=Paper=
{{Paper
|id=None
|storemode=property
|title=Contrasting Temporal Bayesian Network Models for Analyzing HIV Mutations
|pdfUrl=https://ceur-ws.org/Vol-962/paper04.pdf
|volume=Vol-962
|dblpUrl=https://dblp.org/rec/conf/uai/Hernandez-LealFRGS12
}}
==Contrasting Temporal Bayesian Network Models for Analyzing HIV Mutations==
https://ceur-ws.org/Vol-962/paper04.pdf
Contrasting Temporal Bayesian Network Models for Analyzing HIV
Mutations
Pablo Hernandez-Leal, Lindsey Fiedler-Cameras, Alma Rios-Flores,
Jesús. A González and L. Enrique Sucar
{pablohl,lfiedlerc,jagonzalez,esucar}@inaoep.mx
Instituto Nacional de Astrofísica, Óptica y Electrónica
Coordinación de Ciencias Computacionales
Sta. María Tonantzintla, Puebla, México
Abstract caused by viral evolution increase drug resistance. Al-
though the mutations which result in drug resistance
are mostly known, the dynamics of the appearance of
Evolution is an important aspect of viral dis-
those mutations and the time of occurrence remains
eases such as influenza, hepatitis and the
poorly understood.
human immunodeficiency virus (HIV). This
evolution impacts the development of suc- Bayesian Networks (BNs) have proven to be successful
cessful vaccines and antiviral drugs, as muta- in various domains, including medicine and bioinfor-
tions increase drug resistance. Although mu- matics. However, classical BNs are not well equipped
tations providing drug resistance are mostly to deal with temporal information. The common ap-
known, the dynamics of the occurrence of proach to handle temporal information is to construct
those mutations remains poorly understood. a Dynamic Bayesian Network (DBN) (Dagum, Galper,
A common graphical model to handle tempo- and Horvitz, 1992), however other options exist such as
ral information are Dynamic Bayesian Net- Temporal Nodes Bayesian Networks (TNBN) (Arroyo-
works. However, other options to address Figueroa and Sucar, 1999).
this problem exist. This is the case of Tempo-
In this paper we use both approaches, Dynamic
ral Nodes Bayesian Networks. In this paper
Bayesian Networks and Temporal Bayesian Networks,
we used both approaches for modeling the re-
to model the mutational pathways for four specific HIV
lationships between antiretroviral drugs and
antiretrovirals. The objective is to compare the path-
HIV mutations, in order to analyze tempo-
ways that we obtain with our models against the path-
ral occurrence of specific mutations in HIV
ways obtained from experimental testing. In this way,
that may lead to drug resistance. We com-
we can see if the models reflect the temporal clinical
pare the strengths and limitations of each of
information reported in many reference sources.
these two temporal approaches for this par-
ticular problem and show that the obtained
models were able to capture some mutational 2 BAYESIAN NETWORKS
pathways already known (obtained by clini-
cal experimentation). BNs are directed acyclic graphs used to model condi-
tional dependencies between random variables. The
data represented by a BN is typically static, however
in many contexts a need arises to model processes
1 INTRODUCTION
whose state variables change throughout the course of
time. Dynamic Bayesian Networks evolved to tackle
Viral evolution is an important aspect of the epi-
this shortcoming.
demiology of viral diseases such as influenza, hepati-
tis and human immunodeficiency virus (HIV). HIV is
the causal agent for the disease known as Acquired 2.1 DYNAMIC BAYESIAN NETWORKS
Immunodeficiency Syndrome (AIDS), a condition in
A Dynamic Bayesian Network extends the concept of a
which progressive failure of the immune system allows
Bayesian network to incorporate temporal data. Just
opportunistic life-threatening infections to occur.
as with classic BNs, a static causal model is created to
This viral evolution impacts the development of suc- represent a process at a single point in time; multiple
cessful vaccines and antiviral drugs, as mutations copies of this model are then generated for each time
point or slice belonging to a temporal range of inter-
est and links between copies are inserted to capture
temporal relations.
When modeling dynamic information, DBNs obey the
assumption that future states are conditionally in-
dependent from past states given the present state
(Markov property); additionally they assume that the
conditional probabilities which describe the temporal
relations between random variables of adjacent time Figure 1: An example of a TNBN. The Drug node
slices do not change (stationary process). By allowing is an Instantaneous Node, so it does not have tempo-
these two basic assumptions, DBNs can offer a more ral intervals. The Nausea and Headache are temporal
compact model of the dynamic process by defining a nodes with intervals associated to them.
2-time-slice Bayesian network (2-TBN). This 2-TBN
can be further unrolled to do inference on the entire
temporal range of interest.
The learning of a DBN can be seen as a two stage defined for a child node represents the possible delays
process (Friedman, Murphy, and Russell, 1998). The between the occurrence of one of its parent events and
first stage refers to the learning of the static model the corresponding child event. If a node lacks defined
and is done in an identical manner as with classic BNs. intervals for all its states then it is referred to as an
The second stage learns the transition network, that instantaneous node. There is at most one state change
is, the temporal relations between random variables of for each variable (TN) in the temporal range of inter-
different time slices. est.
An alternative to DBNs are Temporal Nodes Bayesian Formally, let V be a set of temporal and instantaneous
Networks (Arroyo-Figueroa and Sucar, 1999) which nodes and E a set of arcs between nodes, a TNBN is
are another extension of Bayesian Networks. defined as:
Definition 1. A TNBN is a pair B = (G, Θ) where
2.2 TEMPORAL NODES BAYESIAN G is a directed acyclic graph, G = (V, E) and, Θ is a
NETWORKS set of parameters quantifying the network. Θ contains
TNBNs (Arroyo-Figueroa and Sucar, 1999) were pro- the values Θvi = P (vi |P a(vi )) for each vi ∈ V; where
posed to manage uncertainty and temporal reasoning. P a(vi ) represents the set of parents of vi in G.
In a TNBN, each Temporal Node has intervals associ- The following is an example of a TNBN of a patient ad-
ated to it. Each node represents an event or a state ministered with a drug causing two side effects. Its cor-
change of a variable. An arc between two Temporal responding graphical representation is shown in Figure
Nodes corresponds to a causal-temporal relation. One 1.
interesting property of this class of models, in contrast
to Dynamic Bayesian Networks, is that the temporal Example 1. Assume that at time t = 0, a Drug is
intervals can differ in number and size. So, only one administered to a patient. This kind of drug can be
(or a few) instance(s) of each variable is required, as- classified as strong, moderate and mild. To simplify
suming there is one (or a few) change(s) of a variable the model we will consider only two consequences for
state in the temporal range of interest. No copies of the patient, Nausea and Headache. These events are
the model are needed, thus compacting the represen- not immediate, we will assume that they depend on the
tation without losing expressiveness. type of drug, therefore, they have temporal intervals as-
sociated. For the Nausea node two intervals are defined
A TNBN is composed by a set of TNs connected by [0 − 60], [60 − 180], for the Headache node three inter-
arcs. A TN, vi , is a random variable characterized vals are defined [60 − 120], [120 − 180], [180 − 360].
by a set of states S. Each state is defined by an or- These intervals represent that the state of the node
dered pair S = (λ, τ ), where λ is the particular value changed during that period of time.
taken by vi during its associated interval τ = [a, b],
corresponding to the time interval in which the state The learning algorithm for TNBN used in this work
changes, i.e. change in value occurs. In addition, each has been presented in (Hernandez-Leal, Sucar, and
TN contains an extra default state s = (’no change’, ∅) Gonzalez, 2011). We now present a brief description.
with no associated interval. Time is discretized in a
finite number of intervals, allowing a different number 1. The algorithm begins by performing an initial dis-
and duration of intervals for each node . Each interval cretization of the temporal variables, for example
using an Equal-Width discretization. With this cross-resistance within the same class of medications
process it obtains an initial approximation of the complicates the therapeutic options for patients who
intervals for all the Temporal Nodes. have treatment regimen failure. Cross-resistance is
particularly common among the protease inhibitors
2. It then performs a standard BN structural learn- (PIs), making the sequential use of these agents fre-
ing using the K2 learning algorithm (Cooper and quently problematic. Although the mutations which
Herskovits, 1992) to obtain an initial structure. result in drug resistance are mostly known, the dy-
This structure will be used in the third step, the namics of the appearance of those mutations on the
interval learning algorithm. time of occurrence remains poorly understood.
3. The interval learning algorithm refines the inter- The relationship between phenotypic susceptibility to
vals for each TN by means of clustering. For this, some inhibitors and the genotypic pattern was inves-
it uses the information of the configurations of the tigated in the same inhibitors. From these studies we
parent nodes. To obtain the initial set of intervals now know the resistant patterns associated with the
a Gaussian mixture model is used as a cluster- inhibitors most frequently used. This information has
ing algorithm for the temporal data. Each cluster led to the ability to select a new salvage therapy. In ad-
corresponds, in principle, to a temporal interval. dition, if we know the pathway and time of occurrence
The intervals are defined in terms of the mean and of resistant mutations of common and well known ther-
the standard deviation of the clusters. The algo- apies, then this might lead to predicting the duration
rithm obtains different sets of intervals that are of new therapies, that use inhibitors that have similar
merged and combined, this process generates dif- structures or belong to the same class. It is also inter-
ferent interval sets that will be evaluated in terms esting to compare two or more mutational patterns to
of the predictive accuracy (Relative Brier Score). see if they share the same mutational pathways, which
The algorithm applies two pruning techniques in at the end will help to reduce the possibility of drug
order to remove some sets of intervals that may resistance.
not be useful and also to keep a low complex-
ity of the TNBN. The best set of intervals (that To combat HIV infection several antiretroviral (ARV)
may not be those obtained in the first step) for drugs belonging to different drug classes that affect
each TN is selected based on predictive accuracy. specific steps in the viral replication cycle have been
When a TN has as parents other Temporal Nodes, developed. Antiretroviral therapy (ART) generally
the configurations of the parent nodes are not ini- consists of well-defined combinations of three or four
tially known. In order to solve this problem, the ARV drugs. Due to its remarkable variation capabil-
intervals are sequentially selected in a top-down ities, HIV can rapidly adapt to the selective pressure
fashion according to the TNBN structure. imposed by ART through the development of drug re-
sistant mutations, that are fixed in the viral popula-
The algorithm then iterates between the structure tion within the host in known mutational pathways.
learning and the interval learning. However, for the The development of drug resistant viruses compro-
experiments presented in this work, we show the re- mises HIV control, with the consequence of a further
sults of only one iteration. deterioration of the patient’s immune system. Many of
these ARV drug resistant mutations reduce HIV sus-
ceptibility to ARV drugs by themselves, while others
3 HIV AND ANTIRETROVIRAL need to accumulate in order to cause resistance.
THERAPY
3.1 RELATED WORK
Viral evolution impacts the development of successful
vaccines and antiviral drugs, as mutations (caused by There are several works describing computational
viral evolution) increase drug resistance. In HIV, this models aimed to better understand HIV evolution and
is particularly relevant as the virus ranks among the immunopathogenesis. A portion of these models is
fastest evolving organisms (Freeman, Herron, and Pay- devoted to predict phenotypic HIV resistance to an-
ton, 1998). In viral diseases, such as HIV, it would be tiretroviral drugs using different approaches such as
important to develop proactive therapies that predict decision trees (Beerenwinkel et al., 2002) or neural net-
the advent of mutations, thus reducing the possibility works (Draghici and Potter, 2003). Other works try to
of drug resistance, which will then help to predict the identify relevant associations between clinical variables
duration of a new treatment. Viral therapy failure in and HIV disease (Ramirez et al., 2000). In (Chausa
patients treated for the HIV-1 infection is commonly et al., 2009), association rules between clinical vari-
associated with the emergence of mutations which are ables and the failure of the treatment are extracted.
resistant to specific drugs. In addition, a troublesome The results obtained are temporal rules that have as
temporal evolution of the mutational networks, we fil-
Table 1: An example of the HIV patient data. It
tered those patients having less than 2 studies. The fil-
presents two patients P1 with 3 temporal studies, and
tered dataset consisted of approximately 300 patients.
P2 with two temporal studies.
Patient Treatment Mutations Weeks Antiretrovirals are usually classified according to the
L90M, V82A 15 enzyme that they target. We focus on protease as
P1 IDV, RTV I54V 45 this is the smallest of the major enzymes in terms of
M46I 55
V82A 25 number of aminoacids. For the experiments we used:
P2 LPV,IDV, RTV Atazanavir (ATV), Lopinavir (LPV), Indinavir (IDV),
I54V 45
Ritonavir (RTV). According to the expert’s opinion
ATV and LPV are the most commonly used antiretro-
antecedent the increasing of a subset of clinical vari- virals nowadays. IDV was selected because it shares
ables and as consequent the failure of the treatment, mutational pathways with LPV, and RTV was selected
given by side effects of the drugs or by the elevated because its frequently used in combination with the
viral count (unsuccessful therapy). None of the clini- other three.
cal variables considered are HIV mutations. Finally, in
To define the target set of mutations of interest, we
(Hernandez-Leal et al., 2011) TNBNs are used to an-
used the Major HIV Drug Resistance Mutations ac-
alyze the temporal relationships between all the pro-
cording to (Stanford University, 2012). The mutations
tease inhibitors and some high frequency mutations.
selected for both experiments are: L90M, V82A, I54V,
In contrast, the present work uses two different tem-
I84V, V32I, M46I, M46L, I47V, G48V.
poral models: DBN and TNBN. Moreover, the experi-
ments presented here are aimed to analyze specific and Ir order to evaluate the models and to measure the
highly used antiretrovirals (IDV, APV, LPV, RTV), statistical significance of edge strengths we used non-
and its corresponding known resistance mutations in parametric bootstrapping. For this we obtained a re-
order to analyze the mutational pathways. shuffled (re-sampling with replacement) dataset gener-
ated from the original dataset and learned the models
4 EXPERIMENTS from this new dataset; this procedure was repeated 10
times. Confidence in a particular directed edge is mea-
sured as a percentage of the number of times that edge
In this section we present the data used in the exper-
actually appears in the set of reconstructed graphs.
iments, along with the selection method for the drugs
We used two thresholds for considering a relation as
and mutations. The first experiment presents the re-
important. The first one is a strong relation that ap-
sults using a DBN, while the second experiment uses
pears at least in 90% of the graphs, and the other is
a TNBN. Finally, we contrast the results and models
a suggestive relation, this occurs with values between
obtained.
70 and 90%. In Figures 2(a)-2(b) a suggestive rela-
tion is shown as an arrow labeled with *, and a strong
4.1 DATA AND PREPROCESSING
relationship is presented as an arrow label with **.
Data was gathered from the Stanford HIV Database
(HIVDB) (Shafer, 2006) obtained from longitudinal 4.2 DYNAMIC BAYESIAN NETWORK
treatment profiles reporting the evolution of mutations
in individual sequences. In order to obtain the corresponding DBN from the
data we began by learning the structure of the static
We retrieved data from patients with HIV subtype
network. For this stage each variable in a patient
B. We choose to work with this subtype because it
record was seen to have a binary value, where this
is the most common in America (Hemelaara et al.,
value was equal to 1 if that variable was present and
2006), our geographical region of interest. For each
0 if not present. While there are many approaches for
patient data retrieved contains a history consisting of
learning DBNs such as (Friedman, Murphy, and Rus-
a variable number of studies. Information regarding
sell, 1998; Wang, Yu, and Yao, 2006; Gao et al., 2007)
each study consists of an initial treatment (cocktail
we decided to use a simple approach, therefore the
of drugs) administered to the patient and the list of
structure of the static network was learned by apply-
the most frequent mutations in the viral population
ing (Chow and Liu, 1968) from which a fully connected
within the host at different times (in weeks) after the
tree is obtained. Since the Chow-Liu algorithm does
initial treatment. An example of the data is presented
not provide the direction of the arcs, we subsequently
in Table 1.
applied (Rebane and Pearl, 1987) in conjunction with
The number of studies available varies from 1 to 10 expert knowledge in order to obtain the final directed
studies per patient history. Since we are interested in acyclic graph. We mention that Rebane and Pearl’s
algorithm found the antiretroviral RTV and the mu- We evaluated different orderings for the K2 algorithm.
tation L90M to be parent nodes of the antiretroviral Specifically, we evaluated all the different combina-
IDV; however this relation was found to be invalid and tions for the first two mutations and the order of the
was not established since we know that a mutation rest was chosen randomly. In Figure 2(b) the model
cannot be a cause of a medication (expert knowledge). with highest predictive accuracy is presented.
By establishing mutations as effects of medications the
The model shows a relation between IDV and RTV,
directions of the remaining arcs are easily determined.
this may suggest that they are mainly used together.
To obtain the structure of the transition network each ATV is shown isolated from the rest. A reason for this
record was discretized into equal length time inter- may be that the number of cases that used this drug
vals, where the value of a variable was set to 1 if it was low and the algorithm could not find any relations
was present during that time interval and 0 otherwise. with other drugs or mutations.
Once a variable is observed it remained set to 1 for all
The mutations L90M, I54V and I84V appear to be
subsequent time intervals. If a variable was observed
the first mutations caused by the effects of the drugs.
at a time point between state changes, its value was
Mutation V82A appears to be important since it has
set to 1 for all time intervals greater than the observed
three arcs directed to other mutations. In this model,
time. For our experiments we used different granulari-
the mutations M46L, I47V, V32I, V82A and M46I had
ties: 5, 8,10 and 20, that corresponds to different num-
only a causing mutation as parent. Finally, the muta-
ber of weeks. The obtained structures were the same
tion G48V appears isolated; this may happen due to
except for one new arc in one experiment. When learn-
the fact that this mutation was infrequent in the data.
ing the transition network, a node in a time slice can
only choose its parents from the previous time slice.
In order to choose the best set of parents we applied 4.4 CONTRASTING THE MODELS
the Bayesian Information Criterion (BIC) scoring met-
ric to evaluate each selection. This metric returns the Structure
probability of the data given the model penalizing the
complexity of the model, in other words it favors sim- In order to compare the two models we begin by con-
pler models. The learning of the transition network trasting the structure displayed by each one. A DBN
was done by using Kevin Murphy’s Bayesian Network is typically represented as a 2-TBN in order to give a
Toolbox for Matlab (Murphy and others, 2001). Fig- smaller representation and therefore inference for fu-
ure 2(a) presents the resulting DBN. ture times requires the network to be unrolled. Unlike
the DBN, a TNBN only has one base network, which
From the model in Figure 2(a) we can observe, that all can be interpreted as the causal temporal relationships
the nodes, except ATV, have persistent arcs between existing between random variables. In a TNBN there
time slices. In the transition network, arcs from mu- is no need to repeat the structure. Therefore, TNBNs
tations in time slice t appear to be catalysts to the offer a more compact representation than DBNs, as
mutations they point to in time slice t + 1. The static DBNs can grow to become increasingly complex, as
network provides more information on which antiretro- they are further unrolled to include greater time inter-
virals are the causing agents of certain mutations. For vals. Unrolling a DBN can also result in the repetition
example, we can observe that the mutation L90M is of nodes whose state has not changed, thus generating
a reaction to the IDV drug. By following the arcs in unnecessary replications that clutter the model.
the static network and moving through the transition
network we can begin to detect mutational pathways. The way in which a TNBN is constructed also pro-
vides us with different visual information. Given that
4.3 TEMPORAL NODES BAYESIAN a TNBN is learned using the K2, the nodes of the re-
NETWORKS sulting model have a temporal ordering, and because
the TNBN only consists of one base structure, order
To apply the learning algorithm for the TNBN the of occurrence between different variables is easily visu-
data is arranged as a table where each column rep- alized. For example, in the context of HIV, pathways
resents a drug or mutation and each row represents formed between mutations can be determined by fol-
a patient case. For the drugs the values are USED lowing the directions of the arcs. In Figure 2(b) we can
or NOT USED, and for the mutations the values are: detect the pathway L90M→V82A→M46I. In contrast,
APPEAR, with the number of weeks in which the mu- in a DBN temporal orderings are more difficult to vi-
tation appeared for the first time, or NOT, if the mu- sualize solely from the model. However, DBNs offer
tation did not appear in that case. Thus, the drugs are their own distinct interpretation of the process being
instantaneous nodes, and the mutations are temporal modeled. In DBNs, variables that are strongly related
nodes of the TNBN. can be visualized from the arcs in both the static and
(a) A learned DBN model. Discontinuous lines represent persistent arcs.
(b) A learned TNBN model. Some intervals associated with their respective tem-
poral nodes are shown.
Figure 2: The two temporal models: DBN and TNBN. White nodes represent drugs and grey nodes represent
mutations of protease. An arc labeled with a * represents a suggestive relation. An arc with ** represents a
strong relation.
transition networks. For example, in Figure 2(a), in 5 CONCLUSIONS
time slice t arcs go from mutations L90M and M46I
to V82A in time slice t + 1, indicating a correlation Mutational pathways provide important information
among V82A and both of these other two mutations. for decision making in multidrug therapy. In our re-
search, we used HIV data from several patients in or-
der to analyze the temporal occurrence of mutations
Bootstrapping results and create such mutational pathways. We present a
comparison of the DBNs and TNBNs models created
The relations found after performing bootstrapping in with this data. Even when Dynamic Bayesian Net-
the models can be seen in Figures 2(a)-2(b). Both works have become a standard for time series mod-
models successfully detected several well known rela- eling, TNBNs offer different advantages. We show
tions among mutations, and while they both coincide why they should be considered as an option when fac-
in many of these, each one also displays a set of unique ing problems with dynamic information. Both models
relations found. For example, the TNBN detected were able to capture pathways previously discovered
V82A→V32I as a strong relation, this is consistent by clinical experiments. These results suggest that
with the literature, but was not found by the boot- temporal BNs are models that can have a significant
strapping preformed for the DBN. On the other hand, impact in the battle against the HIV disease. For ex-
the DBN was able to detect the relation L90M→I54V; ample, we could use these models to predict muta-
this relation is not present in the TNBN but exists in tional pathways and how long new antiretrovirals can
the literature. be used in specific cases. These models would also help
Overall the TNBN was more successful at detecting physicians to follow up on patients that are undergoing
mutational reactions to specific antiretrovirals. The a therapy that shares similar chemical properties with
mutational effects of the medications used are well doc- another treatment whose mutational pathways are al-
umented and the TNBN reflects this knowledge. For ready known. As future research, it would be interest-
example, RTV→I54V was found as a suggestive rela- ing to compare two different cocktail treatments along
tion; however it is known that when RTV is taken as with the temporal occurrence of drug resistant muta-
a booster in combination with IDV, I54V is a com- tions, in order to predict the most effective treatment.
mon mutational reaction. We note that the TNBN We believe this could aid the experts in the selection
also displays the relation between IDV and RTV. of the best treatment for the patient.
We also mention that not all relations found by the Acknowledgements
models have been previously reported. V82A→I84V
(found in the DBN) and M46I→M46L (found in both) We would like to thank Dr. Santiago Ávila-Rios and
are as far as the authors know unreported. Further Dr. Gustavo Reyes-Terán from CIENI-INER for their
research is needed to determine the correctness of these valuable comments and suggestions.
relations.
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