020526
[5] C. Abad-Zapatero and J. T. Metz, “Ligand Efficiency In-
dices as Guideposts for Drug Discovery,” Drug Discovery
Today, Vol. 10, No. 7, 2005, pp. 464-469.
doi:10.1016/S1359-6446(05)03386-6
[6] C. Hetenyi, et al., “Structure-Based Calculation of Drug
Efficiency Indices,” Journal of Structural Bioinformatics,
Vol. 23, No. 20, 2007, pp. 2678-2685.
doi:10.1093/bioinformatics/btm431
[7] P. Tirupathi Rao and R. Bharathi, “Stochastic Modeling
in the Evaluation of Drug Efficiency,” International Jour-
nal of Statistics and System, Vol. 5, No. 3, 2010, pp.
427-438.