Application of a Causal Discovery Algorithm to the Analysis of Arthroplasty Registry Data

Abstract

Improving the quality of care for hip arthroplasty (replacement) patients requires the systematic evaluation of clinical performance of implants and the identification of "outlier" devices that have an especially high risk of reoperation ("revision"). Postmarket surveillance of arthroplasty implants, which rests on the analysis of large patient registries, has been effective in identifying outlier implants such as the ASR metal-on-metal hip resurfacing device that was recalled. Although identifying an implant as an outlier implies a causal relationship between the implant and revision risk, traditional signal detection methods use classical biostatistical methods. The field of probabilistic graphical modeling of causal relationships has developed tools for rigorous analysis of causal relationships in observational data. The purpose of this study was to evaluate one causal discovery algorithm (PC) to determine its suitability for hip arthroplasty implant signal detection. Simulated data were generated using distributions of patient and implant characteristics, and causal discovery was performed using the TETRAD software package. Two sizes of registries were simulated: (1) a statewide registry in Michigan and (2) a nationwide registry in the United Kingdom. The results showed that the algorithm performed better for the simulation of a large national registry. The conclusion is that the causal discovery algorithm used in this study may be a useful tool for implant signal detection for large arthroplasty registries; regional registries may only be able to only detect implants that perform especially poorly.

Keywords: Causal discovery; arthroplasty; hip; probabilistic graphical models.

Figure 1.

Example of causal discovery algorithm PC using 4 variables, x₁, x₃, x₃, and x₄, assuming that x₁ and x₂ are independent, x₁ and x₄ are conditionally independent given x₃, x₂, and x₄ are conditionally independent given x₃, x₁ is a cause of x₃, x₂ is a cause of x₃, and x₃ is a cause of x₄. This is illustrated as a DAG in (A). The algorithm has 3 steps. Step 1 consists of constructing a fully connected undirected graph (B). Step 2 consists of removing all edges where the data do not support a direct cause between 2 nodes. The edge between x₁ and x₂ is removed because they are independent. The edge between x₁ and x₄ is removed because x₁ and x₄ are conditionally independent given x₃. This means that if x₃ is fixed, any change in x₁ does not cause a change in x₄. Similarly, the edge between x₂ and x₄ is removed, resulting in the DAG shown in (C). Step 3 determines the direction of the edges remaining at the end of step 2. Directed edges from x₁ to x₃ and from x₂ to x₃ are determined because x₃ must be a collider node due to x₁ and x₂ being independent (the “collider test” for edge direction), resulting in (D). The “from collider test” is used to determine that the edge from x₃ to x₄ is directed from x₃ to x₄ (E). Observe that the PC algorithm reconstructed (E) from the statistical independence assumptions implied by the DAG in (A). DAG indicates directed acyclic graph.

Figure 2.

Causal diagram for simulated data. The simulation included 3 variables: (1) implant, (2) sex, and (3) time to first revision (TTR). Causal relationships are indicated by directed edges between nodes.

Figure 3.

Proportion of reconstructed graphs with an edge between implant and TTR for a given effect size. Figure panels 3A and B use a registry size of 799 revised cases, and figure panels 3C and D use a registry size of 20 800 revised cases. Figure panels 3A and 3C use a $p_{I,F}$ and $p_{I,M}$ of 0.02, and figure panels 3B and 3D use a $p_{I,F}$ and $p_{I,M}$ of 0.04. Error bars represent 95% confidence interval. TTR indicates time to first revision.

Figure 4.

Proportion of reconstructed graphs with an edge between implant and TTR for a given number of revised cases. Both panels use an effect size $(E_I)$ of 2.0. Figure panel 4A uses a $p_{I,F}$ and $p_{I,M}$ of 0.02 and figure panel 4B uses a $p_{I,F}$ and $p_{I,M}$ of 0.04. Error bars represent 95% confidence interval. TTR indicates time to first revision.

Figure 5.

Proportion of reconstructed graphs with an edge between implant and TTR for a given $p_{I,F}$ and $p_{I,M}$. Number of revised cases is set at 799 for all panels. Effect size $(E_I)$ is set at 1.5, 2.0, and 4.0 in figure panels 5A to C, respectively. TTR indicates time to first revision.

Figure 6.

Proportion of reconstructed graphs with an edge between implant and TTR for a given $p_{I,F}$ and $p_{I,M}$. Number of revised cases is set at 20 863 for all panels. Effect size ($E_I$ is set at 1.25, 1.5, and 2.0 in figure panels 6A to C, respectively). TTR indicates time to first revision.