Jankovic, M Lourdes A Medina

Marija Jankovic

Gül E Okudan Kremer

Okudan Kremer

G Yannou

An investigation of

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Although advances in technology has provided many indispensable medical products to improve human health and sustain it, the development cost of medical devices burdens the healthcare systems as the industry is more technology-centric than ever before.

Accordingly, the identification of critical success factors for medical device development (MDD) has become increasingly important. These critical factors should be identified so that device development can be managed to minimize the adverse effects of these factors.

Many factors are related to the likelihood of success of devices in the market; and based on a company's ability to react to them, these factors are considered to be either internal or external [START_REF] Medina | An analysis of critical factors in medical device development to design for FDA[END_REF]. Internal factors mostly focus on the organizational context within which design is executed, and among others these factors include organization's composition in terms of the level of experience in design teams (Lucke et al., 2008) and effective communication of the development priorities [START_REF] Brown | A survey of success factors in new product development in the medical devices industry[END_REF]. Likewise, several publications [START_REF] Brown | A survey of success factors in new product development in the medical devices industry[END_REF][START_REF] Rochford | New product development process: stages and successes in the medical products industry[END_REF][START_REF] Millson | Managing innovation in the medical device industry[END_REF] report that the execution of a complete development process that includes preliminary market analyses, financial analyses, and customer involvement is critical for the further commercial success of medical devices.

On the other hand, external factors are mostly related to costs and profits, research and development (R&D), clinical research and insurance companies' reimbursement (Advanced Medical Technology Association 2003). Intellectual property protections and overseas market opportunities are also among these external factors. More importantly, the Food and Drug Administration (FDA), regulatory agency of medical devices marketed in the Unites States, has been suggested as the primary external factor influencing the development priorities (Advanced Medical Technology Association 2003).

Success factors in product development have been examined in various ways thus far. However, existing methods used for the identification of critical success factors have a number of shortcomings; among these are the subjectivity of survey-based studies and the complexity to comprehensively and rigorously address both internal and external factors [START_REF] Medina | An analysis of critical factors in medical device development to design for FDA[END_REF]. This paper discusses these shortcomings and proposes to overcome them with the application of a Bayesian network (BN) approach to examine the impact of product characteristics, company context and regulatory environment related factors on MDD. methodologies (e.g., [START_REF] Venter | New product development with dynamic decision support[END_REF][START_REF] Kim | The impact of R&D collaboration on innovative performance in Korea: A Bayesian network approach[END_REF]. The BN approach allows for a scientifically objective analysis with the ability to simultaneously consider quantitative and qualitative data [START_REF] Chiang | A fuzzy robust evaluation model for selecting and ranking NPD projects using Bayesian belief network and weight-restricted DEA[END_REF][START_REF] Venter | New product development with dynamic decision support[END_REF].

In the paper, we use the BN approach to investigate the critical factors of MDD.

BN analysis is performed using data from 2400 FDA approved orthopedic devices. In the remaining sections of the paper, we first provide a summary of the reviewed literature to identify potential factors with implications on MDD; then, we introduce the methodology. Details about the data set and results follow before we provide conclusions.

Literature Review

The design, development and manufacture of medical devices is challenged with the requirements from regulatory agencies, such as FDA. This fact is considered to set MDD apart from generic new product development (NPD). However, investigations of critical factors for MDD have been similar to those of generic products for which survey-based studies were conducted to separately examine internal and external factors (e.g., [START_REF] Ernst | Success factors of new product development: a review of the empirical literature[END_REF][START_REF] Brown | A survey of success factors in new product development in the medical devices industry[END_REF][START_REF] Rochford | New product development process: stages and successes in the medical products industry[END_REF][START_REF] Millson | Managing innovation in the medical device industry[END_REF]Advanced Medical Technology Association, 2003). An exception to the predominant choice of using surveys is Lucke et al.'s (2008) work, which followed multiple years of device developments in order to show the relevance of the development team's experience as an internal factor with implications for development time, a performance measure.

In order to address the shortcomings of survey-based studies and the time constraints of following the complete development process, prior research efforts employed statistical methods (e.g., ANCOVA) to explain important factors in relation to FDA's decision time [START_REF] Medina | An analysis of critical factors in medical device development to design for FDA[END_REF]. However, this analysis did not allow for a holistic study of quantitative variables that were related given that variables with strong correlations should not be included together in the ANCOVA analysis. Accordingly, in this paper BN approach is selected for a more robust analysis, where both internal and external factors are considered.

BN was applied in the area of new product development (NPD) as a technique for decision-making support. For example, in response to the shortcomings outlined above and others, BN has been used to develop a decision framework that can (1) manage quantitative and qualitative data simultaneously, (2) provide input for the several stages of the development process, and (3) integrate multiple aspects in one visual model [START_REF] Venter | New product development with dynamic decision support[END_REF]. Accordingly, a decision support model was built to incorporate expert knowledge and perform what if analyses that would support decision makers taking actions within an NPD process.

The NPD risks and uncertainties are major concerns, for which BNs have helped to assess these risk factors [START_REF] Chin | Assessing new product development project risk by Bayesian network with a systematic probability generation methodology[END_REF][START_REF] Chiang | A fuzzy robust evaluation model for selecting and ranking NPD projects using Bayesian belief network and weight-restricted DEA[END_REF][START_REF] Cai | Identifying product failure rate based on a conditional Bayesian network classifier[END_REF]. Some of the considered risk items include the time-to-market, manufacturability, maintainability and expected revenue of new products [START_REF] Chiang | A fuzzy robust evaluation model for selecting and ranking NPD projects using Bayesian belief network and weight-restricted DEA[END_REF]. The consideration of risks is a major issue for MDD, where the design of risk mitigation strategies is used to reduce the medical use error. This includes the development of the Bayesian risk identification model (BRIM) to manage and mitigate the risks related to human response failures that could come from a combination of interface, environment, or contextual influences [START_REF] Rieger | Bayesian risk identification model (BRIM): A predictive model to reduce use error risk in medical device interface design[END_REF]. BRIM defines performanceinfluencing conditions as the root causes that relate to the probability of human response failures. The result focusing on product interface design is a user error likelihood that can be used to assess product performance in terms of human interaction. While BRIM impacts the design stage of MDD, other efforts have been focused on the assessment of risk for devices already released to the market. At this stage, issues in the manufacturing process or supply chain have been addressed proactively with a BN based approach for the Health Hazard Analysis (HHA) [START_REF] Jiang | A quantitative approach for medical device Health Hazard Analysis[END_REF]. The results from this analysis are used by industry to perform corrective actions in the field, in addition to being considered by FDA for the classification of device recalls.

A different use of BN in medical device applications include the costeffectiveness analyses of MDD. This analysis has been improved with a BN based approach of iterative economic evaluations of new medical device technologies throughout their development process [START_REF] Vallejo-Torres | Integrating health economics modeling in the product development cycle of medical devices: A Bayesian approach[END_REF]. These included the implementation of simple analyses at early stages that will become more robust by incorporating more evidence as the development process moves forward [START_REF] Vallejo-Torres | Integrating health economics modeling in the product development cycle of medical devices: A Bayesian approach[END_REF].

In general, the reviewed studies have shown successful implementations of BN, establishing BN to be a robust technique. At the same time, as summarized, there are studies that investigated the critical factors in MDD; although they are either not comprehensive (i.e., omitted consideration of external and internal factors simultaneously), or the nature of the survey methods and analytical techniques implemented limit the ability to generalize. Accordingly, as our first step on route to developing an expert system to aid medical device developers, we have devised the following methodology to investigate the critical factors relevant to the MDD context.

Data and Variables

Data availability was dependent on the number of approved orthopedic devices in the FDA's public database to date. As a consequence, the raw data did not have an equal number of samples per category, i.e. product codes1 . From the complete data set of 9013 orthopedic devices (from 166 product codes), some product codes only had one data point while others had hundreds of data points. Only a subset (24) of these product codes was found to consistently have more than 100 data points for each code. In order to account for equal representation and hence to limit undue bias, we have randomly selected 100 devices per product code and included them along with their full FDA dataset. As a result, 2400 FDA approved orthopedic devices were randomly selected to study the critical factors of MDD.

Table 1 summarizes the variables under study with a description of their meaning.

Note that the information contained in the table was a deduction of our review of the literature (presented in [START_REF] Medina | A review of design for X methods for medical devices: The introduction of a design for FDA approach[END_REF][START_REF] Medina | An analysis of critical factors in medical device development to design for FDA[END_REF][START_REF] Medina | Supporting medical device development: A Standard product design process model[END_REF] as well as an evaluation of the FDA data and how the available data could be used to represent factors cited in the literature. As can be observed in the table, for each variable we have listed if they are internal-or external-variable, and quantitative-or qualitative-variable; we have also associated each variable either to the product, to the company or the regulatory environment (FDA). This association assignment process was done in an ad hoc manner. The variables were classified to be internal or external depending on the applicant's ability to influence such a factor. For instance, variables related to the regulatory environment (e.g., FDA's decision time and classifications) are not under the control of the applicant company. At the same time, product specific characteristics (e.g., context of use, body part, function) are under the control of the applicant company given their absolute power on the products they decide to develop and manufacture.

The variables were also classified given their direct association to the product, company or regulatory environment (FDA). The variables associated to the regulatory environment include different types of classifications, such as submission type, regulation number, but also evaluate the level of experience of FDA with historical reference. There are two submission types, pre-market notification (510(k)) and pre-market approval (PMA). Both submission types differ in their requirements, having most medical devices cleared with 510(k)s given that this is a simpler and faster pathway.

The historical reference is used to measure the level of experience in multiple aspects by quantifying the number of devices previously approved with the particular characteristic. Most of the historical reference variables are related to FDA's experience with the particular product code, body part, function or material. The company experience is also considered, with the company's historical reference measuring the number of devices previously cleared/approved for the same company. Other variables associated to the company include the name of the applicant and the year of submission.

The year of submission is an important variable to consider the changes in the regulations throughout the years that might have an impact on different factors.

Finally, variables associated to the product are several, ranging from different types of classifications, e.g., product code and risk classification, to product specific characteristics. Some of the product specific characteristics include the material, intended use, context of use and body part, among others. Regulation numbers (associated to regulatory environment) and product codes (associated to the product) are used to group medical devices in generic classifications of devices with the same characteristics and therefore the same requirements. Product codes provide a more detailed classification of homogeneous devices; whereas a regulation number could have multiple product codes, the vice versa is not allowed. This allows two devices with the same regulation number but different product codes to have different requirements. For instance, all the devices with the same product code will share the same risk classification. The risk classification consists of three levels (I, II and III), where devices in the highest level represent the higher risk. Other product characteristics are related to the device specific use, which may include the intended use that defines the clinical problem to be solved and the context of use, which defines whether the device is used in the operating room or doctor's office.

The performance measure (dependent variable) in the analyses is the FDA decision time. This value results from the calculation of the elapsed time between the company's submission date and FDA's decision date. FDA's decision time is important given its impact on the time-to-market for new medical devices.

Product

Expected use of the device based on the clinical need.

Examples: to be implanted to replace a joint, to be implanted to replace the head and neck of the femur.

Context of Use † ‡ (2)

Product

Setting in which the device is used: 1-surgery-operating room or 2-doctor's office.

Body Part † ‡ (7)

Product

Refers to the part of the body in which the device should be used. For example: hip, shoulder, elbow, etc. Function † ‡ (5)

Product

Defines the main function that the device was designed for. For example: prosthesis, surgical instrument, fixation, etc.

Number of Descriptors

Product

Amount of descriptors used for the device's product code.

Number of Materials ‡

Product Amount of materials described for the device's product code.

FDA Historical Reference for Product Code

Regulatory environment (FDA) Number of devices previously approved by FDA with same product code.

Company Historical Reference

Company Number of FDA approved orthopedic devices for the same applicant.

Historical Reference for Body Part

Regulatory environment (FDA) Number of devices previously approved by FDA for the same body part.

Historical

Reference for Function

Regulatory environment (FDA) Number of devices previously approved by FDA for the same function.

Historical

Reference for Material

Regulatory environment (FDA) Number of devices previously approved by FDA with the same material. †Qualitative (otherwise is quantitative), ‡Internal/controllable variable by company (otherwise is external) 4 Methodology

Bayesian network and algorithm selection

A Bayesian network (BN) gives a graphical representation of probabilistic causal interactions between a set of variables [START_REF] Kjaerulff | Bayesian networks and influence diagrams: A guide to construction and analysis[END_REF]. The nodes in this network represent the variables that are observed, where vertices or direct links represent interactions. The existence of vertices implies conditional dependence between two given variables. In general, a BN network can be seen as a graphical visualization of a set of "fuzzy" cause-effect rules that support different types of reasoning and predictive modeling.

BNs are represented using directed acyclic graphs (DAGs) [START_REF] Jensen | Bayesian networks and decision graphs[END_REF],

where the network is defined through a couple BN=(S, P):

 S=(N, A) represents the structure (i.e., the graph);

 "N" is a set of nodes. Each variable is represented as a set of mutually exclusive states;

 "A" is a set of edges representing the causal interaction between variables. The link from node N1 to N2 is read (defined) as "N1 is a parent of N2", and represents the fact that if we know the information on N1 then we can deduce the knowledge on N2.

 P represents a set of conditional probability distributions that define the probabilistic dependency between a node and its parents. Conditional Probability tables associated with each state of the variables are calculated, and provided for all variables using a generalization of the well-known Bayes Theorem (provided in Equation 1).

( ) ( ) (1)
Bayesian networks can be used for building predictive models based upon learned knowledge [START_REF] Heckerman | Bayesian networks for data mining[END_REF] concerning a specific domain but also to discover relationships between a large set of variables. The latter case is known as a learning BN network. Two main approaches are used for Bayesian network learning: (1) Constraintbased approaches, and (2) Score-based approaches. Constraint based approaches form the network using the conditional dependence relationships found in the data [START_REF] Spirtes | Causation, Prediction, and Search[END_REF]. Although very reliable in network learning scenarios, constraint-based approaches have limitations in the reliability of high-dimensional conditional independence tests.

Score-based approaches are based on definition of an evaluation function for candidate network quality [START_REF] Heckerman | Learning bayesian networks: The combination of knowledge and statistical data[END_REF][START_REF] Friedman | Learning bayesian networks with local structure[END_REF]. These approaches are less sensitive to data quality.

In this research, we use a novel hybrid approach, Smart Greedy+ algorithm [START_REF] Jouffe | Smart-Greedy+ : Apprentissage hybride de réseaux bayésiens[END_REF][START_REF] Jouffe | New search strategies for learning Bayesian networks[END_REF]. This hybrid algorithm consists of three steps:

1. Pre-processing algorithm that collects data on the best local network configuration for each node, Experimental results that compare this approach with greedy search and tabu search have shown that Smart Greedy+ outperforms these classical approaches of learning using Bayesian networks and that the precision of the network is higher in all classes [START_REF] Jouffe | New search strategies for learning Bayesian networks[END_REF]. Thus, our reasons for the choice of Smart Greedy+ include the precision of the network, the avoidance of local optima in the network and the possibility of discovering causal relationships.

Use of Bayesian networks for relation discovering

In this study we propose to use Bayesian network learning algorithms in order to explore data relationships. The choice of using a BN-based data mining and exploration is motivated by the advantages that BNs present when exploring different data and uncertainty modeling capabilities. First, BNs are effective in providing models for direct causal relationships, i.e., mathematical definition of probabilities and conditional independence statements can be connected to the definition of causality (Pearl and Verma, 1991;[START_REF] Heckerman | A Bayesian approach to causal discovery[END_REF][START_REF] Friedman | Using Bayesian networks to analyze expression data[END_REF]; thus, when relationship discovering is intended, BNs can be used to discover and represent the causal relationships. Like in our case, when the data set is relatively large and mixed data types are used (quantitative and qualitative), and in cases where data sets might be incomplete, BNs are considered to be the appropriate methodology for relationship mining [START_REF] Heckerman | Bayesian networks for data mining[END_REF][START_REF] Chen | Data-mining and uncertain reasoning: an integrated approach[END_REF][START_REF] De Santana | Strategies for improving the modeling and interpretability of Bayesian networks[END_REF][START_REF] Chang | Modeling semantics of inconsistent qualitative knowledge for quantitative Bayesian network inference[END_REF]. It is also noteworthy that BN relationship mining affords identification of local interactions within one process, where the value of one variable directly depends upon a small number of other variables [START_REF] Friedman | Using Bayesian networks to analyze expression data[END_REF]. This is indeed the objective of our study, to identify factors that directly influence FDA decision time, as well as investigating the propagation of information throughout the entire network. Finally, it is important to underline that one of the major advantages of BNs is the possibility of integrating uncertainty in the network structure modeling [START_REF] Barton | Bayesian belief networks as a meta-modeling tool in integrated river basin management -Pros and cons in evaluating nutrient abatement decisions under uncertainty in a Norwegian river basin[END_REF]).

The research methodology followed in this study is shown in After validating the network performance and precision, the capability of information propagation is used to evaluate possible changes within the network. This information propagation can be considered as "What-if" simulations [START_REF] Yannou | Empirical Verifications of some Radical Innovation Design Principles onto the quality of innovative Designs[END_REF][START_REF] Yannou | Observations from radical innovation projects considering the company context[END_REF]. We addressed scenarios related to changes in FDA decision time subject to changes in three variable categories: product, company and FDA regulation variables.

Results & Discussion

We have used values of 2400 FDA approved orthopedic devices across 20 variables listed in Table 1. Although hypothesized relationships can be formed by the decisionmaker for testing, we have opted for the use of unsupervised learning in order to explore the structure of the network (i.e., the relations between the given set of variables), for which the conditional joint probability computations are used. This network gives an overview of explored variables as well as their influence. The structure of the BN network shows probabilistic inferences of the variables studied (shown in Figure 2). One of the first things that can be observed is that the FDA decision time is impacted by the type of submission that is in turn impacted by the year of decision. The different submission types, Pre-market Approval (PMA) and Pre-market Notification (510(k)), have different requirements making the first one the strictest (or more complex) pathway with a longer decision time. Year of decision (FDA regulatory variable) seems to be a crucial factor linking FDA decision time with product and company variables. One possible explanation to this might be that in operational policy decisions FDA takes into account contemporary market needs in the Unites States.

Another central part of this network structure (in Figure 2) is the regulation number. The FDA regulatory factor seems to be influenced by different materials used in the device, and influenced by the intended use as well as the risk classification. Device risk classification is dependent upon the type and number of materials used in the device as well as the FDA regulations represented with the regulation number. These results also underline the obvious importance of regulation number as it is connected to a large number of product variables: materials, number of descriptors, function, product ID and intended use. Supporting this, the regulation number is significant by definition as it classifies similar medical devices.

The network structure also highlights the requisite expertise of companies. The historical reference (HR) per function is a parent node of the company HR, which in turn is related to the applicant. It seems also that year of decision is a parent node of the applicant. Taken together, these confirm that companies are specialized more on product functions and that their historical records support that claim.

A further reflection of the complex medical device development environment perhaps, year of decision is a parent node of applicant; that is, companies with different expertise might be focusing on product approvals that are advertised/recommended by FDA as areas of need. While this might be seen as directing attention (as recommended by FDA to developers) to contemporary needs, it might also negatively impact the decision time for other devices in niche areas. How this fact impacts medical product innovation strategies for companies should be explored as innovation patterns might be impacted by FDA guidelines and recommendations.

Although the network shown in Figure 2 is sufficient to understand the significant relations among the variables, "What-If" simulations can enrich our understanding.

Accordingly, based on the predictive capabilities of the observed BN, the distribution of the FDA decision time is varied in three cluster levels, and other product, company and regulatory environment variables are studied. We present these details in the following three sections.

FDA Decision Time & Product Variables

Studying the product variables for their potential impact on FDA decision time is important as an enhanced understanding can better prepare companies in their planning For the second cluster of the FDA decision time (139.961<Decision

Time<354.043 days), shown in Figure 6, we observe that although the variation is still minimal, there is a noticible decrease in the function variable. The fixation is used in 55.88% of the devices whereas the similar value for the first cluster was 57.5%. At the same time, an increase is detected across the first and second clusters in the prostheses from 25.34% to 27.96%, respectively. The change in the body part variable is minimal where only the spinal mode decreases from 26.27% (in cluster one) to 24.19%. Usage of 2 or more materials increases from 36.63% to 39.91% with the shift from cluster 1 to 2. When the FDA decision time is longer than ~355 days (Figure 7), there is almost no change in the distributions. Overall, it seems that product variables do not contribute much to the decrease in FDA decision time, and that there is no evidence showing that product related variables are the main reasons for the FDA decision time changes across clusters. These simulations might reflect the dynamics of the MDD market. For instance, the context of use is not changing; there is between 5.41% and 5.70% projects that are intended for the doctors' office. Very large percentage of the developed devices is for the surgery/operating room (from 94.30% to 94.59%). Function is mostly impacted by fixations and prosthesis; very small percentages are related to fusion, surgical instruments and bone void fillers. Finally, in most of the cases body parts are bone, hip or spine.

FDA Decision Time & Company Variables

Company variables characterize companies partaking in the MDD market. The analysis of these variables could potentially show why some companies are more successful and their impact on global FDA decision time. At a first glance, the number of company related variables followed by the FDA is very limited. There are three variables that are taken into account in this study: (1) type of submission, (2) applicant, and (3) company HR. Initially observed distribution (Figure 8) shows that in majority of the cases, the type of submissions is either a special 510(k) or traditional 510(k). As per the FDA guidelines, the special 510(k) is an alternate method to the traditional 510(k), and is instituted in order to facilitate the review process for cases when a previously cleared device has been modified [START_REF] Medina | A review of design for X methods for medical devices: The introduction of a design for FDA approach[END_REF]. Together they represent 98.45% of submissions. It seems also that companies in general have relatively significant experience levels. For example, in 67.57% of cases, companies have already submitted 72 projects, and 83.83% of the companies have previously submitted projects. For the third cluster of the company related variables, the submission type is predominantly the original PMAs. It appears that almost all original PMAs need more than ~354 days to evaluate and arrive at a decision. There are also a large number of traditional types that is treated this way (95.14%). The PMA is the strictest pathway of approval used for those devices of higher risk with the need for additional information to prove their safety and effectiveness with scientific evidence that may include non-clinical laboratory studies and clinical investigation [START_REF] Medina | A review of design for X methods for medical devices: The introduction of a design for FDA approach[END_REF]. Original PMAs refer to the first submission made for the particular device, while supplements are used to approve modifications of original submissions. Supplemental submissions were out of the scope of this work. FDA Regulation variables cover the type of the submissions, year of decision, HR for materials, FDA HR for product code and other devices, regulation number and risk classification. Initial distributions (shown in Figure 12) show that majority of submissions are 510(k)s (~99.79%). As for the year of decision, it seems that from 1992 until 2004 the number of submissions was relatively stable ranging between 13.80% and 18.45%. There is a considerable shift in 2004, however; the submissions increased to 37.14% in that year. It is also apparent that most of the submissions involved already known materials or products. HR variables show similar tendencies. However, the (94.44%). There are no class I devices given that most of these are exempt from having to obtain clearance/approval from FDA [START_REF] Medina | A review of design for X methods for medical devices: The introduction of a design for FDA approach[END_REF]. The differences between the distributions when FDA decision time is between 140 and 354 days and where it is larger than 354 days (see Figures 14 and15) are very small. This lack of shift/change in distributions shows that FDA Regulation variables do not contribute considerably to the increase of FDA decision time. One point of note is that there is an increase of submissions with the Regulation No. ID that are <=14.75 and <=51.083 in comparison to the initial distributions. When we compare these distributions to the initial ones, it can be seen that for the FDA decision time > ~354 days there are less number of projects submitted in the year 2004 (42.83% in comparison to 51.58%). This shift might underline the effort to reduce the FDA decision time in recent years.

The difference in number of applications concerns also the HR per function.

Although the mean decision time is (μ) 124.292 in the observed distribution, for the specific cluster three cases, the mean value for functional reference drops to 1706 from the overall mean of ~1857. It is possible that the projects that need more time concern new functions that FDA has less knowledge about. Companies should be aware and prepared for this situation. Of course, the market potential for an innovative product can be considerable and the safety of patients is important; however, the elongated FDA evaluations of products with newer functions might discourage companies. Given the provisions of the special 510(k) submissions, companies might focus more on incremental innovations rather than drastic ones, potentially with very long FDA decision times.

Summary

Unsupervised learning network structure developed using actual data underlines the importance of the FDA policies in medical device development. The dominant factor is the type of submission and the change of efforts in FDA policy that can be observed in the year of decision. The decision times for different types of submissions are consistently different as per FDA guidelines, although actual times could be longer than those specified by FDA. It also seems that recently (since 2004) there have been efforts to reduce the FDA decision time given the increase in number of submissions.

A very noteworthy fact lies in the discovery of very small relevance of product variables on the decision time. This underlines the recommendations for the companies to acquire the necessary knowledge on the FDA regulations in order to succeed in their efforts. Moreover, company variables proved to be relevant mostly based on their selection of submission types.

BN structure also demonstrates that risk classification is related to the materials used and especially the number of materials used. This link is reinforced also by the fact that regulation number is also dependent upon materials used. The network also highlights the impact of FDA policy in integrating previous knowledge, in particular the importance of different HR and the year of decision. It appears that a particular attention by the FDA is directed to materials used, as evidenced by the fact that material used is the only product variable having causal relationship with the year of decision.

Simulations also pointed out that the FDA decision time varies with regards to the variation in HR per function. HR is an indicator of experience, which quantifies the number of devices previously approved with the same characteristic. The relevance of these variables along with the longer decision times for PMAs makes us question the likelihood of innovative products to go through the process in an efficient manner. FDA has been identified as an inhibiting factor for the discovery of medical devices [START_REF] Foote | Medical technology development: limiting regulation[END_REF]; however, FDA has recently created a new regulatory pathway for innovative medical devices [START_REF] Fda | Innovation Pathway[END_REF] to overcome this barrier.

Conclusions

This paper presents our inference framework along with initial observations in an effort to solidify the relationships of the MDD setting in an evidence-based fashion in order to result in a useful expert system. Causal relationships identified in the network structure will be used as the significant predictors within the expert system. Although we have used only 2400 actual data points, we are able to show the legitimacy of the chosen methods in yielding useful inferences. In the subsequent expert system development, not only will the data set be enhanced but also cases from other regulatory settings will be considered.

A valid network is developed and analyzed in detail based on product, company and regulatory environment variables in relation with FDA decision time. Some of the relevant variables included the type of submission, year of decision and historical reference. Based on these results, further research should include the application of supervised learning along with further study of other aspects of MDD.

Of importance are the potential impacts of this planned expert system with implications on innovation/technology development with a focus on MDD. The variables included, relating to product, company and regulatory setting, show the most pertinent factors with which product launch time can be reduced. Companies armed with this knowledge can preplan their knowledge and monetary capital in seeing through the projects to their completion.

This paper also extends the literature on MDD and the identification of critical factors with the implementation of a BN approach with unsupervised learning. Some of the future research directions may include investigating the importance of historical reference and innovation further, along with the interrelations between different variables.

  2. A hybrid learning algorithm combining classical transformation operators of the score-based algorithms with a novel heuristics for arc orientation and post-processing steps based upon constraint-based approaches, 3. A post-processing algorithm to improve the final structure by conducting a restricted search in the ordered topological space.

  Figure 1. Utilizing actual FDA medical device development data and different factors identified in the literature, the unsupervised BN algorithm is implemented to discover relationships between different variables. Examination of various factors also required combing through the published sources in engineering and business literatures focusing on product development. In this study 19 variables are examined and integrated into 2400 data vectors (in total 45600 data points).

Figure

  Figure 1. Research Methodology

Figure 2 .

 2 Figure 2. Unsupervised Learning Using the Taboo Order Algorithm

  stage. Product related variables that are taken into consideration are: context of use, product function, body parts, number of descriptors, number of materials, product ID and intended use. Initial observed distributions (see Figure4) show that in majority of the cases (73.88%) the FDA decision time is less than 139.961 days. Most of the products are intended for surgery, and relate to bone (33.21%), hip (21.13%) and spine (25.71%).Most of the approved devices are made up of three different materials, and very few (4.1%) combine four different materials. An interesting fact is that a large number of materials, approximately 29.17%, are not specified; this means that the material was not a relevant factor for those devices.

Figure 4 .

 4 Figure 4. Initial distributions for the Product Variables of the product sample

Figure 5 .

 5 Figure 5. Product Variables for the FDA Decision Time Cluster1 (Decision Time<139.961 days)

Figure 6 .

 6 Figure 6. Product Variables for FDA Decision Time Cluster 2 (139.961<Decision Time< 354.043)

Figure 7 .

 7 Figure 7. Product Variables for FDA Decision Time Cluster 3 (Decision Time>354.043 days)

Figure 8 .

 8 Figure 8. Association of the Company Variables with the FDA Decision Time

Figure 9 .

 9 Figure 9. Company Variables for the FDA Decision Time Cluster1 (Decision Time<139.961 days)

Figure 10 .

 10 Figure 10. Company Variables for FDA Decision Time Cluster 2 (139.961<Decision Time< 354.043)

Figure 11 .

 11 Figure 11. Company Variables for FDA Decision Time Cluster 3 (Decision Time>354.043 days)

Figure 12 .

 12 Figure 12. Association of the PFDA Regulation Variables with the FDA Decision Time

Figure 13 .

 13 Figure 13. FDA Regulation Variables for the FDA Decision Time Cluster1 (Decision Time<139.961 days)

Figure 14 .

 14 Figure 14. FDA Regulation Variables for FDA Decision Time Cluster 2 (139.961<Decision Time< 354.043)

Figure 15 .

 15 Figure 15. FDA Regulation Variables for FDA Decision Time Cluster 3 (Decision Time>354.043 days)

Table 1 .

 1 Description of Variables (Where a number is present in parentheses, it refers to the levels of the variable, or the number of different categories considered for the variable) Regulatory environment (FDA) FDA classification in reference to the Code of Federal Regulations (CFR). It is a more aggregated grouping of devices within different product codes. For example, PCs JDJ and JDK have regulation number 878.33.

	Variable Name (Number of levels)	Association	Description
	FDA's Decision	Regulatory environment (FDA) Difference between the decision date and the date received:
	Time		-Decision date: when FDA made a resolution about the
			submission
			-Date received: when FDA received the submission
	Applicant † ‡	Company	Company making the submission.
	(474)
	Submission	Company	Year in which the company submitted to FDA. Accounts
	Year † ‡ (33,		for potential changes in the regulations throughout the
	1977-2010)		years.
	Submission	Regulatory environment (FDA) Submission used for the devices:
	Type † (2)		-Premarket Notification (510(k))
			-Premarket Approval (PMA)
	Submission	Company	Sub-category for the submission type. For PMAs only the
	Sub-type † (4)		original application is included (1) and the supplements are
			excluded. For 510(k) all the categories are included: 2-
			Traditional, 3-Special 510(k), and 4-Abbreviated.
	Product Code †	Product	FDA classification that groups devices with same
	(24)		characteristics and requirements.
	Regulation
	Number †
	(16)
	Risk
	Classification †
	(2)
	Material † ‡	Product	Material used for the device or device component.
	(7)		Examples: polymer, metal, ceramic.
	Intended Use † ‡
	(9)

Product

FDA classification to explain the level of risk: I, II and III.

Class III represents the higher level of risk. The data set includes class II and III.

Product codes are FDA classifications used to group medical devices with the same characteristics and requirements.