# New Insights in Computational Methods for Pharmacovigilance: E-Synthesis, a Bayesian Framework for Causal Assessment

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## Abstract

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## 1. Introduction

## 2. State of the Art

#### 2.1. Aggregation of Spontaneous Reports

#### 2.2. Aggregation of Human and Animal Data

#### 2.3. Bayesian Aggregation of Safety Trial Data

#### 2.4. Data Mining and Fusion Methods

#### 2.5. Semantic (Web) Methods

## 3. E-Synthesis: A Bayesian Epistemology-Driven Framework for Pharmacovigilance

**hypothesis of interest**is: ‘Drug D causes harm E in population U and model $\mathcal{M}$”. To facilitate the inference from all the available evidence,

**indicators of causality**are used. These indicators are based on Hill’s nine viewpoints for causal assessment [55]. Below, we detail the main components that build up E-Synthesis.

#### 3.1. Bayesian Network Model

#### 3.2. Theoretical Entities

#### 3.2.1. The Causal Hypothesis (©)

#### 3.2.2. Indicators of Causation

“None of my nine viewpoints can bring indisputable evidence for or against the cause-and-effect hypothesis and none can be required as a sine qua non. What they can do, with greater or less strength, is to help us make up our minds in the fundamental question—is there any other way of explaining the set of facts before us, is there any other equally, or more, likely than cause and effect?” (Bradford Hill both refers to explanatory power and likelihood as reliable grounds to justify causal judgements, and presents the respective criteria as opposed to tests of significance: “No formal tests of significance can answer those questions. Such tests can, and should, remind us of the effects that the play of chance can create, and they will instruct us on the likely magnitude of those effects. Beyond that, they contribute nothing to the proof of our hypothesis.” [55])

**Difference-making (Δ)**: If D and E stand in a difference-making relationship, then changes in D make a difference to E (while the reverse might not hold). In contrast with mere statistical measures of association, the difference-making relationship is an asymmetric one. Probabilistic dependence can go in both ways (e.g., if Y is probabilistically dependent on X, then also X is probabilistically dependent on Y); the same does not hold for difference making, which provides information about its direction. This explains why experimental evidence is considered particularly informative with respect to causation; the reason is exactly that in experiments, putative causes are intervened upon, in view of establishing whether they make a difference to the effect. (In philosophical terms, difference-making is understood as ideal controlled variance along the concept of intervention in manipulationist theories of causation (see [20] for a detailed treatment, see also [62] and [56]): X is called a cause of Y if Y’s value can be varied by varying X (possibly upon controlling for additional variables in the given situation)). Hence, randomised controlled trials (RCTs) are the privileged source of evidence for Difference-making (Δ): Reports from RCTs contribute to the (dis)confirmation of causal hypotheses via the Δ node.

**Probabilistic dependence (PD)**: PD encodes whether D and E are probabilistically dependent or not—such dependence naturally increases our belief in some underlying causal connection (as an indicator of causation; see, e.g., [63]). Probabilistic dependence is an imperfect indicator of causation because neither the former entails the latter nor the reverse. There are cases in which probabilistic dependence is created by confounding factors, and cases where two opposite effects of a single cause cancel each other out and produce a zero net effect. (A well-known example of this type of cancellation is Hesslow’s birth control pills case (see, e.g., [64]): The contraceptive (directly) causes thrombosis but simultaneously (indirectly) prevents thrombosis by preventing pregnancy which is a cause of thrombosis. Cartwright ([64]) discusses this case as one of the pitfalls of reducing causal analysis to probabilistic methodology alone. Of course, if cancellation is suspected, one might disable certain preventative causal routes to check whether the causal relationship actually shows once disabling conditions are held fixed. Cartwright however discusses cases in which this strategy might not even be viable, owing to the complexity of the causal web.).

**Dose-response relationship (DR)**: Dose-response relationships are taken as strong indicators of causation. DR is a stronger indicator than probabilistic dependency alone, because it requires the presence of a clear pattern of ≥3 data-points relating input and output. Indeed DR implies PD. Dose-response relationships can be inferred both at the population and at the individual level, and both in observational and experimental studies. DR abstracts away from these specifications and means that for dosages D > 0 in the therapeutic range, the adverse effect E shows (approximate) monotonic growth for a significant portion of the range (see below, Figure 3, for an illustration of important types of dose-response curves).

**Rate of growth (RoG)**: This indicator signals that the dose-response relationship is a steep one. If we have evidence of DR and evidence of $\overline{RoG}$ means either that the rate of growth is low, or highly non-linear.

**Mechanistic Knowledge (M)**: M represents the proposition: “there is a mechanism”, meaning that there is a physiological pathway from drug use to the effect. In the biological realm, a causal relationship obviously entails the presence of a biological pathway connecting the cause to the effect. Therefore, © ⇒ M. However, this pathway may not be causally responsible for bringing out the effect due to possible inhibitors, back-up mechanisms, feedback loops, etc. M ⇒ © does hence not necessarily hold.

**Time course (T)**: T encodes whether D and E stand in the right temporal relationship (time course), which can refer to temporal order, distance, or duration. If D causes E, T must hold (as a necessary condition): © ⇒ T. T remains an imperfect indicator, nevertheless, because temporal precedence is also compatible with ¬(D causing E) while D and E are connected by a common cause or through reversed causation. Hence T ⇒ © does not necessarily hold.

## 4. Zooming in E-Synthesis: Processing Evidence for Dose-Response

_{i}|θ) that defines the possible functional patterns of dose-responsiveness exhibited in Figure 3.

_{i}represents the dose-level, n

_{i}the number of subjects in each dose-group, y

_{i}the number of subjects with effect in the corresponding dose-group and r

_{i}is the dose-response computed as the ratio y

_{i}/n

_{i}. The index i is a natural number less or equal to G, the number of dose-groups.

_{i}|θ) = k where k is a real number subjected to the following bound: 0 ≤ k ≤ 1. Among all the possible values of k, it is possible to calculate the optimal one ($\tilde{k}$) through a least squares regression analysis based on the given dose-response (r) data. That can be achieved by solving this problem:

_{i}|θ), i.e., which functional pattern of dose-responsiveness has to be used in Equation (4). Here, we do not commit to any particular kind of likelihood but we point at the fact that only data-analysis can provide a correct estimation for Equation (8). Moreover, Equation (7) requires the estimation of P(DR), that is the a priori probability of dose-responsiveness. This probability can be estimated through clinical considerations regarding the expectation of dose-responsiveness for a certain drug, or, more generally, in a specific field of scientific inquiry. The degree of specificity of such a prior depends on the available knowledge.

^{2}and its adjusted version. Such analysis is outlined in Table 2: The exponential model emerges as the best according to all criteria (AIC, BIC, R

^{2}and adjusted R

^{2}), whereas the linear and the cubic models perform worst.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | Adjustment for Confounders |

ADR | Adverse drug reaction |

AIC | Akaike information criterion |

B | Blinding |

BIC | Bayesian information criterion |

D | Duration |

DR | Dose-response Relationship |

ECETOC | European Centre for Ecotoxicology and Toxicology of Chemicals |

ES | Effect Size |

EUDRAVIGILANCE | European Union Drug Regulating Authorities Pharmacovigilance |

FAERS | FDA Adverse Event Reporting System |

FDA | Food and Drug Administration (US) |

IC | Information Component |

M | Mechanistic Knowledge |

MCP-Mod | Multiple Comparison Procedures and Modeling algorithm |

MGPS | Multi-item Gamma Poisson Shrinker |

PD | Probabilistic Dependence |

PRR | Proportional Reporting Ratio |

R | Randomisation |

RCT | Randomized controlled trial |

REP | Report Variable |

RoG | Rate of Growth |

ROR | Reporting Odds Ratio |

SB | Sponsorship Bias |

SS | Sample Size |

T | Temporal Precedence |

WHO | World Health Organization |

© | Hypothesis of Causation |

Δ | Difference Making |

$\mathcal{E}$ | Available Evidence |

Σ | Set of statistical Indicators: PD, DR and RoG |

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**Figure 1.**Graph of the Bayesian network with one report for every causal indicator variable. The dots indicate that there might be further indicators of causality not considered here. As explained in text, we here take it that M entails T and hence introduces an arrow from M to T which is not in [20]. REL and RLV act as evidential modulators of data (REP nodes).

**Figure 2.**Graph structure of the Bayesian network for one randomised controlled trial (RCT) which informs us about difference making (Δ) which in turn informs us about the causal hypothesis. The information provided by the reported study is modulated by how well the particular RCT guards against random and systematic error.

**Figure 4.**This figure shows the conditional probability P(DR|data) computed for the data presented in Table 1. X-axis represents P(DR) and Y-axis P(DR|data). On the left panel, P(DR

_{exp}|data) (blue line), embodying an exponential likelihood for DR, is pictured against P(DR

_{cub}|data) (violet line), calculated by using a cubic likelihood. On the right panel, P(DR

_{exp}|data) (blue line) is again pictured against P(DR

_{lin}|data) (violet line), computed with a linear likelihood.

**Table 1.**Raw data derived from the asthma association study [70] (Table 2). The study lasted from 1990 to 1996 and accounted for 297,282 person-years. In this table d

_{i}represents the dose-level, n

_{i}the number of subjects in each dose-group, y

_{i}the number of subjects with effect in the corresponding dose-group and r

_{i}is the dose-response computed as the ratio y

_{i}/n

_{i}.

d_{i} | n_{i} | y_{i} | r_{i} |
---|---|---|---|

0 | 137,568 | 108 | 7.85 × 10^{−4} |

10 | 99,922 | 112 | 1.12 × 10^{−3} |

31.67 | 32,077 | 41 | 1.28 × 10^{−3} |

60 | 10,656 | 16 | 1.50 × 10^{−3} |

86.67 | 17,059 | 22 | 1.29 × 10^{−3} |

**Table 2.**Model evaluation through several criteria: Akaike information criterion (AIC), Bayesian information criterion (BIC), R

^{2}and adjusted R

^{2}. The best statistical model corresponds to an exponential function where θ = (α, β) = (1.01266 × 10

^{−3}; 4.17805 × 10

^{−3}).

Model | θ | Specification of f(d_{i}|θ) | AIC | BIC | R^{2} | Adjusted R^{2} |
---|---|---|---|---|---|---|

exponential | (α, β) | αexp(βd_{i}) | −66.29 | −67.46 | 0.98 | 0.97 |

linear | (α, β) | βd_{i} + α | −66.79 | −67.96 | 0.56 | 0.41 |

quadratic | (α, β, γ) | γd_{i}^{2} + βd_{i} + α | −74.57 | −76.13 | 0.95 | 0.90 |

cubic | (α, β, γ, δ) | δd_{i}^{3} + γd_{i}^{2} + βd_{i} + α | −70.10 | −72.06 | 0.95 | 0.80 |

${\widehat{\mathit{r}}}_{\mathit{i}}$ |
---|

1.01 × 10^{−3} |

1.06 × 10^{−3} |

1.16 × 10^{−3} |

1.30 × 10^{−3} |

1.46 × 10^{−3} |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

De Pretis, F.; Osimani, B.
New Insights in Computational Methods for Pharmacovigilance: *E-Synthesis*, a Bayesian Framework for Causal Assessment. *Int. J. Environ. Res. Public Health* **2019**, *16*, 2221.
https://doi.org/10.3390/ijerph16122221

**AMA Style**

De Pretis F, Osimani B.
New Insights in Computational Methods for Pharmacovigilance: *E-Synthesis*, a Bayesian Framework for Causal Assessment. *International Journal of Environmental Research and Public Health*. 2019; 16(12):2221.
https://doi.org/10.3390/ijerph16122221

**Chicago/Turabian Style**

De Pretis, Francesco, and Barbara Osimani.
2019. "New Insights in Computational Methods for Pharmacovigilance: *E-Synthesis*, a Bayesian Framework for Causal Assessment" *International Journal of Environmental Research and Public Health* 16, no. 12: 2221.
https://doi.org/10.3390/ijerph16122221