**1. Introduction**

58 Amyotrophic Lateral Sclerosis

Zhang R, Hadlock KG, Do H, Yu S, Honrada R, et al. 2011. Gene expression profiling in

Zoccolella S, Beghi E, Palagano G, Fraddosio A, Samarelli V, et al. 2006. Predictors of delay

lateral sclerosis (sALS). *J Neuroimmunol* 230:114-23

population-based study. *J Neurol Sci* 250:45-9

peripheral blood mononuclear cells from patients with sporadic amyotrophic

in the diagnosis and clinical trial entry of amyotrophic lateral sclerosis patients: a

In this chapter, we present a new method, dynamic meta-analysis, which allows the examination of the underlying system dynamics of ALS utilizing the wealth of existing published experimental and/or clinical literature. We perform a small-scale feasibility study of the G93A SOD1 mouse model to show that dynamic meta-analysis can also be utilized to predict treatment outcomes in a high-throughput manner.

### **1.1 Leveraging the wealth of data**

In 2010 alone, 980 articles were specifically published on the fatal neurodegenerative disease Amyotrophic Lateral Sclerosis (ALS), and the cumulative total literature base for this single intractable pathology exceeds 10,300 articles, according to a PubMed search. One might think that with this wealth of information we would have ALS well in hand. Yet, there is no available, life-extending treatment despite the extensive and detailed information obtained by thousands of researchers at the cost of billions of dollars. ALS remains one of the most intractable neurological diseases; there is no apparent quick fix, no smoking gun, and no obvious answers—just mountains of intertwined experimental observations recorded across a host of individual publications. Furthermore, ALS has been remarkably resistant to reductionistic attempts to pinpoint the underlying problem. Potential contributing defects, mutations, and regulatory failures have been cited across a broad range of categories, including axonal transport (Bilsland, Sahai et al.), cellular chemistry (Hayward, Rodriguez et al. 2002), energetics (Shi, Gal et al.), excitotoxicity (Roy, Minotti et al. 1998), free radicals (Bogdanov, Ramos et al. 1998), genetic damage (Nagano, Murakami et al. 2002), inflammation (King, Dickson et al. 2009), necro-apoptosis (Vukosavic, Dubois-Dauphin et al. 1999), proteomics (Wood, Beaujeux et al. 2003), as well as systemic origin (Dobrowolny, Aucello et al. 2008). Yet experimental correction or "treatment" of any individually identified potential contributor has failed to translate into clinically significant and reproducible results (Peviani, Caron et al.).

### **1.2 Identifying and utilizing the system dynamics of ALS for combination therapy**

Based on current evidence, ALS may exhibit system-level abnormalities that emerge from the complexities and interactions of their underlying mechanisms (Mitchell 2009; Rothstein

Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 61

While a major strength of dynamic meta-analysis is that it does provide an approach for aggregating and recapitulating experimental studies, its application is by no means limited to experimental studies. The same method can certainly be used to dynamically examine clinical stuides. The advantages of the implicit inclusion of interactions and explict inclusion

In this chapter we perform a small dynamic meta-analysis feasibility study utilizing the G93A SOD1 ALS mouse model literature to illustrate the potential power of dynamic metaanalysis to reveal key system dynamics, identify treatment strategies, and predict combination treatment outcomes in ALS. This model, developed over 15 years ago, is still the primary experimental model used to investigate ALS mechanisms and treatments.

In this section, we provide the foundation, overview, and detailed processes involved in dynamic meta-analysis. The methods are generalized, such that they could be applied to any experimental or clinical dataset. We use the G93A SOD1 model as our detailed example of the construction, implementation, and analysis required for dynamic meta-analysis in this section. However, we reserve the specific dynamic meta-analysis predictions for the G93A

Traditional meta-analysis leverages an a priori model of relationships to generate a systemwide phenomenological model of the system. What makes this approach effective is the statistical weight of all the measured data behind the regressed coefficients. However, its limitations are that it does not explicitly permit the inclusion of time or the implicit examination of metric interactions. The a priori model used in traditional meta-analysis is based on the idea that all systems can be locally approximated algebraically as first order

constant of proportionality). The a priori model is typically illustrated in the form of the

The central novel premise behind dynamic meta-analysis is that relationships in biological

an a priori model utilizing rates of change treats system relationships much like chemical reactions. Clearly, for much of what constitutes a biological system a reaction metaphor is not just a good approximation, it is literally true. Thus, the meta-regression equation for

where X's are various effectors within the system, Y is one (of many) affected metrics and B's are the interaction gain coefficients. With this meta-regression equation, the concept of

X2 + B3.

X3 + B4.

X where X and Y are metrics within the system and B is a regression

X3 + B4 .

X4… (1)

X4 … (2)

X). Such

**1.4 G93A SOD1 mouse model as a test bed for dynamic meta-analysis** 

**2. The dynamic meta-analysis method** 

SOD1 mouse model for the 3. Results section.

**2.1 Traditional meta-analysis as a foundation** 

Y = B1.

**2.2 Mathematical basis of "dynamic" meta-analysis** 

X1 + B2 . X2 + B3.

systems are better conceptualized as a first order differential equation (dY/dt = B.

X1 + B2.

of time still apply.

(essentially Y = B.

meta-regression equation:

dynamic meta-analysis becomes

dY1/dt = B1.

2009). Like an engineering control loop with many elements that ends up with an unstably high feedback gain, ALS may initiate from the combined effects of many small deviations that, in and of themselves, might be considered normal. To address multiple contributors and their interactions, a distributed intervention like combination therapy is necessary. Combination treatment strategies are typically based on the assumed presence of systemlevel synergistic interactions, which could amplify the desired treatment effects. Thus, before a combination treatment can even be developed, the system dynamics and potential synergistic interactions must first be revealed. That is, we cannot "treat", for example, a high-loop gain abnormality if we are not aware of its existence and have no means to measure it. A further limitation to combination treatment research is the combinatorial explosion of treatment possibilities (often hundreds to thousands) that must be experimentally explored—a daunting task that is neither financially nor temporally feasible. What is needed is a tool or method that can both identify and utilize ALS pathology dynamics to pre-screen treatment combinations in silico, such that treatment combinations predicted to have the highest efficacies could be experimentally assessed first, and thus greatly speed the time from ALS treatment discovery to potential clinical treatment success.

### **1.3 Dynamic meta-analysis as a means of experimental and clinical prediction**

Here we examine the use of a novel and innovative form of meta-analysis, which we call *dynamic meta-analysis*, as a tool that enables the necessary examination of system-level ALS pathology dynamics as well as the prediction of ALS combination treatment outcomes. Traditional meta-analysis, which aggregates the results of multiple, heavily overlapping clinical/epidemiological studies into a larger virtual study from which relationships across a broader array of conditions can be examined and overall statistical power can be increased, has been successfully used to examine individual clinical treatments (Miller, Mitchell et al. 2007; Pastula, Moore et al. 2010).

Much can and has been honed from using traditonal meta-analysis to examine clinical trials. However, clinical trials lack the advantages of in vitro and in vivo experimental models where we can perform protocols and obtain mechanistic insight that is not possible in human studies alone. To examine the dynamics of ALS in order to develop successful ombination therapies, we really need to examine the individual interactions and regulation of multipe cellular- and system-level interactions, which are either too complex, too inaccessible, or inappropriate for human experimentation. The ALS literature, particularly through superoxide dismutase 1 mouse models (G93A, G85R, etc), identified several such interactions and their regulation. What is needed is a method by which we can integrate the individual studies, each of which study different aspects of ALS (axonal transport, excitotoxicity, apoptosis, etc.), into the quilt that is ALS. This indeed does sound like a task for meta-analysis.

However, traditional meta-analysis is not an option for examining experimental literature. The ALS experimental literature base is simultaneously much larger than any single collection of clinical trials, and much less overlapping than clinical protocols. Dynamic meta-analysis overcomes the constraints of traditional meta-analysis by allowing the implicit inclusion of system interactions and explicit inclusion of time, two key ingredients necessary to examine pathology dynamics and subsequent combination treatments. In short, dynamic meta-analysis provides a manageable means to integrate the experimental data published by thousands of researchers into a unified view from which new ALS treatments and treatment combinations can be explored.

While a major strength of dynamic meta-analysis is that it does provide an approach for aggregating and recapitulating experimental studies, its application is by no means limited to experimental studies. The same method can certainly be used to dynamically examine clinical stuides. The advantages of the implicit inclusion of interactions and explict inclusion of time still apply.

### **1.4 G93A SOD1 mouse model as a test bed for dynamic meta-analysis**

In this chapter we perform a small dynamic meta-analysis feasibility study utilizing the G93A SOD1 ALS mouse model literature to illustrate the potential power of dynamic metaanalysis to reveal key system dynamics, identify treatment strategies, and predict combination treatment outcomes in ALS. This model, developed over 15 years ago, is still the primary experimental model used to investigate ALS mechanisms and treatments.

### **2. The dynamic meta-analysis method**

60 Amyotrophic Lateral Sclerosis

2009). Like an engineering control loop with many elements that ends up with an unstably high feedback gain, ALS may initiate from the combined effects of many small deviations that, in and of themselves, might be considered normal. To address multiple contributors and their interactions, a distributed intervention like combination therapy is necessary. Combination treatment strategies are typically based on the assumed presence of systemlevel synergistic interactions, which could amplify the desired treatment effects. Thus, before a combination treatment can even be developed, the system dynamics and potential synergistic interactions must first be revealed. That is, we cannot "treat", for example, a high-loop gain abnormality if we are not aware of its existence and have no means to measure it. A further limitation to combination treatment research is the combinatorial explosion of treatment possibilities (often hundreds to thousands) that must be experimentally explored—a daunting task that is neither financially nor temporally feasible. What is needed is a tool or method that can both identify and utilize ALS pathology dynamics to pre-screen treatment combinations in silico, such that treatment combinations predicted to have the highest efficacies could be experimentally assessed first, and thus greatly speed the time from ALS treatment discovery to potential clinical treatment success.

**1.3 Dynamic meta-analysis as a means of experimental and clinical prediction** 

Mitchell et al. 2007; Pastula, Moore et al. 2010).

and treatment combinations can be explored.

that is ALS. This indeed does sound like a task for meta-analysis.

Here we examine the use of a novel and innovative form of meta-analysis, which we call *dynamic meta-analysis*, as a tool that enables the necessary examination of system-level ALS pathology dynamics as well as the prediction of ALS combination treatment outcomes. Traditional meta-analysis, which aggregates the results of multiple, heavily overlapping clinical/epidemiological studies into a larger virtual study from which relationships across a broader array of conditions can be examined and overall statistical power can be increased, has been successfully used to examine individual clinical treatments (Miller,

Much can and has been honed from using traditonal meta-analysis to examine clinical trials. However, clinical trials lack the advantages of in vitro and in vivo experimental models where we can perform protocols and obtain mechanistic insight that is not possible in human studies alone. To examine the dynamics of ALS in order to develop successful ombination therapies, we really need to examine the individual interactions and regulation of multipe cellular- and system-level interactions, which are either too complex, too inaccessible, or inappropriate for human experimentation. The ALS literature, particularly through superoxide dismutase 1 mouse models (G93A, G85R, etc), identified several such interactions and their regulation. What is needed is a method by which we can integrate the individual studies, each of which study different aspects of ALS (axonal transport, excitotoxicity, apoptosis, etc.), into the quilt

However, traditional meta-analysis is not an option for examining experimental literature. The ALS experimental literature base is simultaneously much larger than any single collection of clinical trials, and much less overlapping than clinical protocols. Dynamic meta-analysis overcomes the constraints of traditional meta-analysis by allowing the implicit inclusion of system interactions and explicit inclusion of time, two key ingredients necessary to examine pathology dynamics and subsequent combination treatments. In short, dynamic meta-analysis provides a manageable means to integrate the experimental data published by thousands of researchers into a unified view from which new ALS treatments In this section, we provide the foundation, overview, and detailed processes involved in dynamic meta-analysis. The methods are generalized, such that they could be applied to any experimental or clinical dataset. We use the G93A SOD1 model as our detailed example of the construction, implementation, and analysis required for dynamic meta-analysis in this section. However, we reserve the specific dynamic meta-analysis predictions for the G93A SOD1 mouse model for the 3. Results section.

### **2.1 Traditional meta-analysis as a foundation**

Traditional meta-analysis leverages an a priori model of relationships to generate a systemwide phenomenological model of the system. What makes this approach effective is the statistical weight of all the measured data behind the regressed coefficients. However, its limitations are that it does not explicitly permit the inclusion of time or the implicit examination of metric interactions. The a priori model used in traditional meta-analysis is based on the idea that all systems can be locally approximated algebraically as first order (essentially Y = B. X where X and Y are metrics within the system and B is a regression constant of proportionality). The a priori model is typically illustrated in the form of the meta-regression equation:

$$\mathbf{Y} = \mathbf{B}\_1 \mathbf{X}\_1 + \mathbf{B}\_2 \mathbf{X}\_2 + \mathbf{B}\_3 \mathbf{X}\_3 + \mathbf{B}\_4 \mathbf{X}\_4 \dots \tag{1}$$

### **2.2 Mathematical basis of "dynamic" meta-analysis**

The central novel premise behind dynamic meta-analysis is that relationships in biological systems are better conceptualized as a first order differential equation (dY/dt = B. X). Such an a priori model utilizing rates of change treats system relationships much like chemical reactions. Clearly, for much of what constitutes a biological system a reaction metaphor is not just a good approximation, it is literally true. Thus, the meta-regression equation for dynamic meta-analysis becomes

$$\mathbf{d}\mathbf{Y}\_1/\mathbf{dt} = \mathbf{B}\_1\mathbf{X}\_1 + \mathbf{B}\_2\mathbf{X}\_2 + \mathbf{B}\_3\mathbf{X}\_3 + \mathbf{B}\_4\mathbf{X}\_4 \dots \tag{2}$$

where X's are various effectors within the system, Y is one (of many) affected metrics and B's are the interaction gain coefficients. With this meta-regression equation, the concept of

Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 63

Literature searches are performed in a semi-automated manner, similar to a systematic review (see Cochrane Review instructions for a full description of this method). Here, we utilize keyword searches in PubMed. Our strategy is not to be over-limiting in our resulting study selection. Rather, we limit the size of our dynamic meta-analysis by decreasing the

For the dynamic meta-analysis presented in this chapter, we perform two different literature searches, Phase I and Phase II. The first literature search (Phase I) is an all-encompassing literature search for primary research studies/articles. Phase I inclusion results in ~1,803 papers, while Phase I exclusion leaves a remainder of 1,144 papers. These 1,144 articles are the studies/data sets for dynamic meta-analysis. The second literature search (Phase II) is for ALS review articles. Phase II inclusion results in ~200 reviews, while Phase II exclusion reduces the number to 52. The review articles are utilized for the purposes of structure and

 All studies must be from peer-reviewed journals, which are indexed in the United States National Library of Medicine and National Institute of Health PubMed database.

 all studies must be from peer-reviewed journals, which are indexed in the United States National Library of Medicine and National Institute of Health PubMed database.

Similar to traditional meta-analysis, dynamic meta-analysis utilizes outcome measures (measures that are calculated or derived from the included studies) as a means of prediction. Unlike traditional meta-analysis, dynamic meta-analysis also includes *interactions* between the outcome measures. However, due to the larger scope of dynamic meta-analysis compared to traditional meta-analysis, it is helpful to combine individual experimental metrics or outcome metrics into aggregates we refer to as *categories*. The outcome measures, interactions, and their respective categories, together, make up the dynamic meta-analysis structure (Figure 1).

**2.5 Literature searches, inclusion and exclusion criteria** 

aggregation (to be discussed in the following sub-sections).

Amyotrophic Lateral Sclerosis" or "ALS" in title/abstract

articles without quantitative, statistically significant results

"Amytrophic Lateral Sclerosis" or "ALS" in title/abstract

articles without verifiable controls for each experimental metric utilized

"G93A" or "transgenic mouse" in title/abstract

studies not measured at two or more time points

clinical or experimental review articles

 articles focused on human case studies articles focused on assessment metrics

 articles focused on ALS variants with dementia articles focused on disease management

articles focused on non-mechanistic based therapies

**2.6 Structure: Outcome measures, interactions, and categories** 

Phase I Inclusion Criteria:

 Most Recent 15 years Primary research artciles Phase I Exclusion Criteria:

Phase II Inclusion Criteria:

 most recent 5 years Phase II Exclusion Criteria:

study scope instead of using highly selective inclusion/exclusion criteria.

time is introduced explicitly. Therefore, dynamic meta-analysis can incorporate experimental data from differing time-points and predict effects over time. These traits make dynamic meta-analysis unique, even when compared to advanced meta-analysis methods such as network analysis (Trelle, Reichenbach et al. 2011). While network analysis does use comparative relationships, it does not include interactions or show how relationship ratios change over time. Thus, where traditional or even advanced metaanalysis produces a static set of linear relationships, dynamic meta-analysis produces a set of differential equations. This results in an innovative way to examine pathology dynamics as we can look at how metrics change and interact over time rather than being limited to how they correlate at a single point in time. Currently, the only other available technique capable of implictly including interactions and explicity including time is relational modeling (Mitchell, 2009; Mitchell and Lee, 2008). In fact, dynamic meta-analysis is, itself, one form of relational modeling. However, traditional relational models typically do not provide the desired statistical weight of dynamic meta-analysis since only one primary study is included per interaction.

### **2.3 Overview of the dynamic meta-analysis process**

Dynamic meta-analysis is similar to traditional meta-analysis in that it utilizes literature searches, inclusion/exclusion critieria, and data aggregation techniques. A key difference in the dynamic meta-analysis process, however, is the study structure and data extraction. In the following sub-sections of the chapter we provide the details necessary to perform each step of dynamic meta-analysis: determining the study scope, performing literature searches and study inclusion/excusion, developing structure, extracting data, aggregating extracted data, implementing dynamic meta-analysis, and analyzing dynamic meta-analysis results.

### **2.4 Defining the study scope**

Just as in traditional meta-analysis, defining the scope is an important step. There are several things to consider, including the outcome goals of the project, the measures and timepoints to be included, the statistical weight, and the desired timeline of the project. There is no methodological limit on the number of studies, measures, and timepoints that can be included in dynamic meta-analysis. Rather, the researcher must impose those limits. There is a balance between including enough studies to obtain statistically significant results and the amount of man-hours it takes to perform dynamic meta-analysis. The one drawback of meta-analysis is it is by no means a completely automated process. Rather, humans must be involved at each step, to search and more importantly extract the data from included studies.

To assist in balancing workload and the time it takes to get preliminary results from dynamic meta-analysis, we divide dynamic meta-analysis into two parts: a feasibility study and a full study. A full study, as the name implies, encompasses all of the primary articles that meet the inclusion criteria. In contrast, a feasibility study can potentially have the same number and breadth of outcome measures as the full study, but utilizes a lesser number of included primary studies for each metric (i.e. a lower "n"). That is, the statistical weight is decreased. The advantage of performing an initial feasibility study goes beyond simply obtaining preliminary results more quickly. The initial results of the feasibility study also provide insight and direction, which can be used to fine tune the targeting of the full study (e.g. determining if more or less measures are needed or if the scope of the study needs revised, etc.).
