Akram Hakiri
email: hakiri@laas.fr

Michel Diaz
email: diaz@laas.fr

A Formal Model for the Specification and Analysis of HLA-based Distributed Multimedia Interactive Simulation using Hierarchical Time Stream Petri Nets

Keywords: Formal Model, Distributed Multimedia Simulation, HLA, HTSPN

This paper proposes a formal model for the specification and analysis of distributed multimedia simulation. This model is based on Hierarchical Timed Stream Petri Nets (HTSPN), which has been proposed for specifying temporal and logical constraints in high level multimedia description and simulation. It takes into account a powerful synchronization definition between different flows issued from distributed multimedia systems. A simulation was done using a special Javabased framework to assess the methodology and analyze the expression and interpretation power of HTSPNs. For instance, such an interpreted model permits powerful analysis techniques for validating the quality of service in computer networks before protocol implementation. Consequently, it allows the specification of both the temporal non-determinism of weakly distributed applications and the temporal variability of the multimedia processing. An example is used to demonstrate the capabilities of this scheme to specify the QoS requirements of simulated applications.

I. INTRODUCTION

The specification and the verification of temporal and logical properties of distributed multimedia interactive simulation is a fundamental step to be conducted before implementation. Therefore, on one hand, synchronization schemes [START_REF] Blakowski | A media synchronization survey: reference model, specification, and case studies[END_REF] bring important contributions to the emerging concepts of distributed simulation systems, especially when these systems must maintain temporal relations between various streams. On the other hand, HLA-based applications [1]) need structural approaches to specify the synchronization scenarios between intra-flow, inter-flows and inter-objects to allow an adequate management of the system resources. This paper suggests to use a formal model based on Hierarchical Stream Timed Petri Nets to specify and analyze synchronization constrains between synchronized units in intra-flow and inter-flow cases for the specification and the verification of the next generation of distributed interactive multimedia simulation.

The proposed model is applied to an HLA based simulation which includes audio, video and interactive streams issued from a selected application. Using the power modeling of Petri Nets suggests the specification of a requested quality of services in distributed asynchronous multimedia application. The synchronization scheme developed here discus applications that involve HLA and are built on HLA-RTI APIs. Its aim is to facilitate the editing phase and the development time required to deliver high fidelity simulation that will respect all structural, temporal and logical application related constraints.

This paper is organized as follow: after a brief introduction, Section II introduces the motivation of multimedia formal specification. In Section III Petri Nets have been selected for specifying distributed multimedia applications. Section IV presents a set of QoS requirements to be used in distributed multimedia simulation. Section V introduces the formal model and shows analysis results. Transport architecture is presented in Section VI and conclusion is given in Section VII.

II. MOTIVATION

In the general case, flows need to satisfy natural synchronization constraints and synthetic synchronization constraints between applications. The natural synchronization constraints are intrinsic to the flow itself and need to be respected when presented to the remote hosts to ensure the comprehension of the associated information. For example, in SECAM systems, a video frame is be displayed 25 times per second. These constraints are given by codecs. Synthetic constraints are imposed by the application itself and results from the abstract global synchronization specified by developers. For instance, an audio stream must start when a given event occurs. To handle the granularity of Figure 1. Correspondence between Information Units and Synchronization Units these constraints, synchronization units have to process the information units, providing a way to modulate a synchronization scheme for each flow and to provide an optimal control of each flow with respect to the system resources.

Figure 1 shows the correspondence between the information units (UI) and the synchronization units (SU). Each synchronization unit, noted SU i , is associated to a sequence of information units (IU i ), together with each starting date d i and finishing date f i . The granularity of the information induces the performance of the scheduling protocol. In order to process streams using a set of available resources, the synchronization scheme has to use synchronization units adapted to the specific flow and to the synchronization of the media acquisition.

The specification of the synchronization scheme should be specified using a formal model to conduct an editing and a verification phase before any implementation. The analysis of the possible expressive power required for distributed interactive systems lead to select a formalism based on Petri nets (PN).

Other research contributions have been proposed to provide a formal approach for the specification of the distributed multimedia communication. Authors in [START_REF] Senac | Modeling logical and temporal synchronization in hypermedia systems[END_REF] and [START_REF] Xie | Complex System Simulation Based on Petri Net Combined with HLA[END_REF] used Petri Nets to simulate a complex military simulation system with HLA, to manage its concurrent properties and to specify the synchronization problems for the simulated commands. Author in [START_REF] Guha | A Framework For Modeling High Level Architecture (Hla) Using Petri Nets[END_REF] explores the impact of Time Service Management in HLA (HLA Time Management Service) to specify an engine based on Stochastic Petri Nets to run the distributed simulation, and proposes the use of HLA as a platform of reference to compare different approaches for partitioning and distributing application executions. [START_REF] Kpatcha | Exploring impact of time management services on HLA-based Petri Nets Simulation Engine[END_REF] presents an approach based on Colored Petri Nets to reduce the bandwidth usage for distributed simulations using HLA. In [START_REF] Combettes | Interoperability Compliance Validation Of HLA Federations Based On Colored Petri Nets[END_REF], the authors propose a colored temporal PN model for simulating the federation execution. The proposed model aims to assist developers of HLA simulations to design high-level simulation and to specify the constraints of the simulation.

However, as we outlined in our previous work [START_REF] Hakiri | Multi-level Model for Synchronizing Temporal Streams on HLA-Based Distributed Multimedia Applications Using HTSPN[END_REF] also with other related works, these approaches do not provide a structured model, and do not provide a comprehensive qualitative analysis of the simulation. Furthermore, no quantitative analysis was presented, particularly when specifying the temporal constraints and the performance analysis of information exchanged during the simulation. As a consequence, in this paper we use the same Hierarchical Time Stream Petri Nets formalism to extend the power of the previous models to express the spatial, temporal, logical and semantic structures that appear in the distributed interactive multimedia simulation.

Our contribution, is an extension this previous works, but with another validation tool, uses primarily a temporal model because it induces a required flexible management of system resources and allows expressing of the non determinism that may occur when a time de-synchronization occurs between different distributed streams, especially when these flows are very heterogeneous, such as the union of streaming media (audio, video, images) and streaming interaction flows coming from the actors of the virtual environments. That is, we can find a tradeoff between two targets: synchronization of stream to reduce the end-to-end latency and eliminating delay jitter. Hence, we aim to improve those QoS parameters and we add real-time scheduling approach for stream synchronization.

III. HIERARCHICAL TIME STREAM PETRI NETS

The HTSPN [START_REF] Diaz | Time Stream Petri Nets a model for timed multimedia information[END_REF] (see also the HTSPN formalism in our previous work cited in Section II) model is an extended Petri Net model that used timed arcs for the modeling of multimedia processing (communication, presentation...). The temporal jitter appearing inside weakly synchronous multimedia systems is modeled by the arc Temporal Validity Interval (TVI). These arcs TVI are tuple [x, n, y], where x, n and y are respectively the minimum, the nominal and the maximum admissible durations of the related processing. Such way of multimedia systems modeling allows the expression of both the temporal non-determinism of weakly synchronization in distributed multimedia applications and the admissible temporal variability of multimedia objects.

Temporal drifts between multimedia streams can be fully and accurately specified with the help of 9 different synchronization semantics that can be selectively associated with transitions. As a consequence, HTSPNs appear to be a powerful tool for the formal modeling, analysis, verification and simulation of distributed multimedia simulation systems. HTSPN models allow three fundamental concepts to be formally described with powerful temporal extensions: the atomic, the composite and the link components. Atomic Component: an atomic component is modeled in HTSPNs by an arc with a TVI and a place associated with one atomic resources type, for example video data with [START_REF] Kpatcha | Exploring impact of time management services on HLA-based Petri Nets Simulation Engine[END_REF][START_REF] Guha | A Framework For Modeling High Level Architecture (Hla) Using Petri Nets[END_REF]12] as TVA. Atomic synchronization layers aim to describe synchronization constraints inside atomic components by specifying intra-stream synchronization. Link Component: a link is modeled in HTSPN by a timed arc (L, t), where L is the link (to be layered) place. The TVA associated with the link introduces the timed link concepts. Using the HTSPN firing rules [START_REF] Willrich | Multimedia Authoring with Hierarchical Timed Stream Petri Nets and Java, Multimedia Tools and Applications[END_REF], timed links allow the modeling and the formal specification of the transversal semantics of the application layer. Composite Component: the composite component provides a hierarchical structuring mechanism based on the recursive composition of atomic and composite component through the use of sub-nets. The HTSPN use these composite type places that are not only structurally, but also temporally, equivalent to a (sub) net. A composite layer is able to describe inter-stream synchronization constraints.

IV. QOS REQUIREMENTS IN DISTRIBUTED MULTIMEDIA SIMULATION

The quality of the mono-media presentation describes the quality of the discontinuity of a single stream. This discontinuity occurs for instance when data are lost; it can cause a significant loss of synchronization, and it becomes very important to optimize the quality of the presentation at the receiver side to present the application. The end to end latency defines the maximum allowable transfer delay between two remote entities. This period corresponds, for example, to the delay when a sender pronounces a word and when the receiver receives the sound. This delay should not exceed a given limit since it affects the interactive communication between the remote users. The intra-stream synchronization ensures the compliance with the time constraints of the timing units for each stream. The synchronization level is given for each flow by the temporal validity intervals (nominal delay, allowable jitter) of each synchronization unit. The intra-stream jitter is given by (1) and illustrated in Figure 2. τ (n) is the arrival time of object n and the maximum allowable jitter intra-flow (equation ( 2)) is then 2× '.

min ≤ τ (n -1) -τ (n) ≤ max (1)
τ (n) is an intra-flow object presented at time n, 2* ' is the intra-flow allowable jitter.

-min = T - ( 2
) max = T + (3)
To ensure the receipt of n objects within a time interval, For the intra-stream synchronization, the QoS requirements, that should be satisfied for instance when an audio and a video streams need to be synchronized, depend on the communication variability. For instance, at the receiver site, if two units of two different flows arrive at 2 different times t1 and t2, the correctness of their synchronization has to be deduced from the specification and the presentation constraints: the synchronization scheme should provide the acceptable interval for synchronized units of the flows, and should define some actions to eliminate the streams discontinuities. As an example, if a flow is behind the other(s) (is late) de-synchronization will occur and the discontinuity may become visible (when sound is no more synchronized with video, this problem is called "Lip-Synchronization). Relation (3) and Figure 3 specifies a periodic traffic, with period T, and an inter-flow jitter equal to 2* for one period.

min ≤ τ (x1, x2) ≤ max (4) min = T - ( 5
) max = T - (6)
Figure 3. Inter-stream Jitter

It is clear from the above equations that the flows must be sent periodically. In particular, the packet size is a very important criteria that has to be carefully chosen for the QoS constraints to be fulfilled. Indeed, for example for audio data, the length of the packet affects the time required to produce it. Table I gives the packet size with respect to the data that has to be transmitted through a network. it shows how audio data should be prepared and sent over Networks. Column 1 presents the sampling frequency that produces the audio data. Column 2 gives the time necessary to produce an IP packet (1518 Bytes). For example, with a 8 KHz sample frequency, the time required to produce this packet is 189 ms. In order to fulfill the QoS requirements for distributed media application, this delay need to be short enough because it delays the packets and implies the quality of the interactivity and of the presentation at the receiver side. Then, Columns 3, 4 and 5 show the size of the frame, given an interval of time, to satisfy the quality of the presentation. It seems that a delay of 20 ms is for sure a correct value because it sends a high audio delay quality with the respect to the frame size. The requirement of low latency means that it is better for the senders to send small packets frequently rather than large packets seldomly. Let us assume that the acceptance purpose is to provide a 150 ms end-to-end latency: 50 ms can be taken as the maximum time allowed for preparing and sending a packet, also for processing and presenting it in the receiving application, and also can be the propagation delay in the network. Distributed multimedia applications are not only presentation driven; they are also data-driven. Therefore, a formal model must describe both the data and their presentation. In addition, the model must provide means for representing the logical and temporal compositions of their interactions. In order to specify the best choice for an audio packet size, Figure 4 gives the functional point able to satisfy our interactive requirements. It displays the variability of the packet size with respect to the time needed to produce the packet. These curves provide the Temporal Validity Interval (TVI) which will be used in our formal model. It follows that the best value of TVI is given by [15,20,25], where 20 ms is the nominal time to produce a packet, and there is a maximal drift per period of 2*5=10 ms. The first curve in Figure 5 indicates the time required to produce a 1518 Byte audio data frame. From the left, this curve shows for example that a voice corresponding to a sequence of samples of 8 bits at a frequency of 8 kHz leads to produce a sample every 125 ms; for a packet size of 1518 Bytes, the sender must wait 189 ms to produce and start to send only this packet. This value does not fulfill the QoS requirements needed to transmit the packets of interactive applications. A 22 kHz sampling allows a processing and production time equal to 34ms. However, it does not lead after these 34 ms to a packet that exceed the proposed maximum size of 1518 Bytes, it is about 2201 Bytes. As said before, we selected 50 ms as the maximum time allowed to produce a packet at the sender side, and as a consequence it is clear in Figure 4 that it is not possible to send a full IP packet. If a 22 KHz sampling frequency would have been selected, it would have fulfilled all temporal and length QoS requirements: the delay to produce the audio data frame is 20ms for a packet size of 881 Bytes, but the packet size is rather short. Using the 50 ms values lead to start the specification of the formal model.

Notice that if some problems come from the network, and if then the different flows are not received at the same time, some application incoherence could results and the corresponding flows need to be re-synchronized, if possible, at the receiver side. For example, as applications of distributed simulations incorporate multimedia flows, together with flows resulting from the interactive system control, they may become incoherent after crossing a (wide area or other) disrupting network. To ensure consistency between these flows, an adequate synchronization scheme between these flows is necessary and has to be specified. Such synchronization between the flows can be defined by successive steps, for example first by ensuring the synchronization in each streams, second between the different multimedia streams, and, third by ensuring the synchronization between these multimedia flows and the control flows of the distributed interactive simulation.

V. FORMAL MODEL OVER HLA-RTI Basically, the application (Figure 5) is a platform for distributed interactive simulation, and it allows end users to interact by voice, video and distributed simulation events sent in real time. Such an application consists of at least three streams: the audio and video streams captured by a camera and the flow coming from the modification of the virtual environment of the distributed simulation. The synchronization scheme considered involves three types of flow synchronization: The corresponding HTSPN synchronization model is defined by a three levels representation: the link level considers the application level, and depends on the developer choices (the application reference is given in Figure 6. The temporal validity interval, [60, 80, 100], at this layer corresponds to the inter-stream synchronization and will be explained later on. It means that the transition will be fired in the interval min, max=[60, 100], the time being started when the transition is enabled, i.e. when the places have all one token.

Thus, knowing that the sound has to be produced and sent in less than 20 ms (Figure 4), and that the image in less than 40 ms (given by the application), we measured the processing of the interactive event: it has been found to be 16. The delay of the interactive flow must be driven by the audio stream because the audio media is the most time sensitive one, and the audio stream will be then selected master stream: it control the time schedule for the firings of the transitions. Therefore, the number of places of this stream must be a multiple integer of the number of the video and simulation units. As a consequence, the synchronization transition will be defined at the rendezvous which occurs at a period equal to the LCM (Least Common Multiple) of the nominal durations of the three streams, i.e. at time equal to 80 ms, the LCM of (16, 20, 40). The granularity of the synchronization is determined by the maximum acceptable inter-stream drift. As the audio stream has a possible drift of 5 ms, the advance of the interactive flow results only from the cumulative effect of the drifts of this flow.

The allowable drift of the video is 10ms: this drift is achieved by the treatment of 2 units of synchronization, which is the treatment of 4 units of sync audio and 5 units of flow synchronization Interactive. The formal modeling of this approach is given by three hierarchical levels and 5 HTSPN nets. Figure 6.a shows the highest level. This highest level specifies the full constraints of the inter-stream synchronization between the audio stream, modeled by Aud, the flow of the interactive simulation, modeled by the Sim, and the video stream, modeled by VID. The atomic or composite components and materials are managed at the HLA-RTI level. The link layer is independent of the middleware, and it represents the application level. Figure 5 describes the synchronization architecture of the distributed interactive simulation governing the HLA-RTI middleware. Within the composite layer, Places, from Sim1 to Sim5, represent the objects of the distributed simulation, AUD1 to AUD4 represent the audio objects and places VID1 and VID2 describe the video objects. Each circle represents a data packet: to ensure the synchronization between the streams, at the model defines a synchronization for each set of 5 packets of distributed simulation (i.e. 544 bytes per packet), of 4 audio packets (of size 881 byte packet) and of 2 video packets. The composite layer fulfills this inter-stream synchronization and prepares the link synchronization Layer.

This net specifies in particular the control that must be implemented to ensure the adequate synchronization between these three flows, e.g. to ensure that the video stream is no later than 30ms compared to the other flows. This control must be applied with a maximum granularity of 20 ms, corresponding to two units of video synchronization, 4 units of sync audio and 5 units of sync interactive flow. The purpose of this architecture is to express all the specified timing requirements. During the simulation, HLA-RTI supports the transmission of audio, video and interactive streaming from the sender application to the remote hosts. It allows both the transport layer and control layer. HLA defines two types of information exchange: the objects and the interactions. Objects are inherently persistent during the simulation, represented by atomic component; they implement the flow control. The intra-stream synchronization is managed by the objects that control the constraints of quality of service required for the flows. The interactions are persistent and will be able to natively transport the flows between the Federates. Finally, the places Sim1 to Sim5 represent the objects of the distributed simulation.

As described in Figure 6, the first point of inter-stream synchronization is of type "MASTER", with the audio stream as "MASTER" is placed at the point go after a nominal duration equal to 80ms (100ms maximum). This synchronization is likely to induce the acceleration (respectively deceleration) of the video and audio flows after 5 units of synchronization and can also cause a delay or the loose of the video stream. The abstract place Sim is specified by the subnet shown at the top of Figure 5. This HTSPN model controls explicitly the advance of the interactive simulation flow with respect to the other flows. Given the jitter units of 10 ms for the video and of 5 ms the audio stream, then after 5 intra-synchronized objects of the interactive flow, this stream can be up to 20ms ahead of the other flows. The control of the jitter of this stream should be done by the HLA-RTI middleware to ensure that all constraints of synchronization with the other streams are enforced. The HLA Objects should control independently each stream using native HLA APIs UpdateAttributeValues() and reflectAttributeValue(). These functions are able not only to control the advance of a flow compared to the others, but also to ensure the intra-stream synchronization.

The HLA-RTI APIs sendInteraction() and receiveInteraction() could be used to send data. Because audio and video objects do not need in many cases to be exchanged between federates, their data packet should be send using the HLA interactions. HLA provides many other APIs that can use in the implementation. As the synchronization is implemented at the receiving side, to schedule the data reception, the API tick(T1,T2) should be used with two arguments that are the minimum and the maximum values used in the temporal validity interval; for example tick(12,20) has to be used.

VI. MULTIMEDIA TRANSPORT ARCHITECTURE

Sender and receiver are involved in the stream transmission. As a requirement of the HLA-RTI middleware, both participants are federates and should follow the HLA rules in order to be compliant with the specification. Hence, RTI supports both "Reliable" and "Best Effort" communication mode. Since Multimedia stream need to be send continuously, it is necessary to optimize the throughput and the reduce the end-to-end latency. This solution need UDP-based "Best Effort" transport protocol.

As we outlined in Section IV, multimedia packets need low latency to meet the QoS requirements, therefore it is mandatory to schedule a stream transmission task in order to share the system resources with other tasks. The synchronization interval validity are used to meet the requirements of the schedule system interval timer provided by the underling operating system. The interval timer allows the application to schedule periodic timer events. Thus, the application receives and requests timer messages at the Temporal Validity Interval (TVI) given in each arc of the HTSPN model-that is, the TVI allows the application to schedule the timer events within the TVI resolution, that is the timer interval of the upadeintercation() and sendInteraction() function is caller in this regular time resolution. In fact, real-time stream transmission over large scale networks adds latency and jitter due to the router scheduling and admission control within the router queues. Using the the value admissible in the TVI is twofold:(1) the re-synchronization of the media frames in the presentation layer at the receiver side without using reliable stream control (TCP protocol), the end-to-end latency can be carefully controller before the stream being displayed, and (2) allows the receiver buffer handling the received stream with minimum frame lost and eliminates jitter issues. Likewise, The longer the reconstruction buffer is, the larger the jitter can be reduced.

VII. CONCLUSION

We have presented a formal model based on Hierarchical Temporal Stream Petri Nets for the synchronization of distributed interactive multimedia systems. This model is able to describe applications implemented using an HLA distributed simulation. It offers a good modeling power for at the same time the expression and the analysis of temporal constraints in such systems. It also allowed us to specify precisely, completely and in a unified way the multi-level logical, temporal and semantics timing constraints that are fundamental for synchronized distributed applications.

Taking into account all these constraints early in the design process leads to a rather efficient development of distributed applications and reduces the cost of this development. Our future work is to design and implement by this model a full distributed application that has been developed to remotely teach car drivers.

Figure 2 .

 2 Figure 2. Jitter in intra-stream

Figure 4 .

 4 Figure 4. Variability of packet size with the processing time

•

  Intra-stream synchronization between the objects of each flow • Inter-stream synchronization between the audio and video streams to meet the timing constraints often called Lip-Synchronization. • Inter-stream synchronization between the two (audio / video) streams and the control stream of the distributed interactive simulation. The intra-stream synchronization considers one flow, the inter-stream synchronization considers all flows, and specifies the acceptable inter-stream drift. The constraints of intra-stream synchronization which must be verified for each flow are: • Units have an audio synchronization nominal duration of 20 ms by assuming a jitter of 5 ms. That is to say, the temporal validity interval of each unit of the sync audio is [15, 20, 25]. • The video synchronization unit has 40 ms as a nominal duration and a jitter of 10ms. The synchronization interval validity of the video is then [30, 40, 50]. • The synchronization units of the distributed interactive simulation flow have a nominal duration of 20 ms wit a 5 ms jitter. The temporal validity interval of this flow is then [15, 20, 25].

Figure 5 .

 5 Figure 5. Platform used for the formal specification

Figure 6 .

 6 Figure 6. Distributed Multimedia Synchronization scheme over HLA-RTI. a) The link synchronization Layer, directly connected to the application, b) the composite synchronization layer for the inter-stream synchronization Layer and c) the atomic synchronization layer which of the intra-flow synchronization

Table I RELATIONSHIP

 I BETWEEN PACKET SIZE AND PROCESSING TIME

	Frequency Time (ms)	Frame Size Frame Size Frame Size
	(Khz)	IP Packet	in 50ms	in 30ms	in 20ms
	8	189	400	240	160
	11	69	1101	660	440
	22	34	2201	1321	881
	44	17	4403	2642	1761
	96	8	9606	5764	3843


Wolfgang Boedeker
email: boedekerw@bkk-bv.de

Thomas Backhaus

The scientific assessment of combined effects of risk factors -different approaches in experimental biosciences and epidemiology

Keywords: combined effect analysis, synergism, antagonism, additivity, independent action

The analysis of combined effects of substances or risk factors has been a subject to science for more than a century. With different goals, combined effect analysis was addressed in almost all experimental biosciences. The major theoretical foundation can be traced back to two distinct origins. First, to the work by the pharmacologist Loewe on the concept of concentration additivity and second to the biometrician Bliss and the concept of independent action. In the search for a general solution and a unified terminology the interrelations of the concepts have extensively been studied and experimental findings reviewed. Meanwhile there seems to be consensus in experimental sciences that each concept has its role in predicting combined effect of agents and both are used for hazard und risk management.

In contrast, epidemiologists describe combined effects mainly in terms of interactions in regression models. Although this approach started from a probabilistic model equivalent to the concept of independent action this origin is rarely acknowledged and effect summation is usually the preferred concept nowadays. Obscure biological meaning, the scale dependency of interaction terms as well as unavoidable residual confounding are taken as reasons why no new insights in combined effect analysis are likely to occur from epidemiology.

In this paper we sketch the history of ideas and the state of the arts in combined effect analysis. We point to differences and common grounds in experimental biosciences and epidemiology.

Introduction

The analysis of combination effects has been a subject to science for more than a century.

Countless publications were produced in experimental sciences like agricultural sciences, cancer research, enzymology, hygiene, drug research, pharmacology, toxicology and ecotoxicology. These studies had vastly different aims such as exploring mechanisms of action, improving drug therapy, reducing toxic side effects, or proposing risk management strategies. Unfortunately, often neither were references made to earlier work nor was crossdiscipline cooperation sought. Hence, fundamental concepts and approaches were reinvented and then applied as novelties in subsequent work without even realizing the conceptual equivalence. Meanwhile several text books and reviews on the topic have been written [e.g. 1,2,3], proposals to unify and standardize methods and terminology were brought forward [START_REF] Berenbaum | The Expected Effect of a Combination of Agents: The General Solution[END_REF][START_REF] Greco | Consensus on concepts and terminology for combined action assessment: The Saariselkä agreement[END_REF], experimental evidence was systematically produced [START_REF] Faust | Algal toxicity of binary combinations of pesticide[END_REF][START_REF] Faust | Joint algal toxicity of 16 dissimilarly acting chemicals is predictable by the concept of independent action[END_REF][START_REF] Silva | Something from "nothing"--eight weak estrogenic chemicals combined at concentrations below NOECs produce significant mixture effects[END_REF][START_REF] Backhaus | Joint algal toxicity of phenylurea herbicides is equally predictable by concentration addition and independent action[END_REF], and corresponding improvements of chemical risk management have been suggested (see [START_REF] Altenburger | Regulations for combined effects of pollutants: consequences from risk assessment in aquatic toxicology[END_REF][START_REF] Altenburger | Extrapolation Concepts for Dealing with Multiple Contamination in Environmental Risk Assessment[END_REF][START_REF] Kortenkamp | State of the Art Report on Mixture Toxicity, Report to the Directorate General for the Environment[END_REF] for compilations). However, there is still ambiguity with respect to the need of addressing combined effects and what scientific concept should be taken as basis.

Also in epidemiology, the analysis of combined effects is a prevailing topic [START_REF] Kaufman | Interaction Reaction[END_REF]. In contrast to experimental sciences where combined effect analysis starts from biological reasoning the topic is addressed in epidemiology often in terms of interactions in regression models [START_REF] Knol | When One Depends on the Other. Reporting of Interaction in Case-Control and Cohort Studies[END_REF].

Given the scale dependency of interaction terms as well as residual confounding it is debated whether epidemiological approaches in general are sufficient for a reliable assessment of combined effects [START_REF] Greenland | Interactions in Epidemiology: Relevance, Identification, and Estimation[END_REF]. This paper was stimulated by a workshop of the German Society of Medical Informatics, Biometry and Epidemiology aiming at an exchange on approaches to combined effect analysis in experimental sciences and epidemiology. In this paper we sketch the history of ideas in order to look for respective differences and common ground in both fields. We follow the ideas in a loose historical way starting from experimental sciences. We retain the terminology used in experimental sciences throughout this paper and will therefore be speaking of "agents" whose effects on organisms are studied in dependence of certain "concentrations" or "doses". However, the wording agent-effect-relationship can easily be translated to factor-risk-relationship which is more familiar in epidemiology or public health.

The concepts for the assessment of combined effects apply rather generally. In what follows we start by introducing the fundamental concepts used as references in the analysis of combined effects, summarize the confusing terminology, and outline the search for the right concept. After sketching how combined effect analysis is addressed in epidemiology we discuss differences and common grounds.

Concepts for analyzing combination effects

Combined effect analysis is dominated by terms like synergism, potentiation or antagonism.

Often without a clear definition, these terms are intuitively used to denote that an observed effect is higher or lower than expected. But what effect size can be expected when organisms or populations are exposed simultaneously to more than one substance or risk factor? The assessment of combined effects therefore relies on biological concepts describing how effects of single substances/factors translate to joint effects.

The major theoretical foundation of the scientific assessment of combined effects can be traced back to two distinct historical origins [START_REF] Unkelbach | Drug Combinations -Concepts and Terminology[END_REF]. First, there is the well known and frequently cited work by Loewe and Muischnek [START_REF] Loewe | Über Kombinationswirkungen I. Mitteilung: Hilfsmittel der Fragestellung[END_REF] leading to the isobologram method and founding what later was termed the concept of concentration additivity. Second, the statistical background of combined effect analysis was introduced by Bliss [START_REF] Bliss | The Toxicity of Poisons Applied Jointly[END_REF] whose ideas were elaborated in a series of publications [START_REF] Finney | The analysis of toxicity tests on mixtures of poisons[END_REF][START_REF] Plackett | Statistical aspects of the independent joint action of poisons particularly insecticides. I. The toxicity of a mixture of poisons[END_REF][START_REF] Ashford | Quantal responses to mixtures of poisons under conditions of simple similar action. The analysis of uncontrolled data[END_REF] and were communicated as the concepts of simple similar action and independent action. Concentration Addition (CA) is given by

c 1 /EC x,1 + c 2 /EC x,2 = 1 (1)
with c i denoting the applied concentrations (of substance/factor 1 and 2, respectively) and EC x their individual concentration that provokes a certain effect x., e.g. the effect concentration 50% (EC 50 ). CA is based on the assumption that any constituent of a mixture or exposure can be replaced totally or in part by the same "toxic unit" (e.g c 1 /EC x,1 ) of another with the effect of the mixture remaining constant. So in the simplest case, according to CA the individual mixture components behave as if they were dilutions of each other. When interpreted in view of the mechanism of action, concentration addition is taken to be applicable if the substances have an identical molecular mechanism and hence display a similar mode of action. In case the concentration effect relationships of the agents are parallel (in a certain sense) equation 1 takes a simple explicit form which is known as simple similar action. Several indexes have been introduced to assess deviation from additivity. The so called additivity index [START_REF] Marking | Toxicity of chemical mixtures[END_REF] and the mixture toxicity index [START_REF] Könemann | Quantitative structure-activity relationships in fish toxicity studies Part 1: relationship for 50 industrial pollutants[END_REF] have been found especially useful.

The concept of Independent Action (IA) is given by P 1,2 = P 1 + P 2 -P 1 P 2 [START_REF] Pöch | Combined effects of drugs and toxic agents[END_REF] with P i denoting the effects/risks of substances/factors 1 and 2, respectively, caused when present singly at the concentration at which they are present in the mixture. IA is therefore given explicitly and the combined effect is directly calculated from the effects of the single agents. From a biological point of view IA is based on the idea that agents contribute to a common endpoint but act upon different subsystems within the same organism, in short:

having different sites and modes of action. A plethora of different names has been used for IA such as simple independent action [START_REF] Finney | The analysis of toxicity tests on mixtures of poisons[END_REF], response addition [START_REF] Anderson | The Toxicity to Aquatic Populations of Mixtures Containing Certain Heavy Metals[END_REF], multiplicative survival model [START_REF] Morse | Some Comments on the Assessment of Joint Action in Herbicide Mixtures[END_REF] effect multiplication [START_REF] Berenbaum | Criteria for Analysing Interactions between Biologically Active Agents[END_REF], response multiplication [START_REF] Christensen | A General Noninteractive Multiple Toxicity Model Including Probit, Logit, and Weibull Transformations[END_REF] and even effect summation [START_REF] Gessner | A Straightforward Method for the Study of Drug Interactions: An Isobolographic Analysis Primer[END_REF].

A third reasoning has greatly influenced and at the same time confused the discussion on the analysis of combined effects. As a naïve approach combination effects were often expected to equal the sum of the individual effects, say

P 1,2 = P 1 + P 2 (3)
Effect summation appears as a special case of IA and according to Plackett & Hewlett [START_REF] Plackett | Statistical aspects of the independent joint action of poisons particularly insecticides. I. The toxicity of a mixture of poisons[END_REF] applies as such to target organisms with negatively correlated susceptibilities (see below). In general however, a closer inspection of Eq. 3 reveals disturbing short-comings of this approach which furthermore lacks pharmacological plausibility. Nowadays, most researchers in experimental sciences seem to agree that combined effects do not simply equal the sum of single effects and that therefore this model does not provide a reasonable reference line although the equation may appear intuitively plausible and is easy to handle.

The concepts are not limited to two agents only and the equations 1, 2 can easily be generalized to n substances or factors [START_REF] Faust | Joint algal toxicity of 16 dissimilarly acting chemicals is predictable by the concept of independent action[END_REF].

Consequences from co-existence of concepts -confusion of terminology

According to many reviews of the field the non-uniform and inconsistent use of terms used to label combination effects has been a main reason for confusion and misunderstandings [START_REF] Calabrese | Multiple chemical interaction[END_REF][START_REF] Pöch | Combined effects of drugs and toxic agents[END_REF][START_REF] Chou | Theoretical Basis, Experimental Design, and Computerized Simulation of Synergism and Antagonism in Drug Combination Studies[END_REF][START_REF] Berenbaum | The Expected Effect of a Combination of Agents: The General Solution[END_REF][START_REF] Greco | Consensus on concepts and terminology for combined action assessment: The Saariselkä agreement[END_REF].

Table 1 gives an overview on terms that have been used in the literature. Not only were various terms used to address the same type of combined effect but also were the same terms used for different understandings. Not surprisingly, re-analysis of the very same data even led to apparently conflicting results by different authors [START_REF] Unkelbach | Drug Combinations -Concepts and Terminology[END_REF]. The terms synergism, antagonism and potentiation are particularly prone to misunderstanding. For example, up to seven different types of antagonisms and synergisms can be found in literature [START_REF] Fedeli | Quantitative Evaluation of Joint Drug Action[END_REF][START_REF] Goldin | The Employment of Combinations of Drugs in the Chemotherapy of Neoplasia: A Review[END_REF].

Whereas synergism usually is meant to denote a greater than additive effect, some authors consider this to be a special case of additivity [START_REF] Unkelbach | Drug Combinations -Concepts and Terminology[END_REF]. Also no clear distinction is made between synergism and potentiation. While it is widely accepted that potentiation refers to a combined effect that is greater than a synergistic effect, both terms are also used synonymously [START_REF] Blanc | Drug interactions Some first principles[END_REF].

Based on pharmacological considerations, it was even proposed to regard potentiation a special case of antagonism [START_REF] Loewe | Die Mischarznei Versuch einer allgemeinen Pharmakologie der Arzneikombinationen[END_REF]. Also the term "interaction" is used with numerous different meanings. Given the different use in pharmacokinetics and -dynamics and in biostatistics it is unlikely that it can be used in a clear and meaningful way for general use. It was therefore repeatedly proposed to refrain from using the term interaction at all in combination effects analysis. This proposal has also been made for epidemiology [START_REF] Greenland | Interactions in Epidemiology: Relevance, Identification, and Estimation[END_REF].

Without a precise definition many terms are used rather intuitively so newcomers are inclined to understand "additivity" as equivalent to simple summation of effects while others misinterpret "independence" or "non-interaction" as toxicologically irrelevant. A standardisation of terminology is still not achieved despite continuous discussions and several proposals [START_REF] Greco | Consensus on concepts and terminology for combined action assessment: The Saariselkä agreement[END_REF][START_REF] Unkelbach | Drug Combinations -Concepts and Terminology[END_REF][START_REF] Plackett | Quantal responses to mixtures of poisons[END_REF][START_REF] Loewe | Randbemerkungen zur quantitativen Pharmakologie der Kombinationen[END_REF][START_REF] Putnam | Pesticides interactions in higher plants[END_REF][START_REF] Chou | Analysis of combined drug effects: a new look to a very old problem[END_REF]. Nowadays it is held that statements on the type of combination effects need to answer first to the question what effect is expected by the combination of agents, namely which biological concepts is taken as the reference. It has therefore been proposed

to refer to the reference model by using the terms "Loewe additivity" when equation 1 and "Bliss independence" when equation 2 is meant [START_REF] Greco | Consensus on concepts and terminology for combined action assessment: The Saariselkä agreement[END_REF].

The quest for the right concept

None of the concepts introduced for the analysis of combination effect found support by all researchers. There is a still ongoing debate on which of the two concepts is the "better" or even the "correct" concept. In this debate several touchstones are addressed: 1. the role of mechanisms and modes of action of agents, 2. the case of a sham combination, and 3.

notions of causality.

Since the concept of concentration addition as well as independent action is derived from basic pharmacological reasoning it has been questioned what role pharmacological similarity or dissimilarity plays in order to select the most suitable concept. On the one hand, it is not clear from the concepts whether an identical or different site of action is a characteristic of the agents or of the biological system. Can there be two agents that do not interfere with each other at all but still contribute to an integral effect such as death? Do agents acting at the same site always show similar (e.g. parallel) concentration-response-curves? Neither concept provides mechanistic explanations for the joint action in complex systems. On the other hand the terms "similar" and "dissimilar" effect are used in the literature with various degrees of stringency. In pharmacology, strictly speaking, an identical molecular mechanism of action at the same substructure of an acceptor has been proposed as a prerequisite for a similar effect of different substances, and correspondingly dissimilar effects would involve different mechanisms of action [START_REF] Pöch | Combined effects of drugs and toxic agents[END_REF]. Other authors require that a similar effect is localized at least in the "same site of primary action", while a dissimilar effect is distinguished from this by the criterion of differences in a substances" fundamental structure (different "parent compounds") [START_REF] Calamari | A proposal to define quality objectives for aquatic life for mixtures of chemical substances[END_REF]. However, recent research has shown that mixtures which were designed of components known to act either by identical or by completely different molecular mechanisms of action were in fact better predicted by concentration addition or independent action respectively [START_REF] Faust | Joint algal toxicity of 16 dissimilarly acting chemicals is predictable by the concept of independent action[END_REF][START_REF] Backhaus | Joint algal toxicity of phenylurea herbicides is equally predictable by concentration addition and independent action[END_REF][START_REF] Altenburger | Predictability of the toxicity of multiple chemical mixtures to Vibrio fischeri: Mixtures composed of similarly acting compounds[END_REF][START_REF] Backhaus | Predictability of the toxicity of a multiple mixture of dissimilarly acting chemicals to Vibrio fischeri[END_REF].

The idea of a "sham combination" has repeatedly been used as a touchstone in the search for the right concept. A sham combination describes a thought experiment in which an agent is combined with itself, e.g. a dilution of the same substance. As the sham combination is literally the agent simply in another concentration the expected combined effect should equal the effect of that agent in the total concentration, say show concentration additivity. However, based on the concepts of independent action or effect summation the sham combination will often result in a synergistic or antagonistic effect. This counterintuitive result was taken as proof for the inconsistency of the concept of independent action [START_REF] Greco | Consensus on concepts and terminology for combined action assessment: The Saariselkä agreement[END_REF][START_REF] Berenbaum | Synergy, additivsm and antagonism in immunosuppression[END_REF].

In epidemiology, notions of causality derived from the sufficient cause model have been introduced as another touchstone. We will discuss this later.

Interrelationships and the importance of concentration-response-curves

All arguments for and against each concept for the analysis of combined effects have been exchanged for quite some time. Given that the two concepts of concentration additivity and independent action are considered legitimate reference standards it is hence straight forward to study the interrelation of the concepts.

Plackett & Hewlett [START_REF] Plackett | Statistical aspects of the independent joint action of poisons particularly insecticides. I. The toxicity of a mixture of poisons[END_REF] introduced a generalised model of correlated independent action (eg 4). For a combination of two agents with concentrations c 1 , c 2 the response surface P 1,2 was modelled by the bivariate normal distribution f. The correlation coefficient Φ was used to differentiate 3 subtypes of independent action. Within this model uncorrelated susceptibility of organisms leads to the (simple) independent action of eq. 2, whereas in case of a total correlation of susceptibilities the effect of the combination equals the effect of most potent agent. The latter case has also been termed "no addition" by Könemann [START_REF] Kaufman | Interaction Reaction[END_REF] and bridges as part of his mixture toxicity index to the concept of concentration additivity. The subtype of total negative correlation is especially interesting as it is one of the rare theoretical foundations of the model of effect summation.

An often cited quantitative relation of eq. 4 was derived by Wahrendorf and Brown [START_REF] Wahrendorf | Bootstrapping a basic inequality in the analysis of joint action of two drugs[END_REF] showing that effect summation always predicts equal or greater combined effects than independent action which in turn predicts a mixture effect that equals or is greater than the effect of the most potent agent.

Interrelations between independent action and concentration addition can not be derived generally but depend on several factors. Both concepts for combined effect analysis assume that concentration-effect-relationships can be modelled and effects (in case of eq. 2) or effect concentrations (in eq. 1) can be extrapolated from monotonous concentration-responsecurves fitted to the experimental data. Combined effects analysis in experimental sciences is very much centred on the study of these concentration-effect-relationships. To this end, it is aimed at an experimentally complete description of these relations, meaning that concentrations of single agents as well as the combinations are chosen to produce effects covering the full response surface well spaced between no and 100% response. The better the relation is described the better justified is the choice of a concentration-response curve to extrapolate. Standard regression models make use of e.g. the functions of the normal distribution (Probit analysis), the logistic distribution (Logit analysis) or the Weibull distribution (Weibit or Gompertz analysis). Several additional functions are available to fit concentrationresponse data even when standard models are not suitable e.g. when special focus is on the estimation of low or high effect concentrations [START_REF] Scholze | A general best-fit method for concentration-response curves and the estimation of low-effect concentrations[END_REF]. These functions have the common feature of being applicable to a monotonic sigmoid or hyperbolic concentration-effect relationship, i.e., when effects increase with increasing concentrations or doses. Although the fundamental curve types (say linear, exponential or sigmoid) are easy to detect it is sometimes ambitious to differentiate functions within the types [START_REF] Scholze | A general best-fit method for concentration-response curves and the estimation of low-effect concentrations[END_REF]. Finally, concentration response curves are different for different outcomes as well as for different risk measures, so changing scope from risk to risk ratios would mean changing the shape of the factor-effect curve.

In combined effect analysis it was discovered early that the quantitative relations between the concepts for the assessment of combined effects depend on features of the concentration response curves. Berenbaum [START_REF] Berenbaum | The Expected Effect of a Combination of Agents: The General Solution[END_REF] showed that the concept of concentration addition equals the concept of effect summation for linear and the concept of independent action for exponential dose-response-curves leading him to the judgement that concentration addition is the general solution in combined effect analysis. Christensen and Chen [START_REF] Christensen | A General Noninteractive Multiple Toxicity Model Including Probit, Logit, and Weibull Transformations[END_REF] gave proof that for Weibull-type dose-response curves concentration addition always predicts greater combined effects than independent action in case of steep curves (steeper than exponential) and vice versa for flat curves. Drescher and Boedeker [START_REF] Drescher | Assessment of the combined effect of substances: The relationship between concentration addition and independent action[END_REF] provided more general relations for normal and logistic curves showing that the concepts interrelations not only depend on the steepness of dose-response curves but also on the concentrations and effect levels. By making use of these known relationships worst case scenarios for risk assessment based on a prediction concept can be derived [START_REF] Boedeker | Combined effects of toxicants: The need and soundness of assessment approaches in ecotoxicology[END_REF]. If detailed information on concentration response curves is not available at least an overall assessment of the deviations is possible. The maximum factor by which predictions of a combined effect based on CA compared to IA differ equals the number of agents combined [START_REF] Junghans | Application and validation of approaches for the predictive hazard assessment of realistic pesticide mixtures[END_REF].

Combined effect analysis in epidemiology

In epidemiology, there is also quite a history of combined effect analysis. This discussion is centred on the term interaction and usually addresses the case when effects of an exposure to one agent differ across strata of another exposure. In a regression model a product term will be needed to address this heterogeneity. Unfortunately, interaction is dependent on the scale and a "no interaction" in a multiplicative model as used e.g. for calculating risk ratios will at the same time show up as an interaction in an additive model used e.g. for calculating risk differences. Furthermore, various understandings of interaction among statisticians and epidemiologists have added to the confusion of terminology in combined effect analysis [START_REF] Kaufman | Interaction Reaction[END_REF].

Despite the broad coverage of the topic of interaction in textbooks the usage is still rather unsatisfactory in present publications. Knol et al [START_REF] Knol | When One Depends on the Other. Reporting of Interaction in Case-Control and Cohort Studies[END_REF] found in a recent study that in a majority of articles interaction between exposures were explicitly addressed but in about half of these papers information provided was insufficient for a valid assessment.

However, there seems to be no longer any controversial discussion in epidemiology on the general concepts of interaction as coined in the writings of Rothman and Greenland. This was different in former times. Rothman [START_REF] Rothman | Synergy and antagonism in cause-effect relationships[END_REF][START_REF] Rothman | The estimation of synergy or antagonism[END_REF] derived from the idea of independence of causes that a combined effect can only be considered to be synergistic, when two factors jointly have an effect which is greater than the sum of the effects of each factor separately. This reasoning that effect summation is the only concept for adequate evaluation of the causal nature of combined effects was later questioned by several authors [START_REF] Walter | Additive, multiplicative, and other models for disease risks[END_REF][START_REF] Miettinen | Causal and preventive interdependence. Elemetary principles[END_REF]. In these publications different and more flexible reference models were considered and the importance of the chosen effect measures was pointed out. It was argued to not restrict considerations to a single model only, but to fit data by the most plausible biologic models.

Basically, the struggle was about whether there is a scale which is generally more suitable to assess biologic interaction [START_REF] Kaufman | Interaction Reaction[END_REF]. Rothman et al. [START_REF] Rothman | Concepts of interaction[END_REF] proposed to settle controversies by specifying the context in which interactions are studied. According to this proposal there is no need for any biologic foundation of the models in statistical contexts that mainly aim at prediction. Furthermore, in biologic contexts a definition for interaction or synergism is deemed not necessary as these terms do not provide information on the mechanism of agents. In public health context, it was finally suggested that synergy should be interpreted as departure from additivity of rate differences whereas for individual decision making departure from additivity of risk differences should be the reference.

Interestingly, the preference for the concept of effect summation was concluded from the model of independent action (eq. 2) only by making the assumption that small effects are studied [START_REF] Rothman | The estimation of synergy or antagonism[END_REF]. Nowadays, the appropriateness of the concept of effect summation is concluded from the sufficient cause model [START_REF] Rothman | Modern Epidemiology[END_REF]. VanderWeele [START_REF] Vanderweele | Sufficient Cause Interactions and Statistical Interactions[END_REF] defined a sufficient cause interaction to be present between two factors if there is a sufficient cause in which both factors are present and derived rules to conclude the presence of sufficient cause interaction from statistical interaction.

Basis for theoretical analysis in epidemiology is the simple setting of a dichotomous effect which is studied as provoked by dichotomous factors. From that scenario all possible response types are derived and reflected with respect to interaction types [START_REF] Rothman | Modern Epidemiology[END_REF][START_REF] Greenland | Invariants and noninvariants in the concept of interdependent effects[END_REF]. However, although the response type approach helps to lighten interaction phenomena it does not provide a reference for a "true" concept for analysis. E.g. the so called "causal synergism" response type of a combination effect of two factors showing no effect singly (at the cut-off for dichotomisation) could also follow from concentration additivity and this response type would then be regarded as a classical example for no interaction. So, for translating response types in combined effect terminology a definition of a reference model is still needed.

In epidemiologic publications, only little notice has been taken of the previous work in experimental biosciences. Kupper and Hogan [START_REF] Kupper | Interaction in epidemiologic studies[END_REF] did one of the rare acknowledgements of the dose additivity concept by a hypothetical example. The example is in fact that of a sham combination showing that summation of effects can give highly implausible results in the case of non linear dose response relations. Kodell & Gaylor [START_REF] Kodell | On the additive and multiplicative models of relative risk[END_REF] compared independent action to dose additivity and noted that both concepts agree for linear dose-responserelations. Miettinen [START_REF] Miettinen | Causal and preventive interdependence. Elemetary principles[END_REF] acknowledged the more general concept of independence (eq. 4) [START_REF] Plackett | Statistical aspects of the independent joint action of poisons particularly insecticides. I. The toxicity of a mixture of poisons[END_REF] and the relations given by Wahrendorf & Brown [START_REF] Wahrendorf | Bootstrapping a basic inequality in the analysis of joint action of two drugs[END_REF]. He pointed out that the ideas of correlated susceptibilities ask for another reference model than simple effect summation.

Discussion

The sketch of ideas brought forward in the scientific analysis of combined effects in experimental sciences and in epidemiology shows that very different lines were followed with little cross-referencing and so far resulted in very different approvals of the state of art.

Experimental sciences claim their potential in disclosing principles of combined effects in a degree of confidence that is sufficient to encourage regulations [START_REF] Kortenkamp | State of the Art Report on Mixture Toxicity, Report to the Directorate General for the Environment[END_REF]. In contrast, from an epidemiologic point of view the scientific means are considered rather modest. It might therefore be interesting to see whether there is common ground.

First, touchstones like models of mechanism of action, the sham combination or causal models seem to have no convincing strengths to opponents as all of them start with an arbitrary definition. Touchstones are derived from an idea and are designed to prove agreement with that idea which itself remains untested and untestable. Concluding effect summation to be a reference model from sufficient cause models might therefore be considered the same tautological approach as requiring sham combination qualities for agents that act independently. However, lack of a touchstone for the right concept is a problem only if synergism is considered a biological phenomenon whose identification must not be dependent on models and scales. However, we prefer to judge synergism as a scientific construct related to a defined concept of combined effects. These concepts can be expressed in different mathematical models which make use of different concentrationresponse-curves. Scale and model dependency in this view follows from interaction concepts rather than limits the knowledge process. Given the complexity of agents-effects relations on the different, interlinked levels of biological complexity, from molecules to individual organisms, and finally to whole populations, the search for natural laws of interaction finds little comfort in simple models of causality.

Secondly, experimental sciences and epidemiology find common ground also in the request to explicitly specify the aim of combined effect analysis. In experimental sciences two main aims can be differentiated: (i) the study of mechanisms of combined action and (ii) the description and prediction of combined effects. Addressing the first aim means that experimental data are checked for agreement or disagreement with specific mathematical models and agreement e.g. with a model of simple similar action would be taken as evidence that agents interfere with the same site of action and have a similar mode of action. Although this approach is rather common in drug-receptor studies it is limited as many mechanisms can lead to experimental data which can be fitted by the same mathematical model. In combined effect analysis it is even worse as agreement with a model could also mean that interaction deterred the effects from another -correct -reference model, and vice versa.

Kupper and Hogan [START_REF] Kupper | Interaction in epidemiologic studies[END_REF] phrased this assessment dilemma as ".. any observed significant interaction (or synergic) effect may be nothing more than an indication that the wrong (null) model was assumed in the analysis". So, agreeing with Rothman et al. [START_REF] Rothman | Concepts of interaction[END_REF] who addressed the aim of mechanism of action studies as the context of biologic interaction nothing can be learned from terms like synergism in this situation.

In contrast, the description and prediction of combined effect is primarily not interested in how combined agents act but whether the combined effects are more/less than expected from the effects of the single components. The focus is on optimizing wanted effects or safeguarding against unwanted effects. Describing combined effects is often done on a caseby-case basis. For example, in Germany, lung cancer from the combined exposure against asbestos and polycyclical aromatic hydrocarbons is now legally considered an occupational disease when individual exposures exceed limits derived from an additive model. In epidemiology, this approach might also be useful for scoring risk profiles. The prediction of combined effects focuses on the expectation rather than on the deviations from the expectation. Prediction typically calls for simple instruments to enable prospective risk management and regulations taking combined effects into account. A prospective model should have been proven suitable to cover a broad range of substances. At the same time the model should be sufficiently simple for being included in legal procedures and indicators should be available to characterize respective agents [START_REF] Backhaus | Joint algal toxicity of phenylurea herbicides is equally predictable by concentration addition and independent action[END_REF]. A suitable concept for addressing combined effect in risk management might as well be based on worst case scenarios [START_REF] Boedeker | Combined effects of toxicants: The need and soundness of assessment approaches in ecotoxicology[END_REF].

This approach is different from the prediction in the context of statistical interaction as laid out by Rothman et al. [START_REF] Rothman | Concepts of interaction[END_REF] because mathematically demanding models might not be used in regulatory practiseeven if they have a high predictive power.

Thirdly, experimental sciences and epidemiology share common problems in combined effect analysis. It is usually taken that in epidemiology effects of single agents can never be observed because there is always a background exposure which might modify or confound. From this perspective, epidemiological studies are always combined effect studies. In contrast, in experimental sciences it is idealized that a causally homogenous background is provided e.g. by genotypic standards of test organism, random allocation of treatment groups, and high standards in the physical or chemical properties of agents. Hence, introducing a factor into this experimental setting is considered the only variation and observed effects are completely attributed to this factor. However, e.g. test chemicals can never be applied without impurities, galenic supplements or solvents, physical exposures are provoked by tools and measures have to be taken to account for avoidance strategies of organisms. In ecotoxicological field studies confounding factors may be present when parts of natural ecosystems (e.g. ponds, streams) are chosen as experimental platforms. After all, the epistemiological framework for the component based analysis of combined effects does not seem to be so much different in experimental sciences and in epidemiology.

Experimenters however, tend to ignore these restraints.

A clear distinction between approaches of combined effect analysis in experimental sciences and epidemiology lies in the study design. Whereas in the former knowledge of the whole concentration-response surface of single agents as well as their combination is thought to be indispensable this is rarely attempted in epidemiological studies. Even theoretical analysis is typically constrained to dichotomous factors. From a concentration-response perspective little can be learned from this design as the responses can not be followed on the concentration-response curve. Furthermore, concentration additive joint effects can result even from no effect concentrations of single agents [START_REF] Silva | Something from "nothing"--eight weak estrogenic chemicals combined at concentrations below NOECs produce significant mixture effects[END_REF][START_REF] Kortenkamp | Low-level exposure to multiple chemicals: reasons fur human health concerns?[END_REF]. Hence, making use of elements of dose-response analysis might add to the tools of combined effect analysis in epidemiology.

Finally, little use has been made from quantitative interrelations of the concepts in epidemiology so far. The preferred use of effect summation as the reference line may be a handy approximation, beyond any reflection on the true nature of combined effect. In case of linear concentration response curves which are assumed e.g. for the estimation of risk differences the concept of effect summation would lead to identical results as concentration addition. However, as has been pointed out already, effect summation may lead to strong underestimation of combined effects for low doses and therefore gives no worst-caseestimation.

Table 1 : Commonly used terms for combination effects Term Combined effect meant to be

 1

	augmentation, enhancement, potentiation,	greater than expected
	sensitation, superadditivity, supraadditivism,
	synergism, synergy
	additivity, additivism, independence,	as expected
	indifference, non-interaction, summation,
	zero-interaction
	antagonism, antergism, depotentiation,	less than expected
	desensitation, infraadditivity, negative
	synergism, non-interaction, potentiation,
	subadditivity, zero-interaction, no addition