Overview of the Diagnostics and Therapy Process

Figure 1 shows an overview of a typical diagnostics and therapy process for an individual patient with two therapy options. There are several decision points following disease diagnosis (red splitters in Fig. 1). If a targeted therapy option (Therapy A in Fig. 1) is associated with a corresponding CDx, the patient will first decide whether to take the CDx (the first red splitter in Fig. 1). In the case of a positive CDx result, the patient will expect Therapy A to be effective and is assumed to automatically opt for it (the automatic decision point is marked by a green splitter in Fig. 1). In the case of a negative result, a second decision point comes into play (the second red splitter in Fig. 1), where the patient can actively choose an alternative therapy (Therapy B in Fig. 1) or decline all therapy options. If the patient declined the CDx at the first decision point, then the following decision point involves the choice between Therapies A, B, or no treatment. The dotted region in Fig. 1 is the main focus of this work.

Fig. 1

Overview of the process of diagnostics and therapy. Red splitters represent active decision points, while the green splitter represents the CDx results for biomarker detection

Description of the Diagnostics and Therapy Process as a Process System Diagram

The dotted region in Fig. 1 is expanded, and a higher resolution pathway is presented in Fig. 2a as a process system diagram. The diagram describes 20 possible patient paths and the split rules leading to each outcome. Each split is defined based on a patient’s decision and/or biological features. Figure 2b presents detailed descriptions of the unit structures used to build the process system diagram in Fig. 2a. Unit structures include splitters, unit operations, and agents. Decision-making splitters are indicated in red and represent active decision points (\(}_\)). The outcome path for a patient is assumed to change based on subjective decisions made at those split points. In contrast, outcome paths will be automatically decided based on biological or statistical features in the other splitters. Biomarker splitters in grey (\(}_\)) indicate the presence or absence of a particular biomarker, where \(x\) [–] represents the ratio of patients with positive biomarkers in a general patient population. Companion diagnostic splitters in green (\(}_\)) indicate the ability of a CDx to detect the biomarker. \(\alpha\) [–] is the probability of type 2 error (false positive), and \(\beta\) [–] is the probability of type 1 error (false negative) in the obtained CDx results. Finally, the therapy splitters in purple (\(}_\)) indicate the probability of the therapy working effectively for a patient. \(\gamma\) [–] is the response rate, indicating the probability of a positive response on the application of a specific therapy for the patient. “Unit operations” in Fig. 2b indicates the different potential unit operations: perform companion diagnostics, apply molecular targeted therapy, e.g., mAb therapies, or apply standard therapy. If several molecular targeted or standard therapies exist, then a new unit operation could be added for each existing therapy option. A path with no unit operations indicates a decision to not undergo any treatment. \(\varepsilon\) [–] is a factor representing the change in the life expectancy at diagnosis following the performance of each unit operation relative to the no-action path. The subscripts “t” and “s” represent the targeted and standard therapies, respectively. Values for \(\gamma\) and \(\varepsilon\) are determined for each patient based on the patient’s biological features and general statistical effectiveness of each therapy for different patient groups. “Agents” in Fig. 2b indicates the agent impacted by the process.

Figure 2a shows the complete process system diagram for the case, where one mAb therapy with one CDx is compared to standard therapy or no treatment options. Different outcomes are expected based on the biological features of each patient. For example, the no-action path will yield different life expectancy for patients with and without target biomarkers. Important splitters in the figure include (1) \(}_\), a patient’s decision to take CDx; (2) \(}_\), the patient possessing a positive biomarker; (3) \(}_\), the result of the CDx; (4) \(}_\), a patient’s response to the targeted therapy (similarly \(}_\), a patient’s response to the standard therapy); (5) \(}_\), the patient’s decision whether to undergo the targeted therapy without undergoing CDx; (6) \(}_\), decisions to terminate the therapy or return to a previous decision point (e.g., \(}_\) to take the same or a different type of CDx); (7) \(}_\), decisions to take the standard therapy. In the figure, the superscripts “1” and “2” indicate biomarker-positive and negative patients, respectively. The subscripts “e” and “ne” indicate patients with a positive or a negative response to a particular therapy, respectively. In total, 20 potential outcomes for changes in the life expectancy are identified for this system, each outcome is defined in the figure with a unique path ID.

Fig. 2

a An overview of the process system diagram leading to potential paths for patients with an option of a targeted therapy with available CDx and a standard therapy; b unit structures used to build the developed model

Individual Paths and Scenarios

Individual patient paths are those determined by a patient’s decisions and features (e.g., biomarker-positive or negative). The different paths, 1 to 20 in Fig. 2a, correspond to the different potential outcomes for each patient. The determination of the likelihood of a patient achieving a specific outcome once their biological features are identified would be useful in the decision-making process for each patient. On the other hand, a scenario is a group of those paths as defined only by decision points (the red splitters). The evaluation of different scenarios would be useful for both patients who do not have enough information about their biological features and payers who want to evaluate the overall system. Both individual paths and group scenarios are the targets of evaluation in this work.

Evaluation IndicatorsFor Individual Paths

The life expectancy at diagnosis for each individual path, \(_}\) (year), the total cost, \(_,\mathrm}\) (Japanese yen (hereafter referred to as JPY)), and the total cost per year of life expectancy for each path, \(CE\) (JPY year−1), were calculated, as shown in Eqs. (1)–(3), respectively.

$$_}=\left(\varepsilon \right)\left(_}\right)$$

(1)

$$_,\mathrm}=_}+(_})\left(_}\right)$$

(2)

where \(_}\) (year) is the life expectancy at diagnosis in the no-action path for each patient. This value may vary depending on the existence of specific biomarkers (difference between paths 19 and 20 in Fig. 2a). The overall \(\varepsilon\) will be greater than 1 for paths with effective combinations of therapies and diagnostics and smaller than 1 for paths with negative overall effects due to the side effects. \(\varepsilon\) is 1 for the ineffective paths or for the paths where no action is taken.

The total cost of an individual path includes the costs of any therapies and applied CDx (\(_}\) (JPY)). \(_}\) (month) is the minimum of the expected remaining lifetime for each patient or the medically recommended duration of each therapy option. \(_}\) (JPY month−1) is the total monthly cost of each applied therapy. Therefore, \(_}\) can be either \(_}\) (JPY month−1) (the cost for targeted therapy per month) or \(_}\) (JPY month−1) (the cost for standard therapy per month) or their sum depending on the recommended medical action path for each disease. A path with a higher \(CE\) value, thus, reflects a less cost-effective option.

Previous studies have commonly used the incremental cost-effectiveness ratio (ICER) as the cost-effectiveness indicator [16]. ICER is generally used to judge the feasibility of an investment by comparing the difference between new and standard applications. For pharmaceutical applications, it is calculated via the evaluation of the additional costs (e.g., \(\Delta _,\mathrm}\)) incurred to achieve a positive outcome (e.g., \(\Delta _}\)) using new technologies (or drugs) relative to the standard technologies which are commonly used. The standard technologies are regarded as the baseline. However, in this work, there are multiple baselines involved even with the application of the standard therapy (e.g., with or without a biomarker or genetic mutation, or showing response to the therapy or not), which makes IECR difficult to apply and compare. Therefore, the individual \(_}\) and \(_,\mathrm}\) were used to calculate the effectiveness of each path instead of defining a specific baseline.

Scenario Definitions

Since scenarios are the groups of several paths which are the potential outcomes of the same decisions, each scenario was evaluated through the expectation of the evaluation indicators of its underlying paths as follows in Eqs. (4) and (5):

$$E\left(_\right)=\left(\begin__}}& \cdots & __}}\end\right)\left(\genfrac__}}}\vdots \\ __}}\end}\right)$$

(4)

$$I, i\in \left\_}, _,\mathrm}, CE\right\}$$

(5)

where \(__}\) and \(__}\) [–] are the evaluation indicator value and the probability of the potential patient path \(j\) in scenario \(s\), respectively. \(_}\) and \(_}\) are the minimum and the maximum path ID representing the range of potential patient paths belonging to scenario \(s\), respectively. \(E\left(_\right)\) is the expectation value of the indicator \(I\), for scenario \(s\).

The probability of each the potential patient path \(j\) was calculated based on the values set for each splitter. For example, the ratio of patients with positive biomarkers in a general population was used to set x [–] for \(}_\). Depending on the set values and assumptions taken, there could be some paths which no patient could reach. Such paths were called zero-paths while the others were called non-zero paths.

Model Assumptions

First, the gradual change in the patient’s health status during the therapy over time was not considered. The effect of therapy was assumed to be achieved at once upon application. In this work, only the cost of therapy and diagnostics was included, but the cost of care during therapy was not considered. A longer treatment process might incur higher personal care costs in that duration. Second, the effectiveness of therapy was only varied based on differences in patient groups (i.e., with or without biomarkers and showing response to therapy or not). Individual differences between patients on the same path were neglected. The effect of therapy was assumed to be constant and identical for everyone going through the same path.

Model Applications

In addition to the patient, a medical doctor, CDx researcher, clinical researcher, and government can be involved as the stakeholders in the system. Model parameters can be updated based on new inputs from different stakeholders. For example, new or improved therapies developed by clinical researchers can affect the determination of the response rate and the estimated change in life expectancy (\(\gamma\) and \(\varepsilon\)), respectively. The model can be expanded to compare the impact of all new therapies on the outcomes for different patient groups. Furthermore, the values of \(\gamma\) could also be affected through the identification of new biomarkers, more closely related to the success of the targeted therapy. Developments by CDx researchers to improve biomarker detection accuracy will affect the values of \(\alpha\) and \(\beta\). The developed model thus provides a standardized method for the comparison of novel developments to existing alternatives. This flexibility provides a systematic and comprehensive framework for quantifying the effects of any developments in the system on all expected outcomes for each patient. Various stakeholders can use the model from different perspectives. For example, the model can be applied to assess all possible outcomes for a single patient, or for entire groups of patients (e.g., by the government), which could be highly beneficial for policy setting or for guiding future research directions.

Sensitivity Analysis

Sensitivity analyses were conducted with the following two objectives: (1) to identify the critical parameters in the system and (2) to quantify the required improvement in the identified critical parameters by assessing the necessary directions to achieve the desired cost-effectiveness. First, a local sensitivity analysis was conducted, where each parameter was varied in a range of 10% of the base case in the direction of a more favorable performance (e.g., reduction in mAb cost, increase in response rate). Then, the parameters with the largest impact on changes in cost-effectiveness were identified. Second, those identified parameters were varied simultaneously in the range of ± 100%. In cases of division by 0, the minimum value was taken as − 99% instead. The upper limit was replaced by the maximum parameter value in cases where + 100% was not feasible. The boundaries were set relatively far from the nominal values to fully investigate any potential changes in cost-effectiveness with future development of the identified influential parameters. All calculations were conducted using inhouse developed Python codes.