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. References Clinical relevance Arroyo-Figueroa, G., and Sucar, L. E. 1999. A tempo- ral Bayesian network for diagnosis and prediction. Both learned models were capable of obtaining known In Proceedings of the 15th UAI Conference, 13–22. mutational pathways. For example, it is known Beerenwinkel, N.; Schmidt, B.; Walter, H.; Kaiser, R.; that the LPV drug causes the pathways:(i) M46I/L, Lengauer, T.; Hoffmann, D.; Korn, K.; and Selbig, I54V/T/A/S and V82T/F/S (Kempf et al., 2001) , and J. 2002. Diversity and complexity of HIV-1 drug (ii) V32I, I47V/A, I50V, I54L/M and L76V (Nijhuis resistance: a bioinformatics approach to predicting et al., 2007; Parkin, Chappey, and Petropoulos, 2003). phenotype from genotype. Proceedings of the Na- For IDV the main mutations are V82A/T/F/S/M, tional Academy of Sciences of the United States of M46I/L, I54V/T/A, I84V and L90M (Bélec et al., America 99(12):8271–8276. 2000; Descamps et al., 2005). Moreover M46I/L, I54V/T/A/S and V82T/F/S are reported as major Bélec, L.; Piketty, C.; Si-Mohamed, A.; Goujon, mutations both to IDV and LPV and we can see that C.; Hallouin, M.; Cotigny, S.; Weiss, L.; and in Figures 2(a) and 2(b) the models were able to dis- Kazatchkine, M. 2000. High Levels of Drug- cover these shared pathways. These results suggest Resistant Human Immunodeficiency Virus Vari- that the models could be applied to new ARVs with ants in Patients Exhibiting Increasing CD4+ T structural similarities to determine the duration of the Cell Counts Despite Virologic Failure of Pro- treatment. tease Inhibitor Containing Antiretroviral Combi- nation Therapy. Journal of Infectious Diseases Hernandez-Leal, P.; Sucar, L. E.; and Gonzalez, J. A. 181(5):1808–1812. 2011. Learning temporal nodes Bayesian networks. In The 24th Florida Artificial Intelligence Research Chausa, P.; Cáceres, C.; Sacchi, L.; León, A.; García, Society Conference (FLAIRS-24). F.; Bellazzi, R.; and Gómez, E. 2009. Temporal Data Mining of HIV Registries: Results from a 25 Kempf, D.; Isaacson, J.; King, M.; Brun, S.; Xu, Y.; Years Follow-Up. Artificial Intelligence in Medicine Real, K.; Bernstein, B.; Japour, A.; Sun, E.; and 56–60. Rode, R. 2001. Identification of genotypic changes in human immunodeficiency virus protease that cor- Chow, C., and Liu, C. 1968. Approximating relate with reduced susceptibility to the protease in- discrete probability distributions with dependence hibitor lopinavir among viral isolates from protease trees. Information Theory, IEEE Transactions on inhibitor-experienced patients. Journal of Virology 14(3):462–467. 75(16):7462–7469. Cooper, G., and Herskovits, E. 1992. A Bayesian Murphy, K., et al. 2001. The bayes net tool- method for the induction of probabilistic networks box for matlab. Computing science and statistics from data. Machine learning 9(4):309–347. 33(2):1024–1034. Dagum, P.; Galper, A.; and Horvitz, E. 1992. Dynamic Nijhuis, M.; Wensing, A.; Bierman, W.; De Jong, D.; network models for forecasting. In Proceedings of the van Rooyen, W.; Kagan, R.; et al. 2007. A novel 8th Workshop UAI, 41–48. genetic pathway involving l76v and m46i leading to Descamps, D.; Joly, V.; Flandre, P.; Peytavin, G.; lopinavir/r resistance. HIVDRW2007 12:140. Meiffrédy, V.; Delarue, S.; Lastère, S.; Aboulker, Parkin, N.; Chappey, C.; and Petropoulos, C. 2003. J.; Yeni, P.; and Brun-Vézinet, F. 2005. Genotypic Improving lopinavir genotype algorithm through resistance analyses in nucleoside-pretreated patients phenotype correlations: novel mutation patterns failing an indinavir containing regimen: results from and amprenavir cross-resistance. Aids 17(7):955. a randomized comparative trial. Journal of clinical virology 33(2):99–103. Ramirez, J.; Cook, D.; Peterson, L.; and Peterson, Draghici, S., and Potter, R. B. 2003. Predicting HIV D. 2000. Temporal pattern discovery in course-of- drug resistance with neural networks. Bioinformat- disease data. Engineering in Medicine and Biology ics 19(1):98–107. Magazine, IEEE 19(4):63–71. Freeman, S.; Herron, J.; and Payton, M. 1998. Evolu- Rebane, G., and Pearl, J. 1987. The recovery of causal tionary analysis. Prentice Hall Upper Saddle River, poly-trees from statistical data. In Third Confer- NJ. ence on Uncertainty in Artificial Intelligence (Vol. 87, pp. 222-228)., volume 86, 222–228. Friedman, N.; Murphy, K.; and Russell, S. 1998. Learning the structure of dynamic probabilistic net- Shafer, R. 2006. Rationale and uses of a public hiv works. In Proceedings of the Fourteenth conference drug-resistance database. Journal of Infectious Dis- on Uncertainty in artificial intelligence, 139–147. eases 194(Supplement 1):S51–S58. Morgan Kaufmann Publishers Inc. Stanford University. 2012. Major HIV Drug Resistance Gao, S.; Xiao, Q.; Pan, Q.; and Li, Q. 2007. Learn- Mutations. http://hivdb.stanford.edu/pages/ ing dynamic bayesian networks structure based on download/resistanceMutationshandout.pdf. bayesian optimization algorithm. Advances in Neu- Wang, H.; Yu, K.; and Yao, H. 2006. Learn- ral Networks–ISNN 2007 424–431. ing dynamic bayesian networks using evolutionary Hemelaara, J.; Gouws, E.; Ghys, P. D.; and Osmanov, mcmc. In Computational Intelligence and Security, S. 2006. Global and regional distribution of HIV-1 2006 International Conference on, volume 1, 45–50. genetic subtypes and recombinants in 2004. AIDS IEEE. 20:W13–W23. Hernandez-Leal, P.; Rios-Flores, A.; Ávila-Rios, S.; Reyes-Terán, G.; González, J.; Orihuela-Espina, F.; Morales, E.; and Sucar, L. 2011. Unveiling HIV mutational networks associated to pharmacological selective pressure: a temporal Bayesian approach. Probabilistic Problem Solving in BioMedicine 41.