Once the model is complete, TreeAge Pro automatically generates the algorithms required to evaluate the model and choose the optimal strategy. This allows you to focus on the problem at hand and not the calculations needed to evaluate the model.
Standard algorithms give weight to each possible outcome within the strategy based on its probability. The combined weighted average generates an overall expected value for each strategy.
TreeAge Pro’s Healthcare Module allows you to compare strategies on the basis of cost-effectiveness via incremental cost-effectiveness ratios and/or net benefits. You can also compare strategies in the same model based solely on cost or comparative effectiveness (CER). You can even use non-standard measurements such as infections, deaths, etc.
The following model compares two treatments for a tumor.
Simple Healthcare Tree
Cost-effectiveness analysis compares the strategies based on a CE frontier.
If there were dominated strategies in this model, they would be presented above and to the left of the CE frontier.
The Rankings report shows the numeric calculations comparing the strategies, including the incremental cost-effectiveness ratio (ICER).
The ICER can then be compared to a willingness-to-pay (WTP) threshold to determine whether we can afford the more effective treatment on the basis of cost-effectiveness.
Study Uncertainty on Healthcare Models
TreeAge Pro allows you to study how uncertainty in a model’s inputs affect the conclusions we can draw via its outputs. TreeAge Pro supports two ways to study uncertainty:
- Deterministic sensitivity analysis
- Probabilistic sensitivity analysis
The Healthcare Module extends the two types of sensitivity analysis to compare strategies via cost-effectiveness analysis.
Deterministic sensitivity analysis In order to study uncertainty individual parameters over a value range. The most common form of deterministic sensitivity analysis studies a single parameter via 1-way sensitivity analysis. 2-way, 3-way and tornado diagrams are also supported.
In order to run 1-way sensitivity analysis on a model, the parameter must be represented by a variable. The variable then can be analyzed over a range of uncertainty rather than using a single point estimate. Consider the model below.
Simple Healthcare Tree
Perhaps we are concerned about the probability of eradicating the tumor with the new treatment – surgery and radiation. We can run 1-way sensitivity analysis on the variable pEradicateRadSurg for a range of 0.5 to 0.9 with 4 intervals. This will recalculate the model five times for values 0.5, 0.6, 0.7, 0.8, 0.9.
CE Sensitivity Analysis
Using secondary outputs, the five sets of results can be used to review the strategy comparison on the basis of cost-effectiveness, cost or effectiveness. The comparison based on effectiveness-only is shown below. This graph generates a threshold of 0.6, above which the new treatment is more effective.
CE Sensitivity Analysis - Effectiveness Graph
The comparison based on cost-effectiveness, using Net Monetary Benefits calculations using a WTP of $50K/LY is shown below. This graph generates a threshold of 0.749, above which the new treatment is more cost-effective (given the WTP assumption).
CE Sensitivity Analysis - Net Benefits Graph
Probabilistic sensitivity analysis (PSA) studies the combined effect of multiple uncertainties upon your model.
To perform PSA, one or more parameters must be represented by distributions. The distributions are then sampled, substituting the sampled values into the model and recalculating the EVs. Repeating this many times provide creates a large set of expected values (EVs), each reflecting a different set of sampled parameters.
Within the overall result set, some sets of EVs will confirm the base case analysis, while others will not. This provides an overall measure of certainty for the base case conclusions.
The model above was modified to include three parameter distributions:
- Probability of eradicating the tumor with radiation only.
- Probability of eradicating the tumor with radiation and surgery.
- Cost of surgery.
A PSA Monte Carlo simulation was run to generate 1000 separate result sets from 1000 sets of parameter samples. The simulation results can then be parsed to find ranges and confidence intervals for all outputs (including ICER) and other secondary outputs that measure the level of certainty in the base case analysis – that the new treatment was most cost-effective given WTP $50K/LY.
The following ICE scatterplot graph shows simulation iterations plotted for incremental cost and incremental effectiveness. The plots below and to the right of the WTP line confirm the base case analysis.
CE PSA - ICE Scatterplot
The following Acceptability Curve shows the percentage of simulation iterations that consider each strategy the most cost-effective over a range of WTP.
CE PSA - Acceptability Curve
There are many other output graphs and numeric reports available from the simulation results.
State Transition/Markov Models
Often, healthcare models need to follow a disease process into the future. The most common approach to this issue is to create a state transition or Markov model.
TreeAge Pro supports Markov models through the decision tree structure. Note the model below.
Markov Model: A Markov model consists of the Markov node and everything to its right. A decision tree model can contain many Markov models for specific strategies, subgroups, etc. Each Markov model is evaluated as a unit, generating an expected value that can feed back into the analysis results for the entire decision tree.
Health States: The direct branches of the Markov node are the health states. The cohort starts each cycle distributed among the health states.
Transition Subtrees: Each health state has its own transition subtree, which specifies the events that can occur within a cycle. At each point where the transition subtree terminates, the cohort is returned to one of the states to begin the next cycle. This results in a different distribution of the cohort among the health states to start each cycle.
Accumulating Value: As the cohort cycles through the health states and transition subtrees, cost, effectiveness and/or other value measures are accumulated, both based on the starting health state and on the events that occur within the cycle.
Expected Value: After all cycles are complete, the overall accumulated cost and/or effectiveness generates the expected value (EV) for the Markov model in its entirety. This accounts for all combinations of events over any number of cycles. The overall Markov model EV can then be fed upstream into an overall evaluation of treatment options for a disease.
Evaluating Markov Models
When Markov models are evaluated, they eventually provide a single expected value (EV) for each active payoff (frequently cost and/or effectiveness). However, you may want to see further into the individual calculations that result in the overall EV. Markov Cohort Analysis provides this detail.
Consider the following model.
Markov Cohort Analysis provides the cycle by cycle accumulation of value from each state and transition.
Markov Cohort Analysis
Review of these transitions and calculations is a valuable tool in verifying whether your model is working as designed. For this cost-effectiveness model, the overall accumulated cost and effectiveness values after the last cycle become the overall EV for the Markov model.
Markov cohort analysis also provides access to graphs showing the distribution of the cohort among the states by cycle and the accumulation of value by cycle. One such graph is the survival curve shown below.
Markov Survival Curve
Heterogeneity and Event Tracking
TreeAge Pro allows you to extend beyond the traditional limitations of expected value and/or Markov models. By running individual “trials” through the model by random walk (microsimulation), you can introduce heterogeneity and event tracking into your model.
When individuals are run through the model, you can assign different characteristics to those individuals to create a heterogeneous cohort. For example, each individual trial could have its own age, gender, ethnicity, weight, tumor type, disease stage, etc. Each such characteristic can be referenced within the model to calculate probabilities, cost, utility, etc.
TreeAge Pro distributions can be sampled for each trial to generate a characteristic for that trial. You can also load known patient data into the model and use that data for a trial within the model.
TreeAge Pro trackers can be used to record events and other characteristics that change as a trial runs through the model. Unlike variables, which apply to the entire cohort, trackers store and retrieve data specific to each trial.
For example, you might have a stroke event in your model. Without microsimulation, the stroke event could only impact that specific cycle. However, with microsimulation, you can record (or count) the stroke event in a tracker. Then you can check the value of the tracker in all subsequent cycles, likely to drive worse transition probabilities and/or utilities after a stroke.
The attached model demonstrates both techniques (click for larger image).
The model includes two distributions to generate heterogeneity, one for starting age and one for tumor type. The properties of the age distribution are displayed below.
Before each trial is run through the model, a sample is drawn to generate a starting age between 30 and 50. The trial’s age for each cycle is then incremented within the Markov model based upon the starting age and the cycle number. The current age is then use for background mortality checks.
The model also tracks strokes via an event within the Metastases state’s transition subtree. See below.
Microsimulation - Update Tracker
When a trial reaches the node Stroke, the tracker t_strokes is incremented by one. The probability variable definition for pMetastasesToDead increases the probability of death in future cycles based on the number of strokes via the t_stroke tracker as follows.
pMetastasesToDead = tDeathMetastases[t_strokes]
This expression pulls a different probability value from the table based on the number of strokes the trial has had.
Discrete Event Simulation
TreeAge Pro supports Discrete Event Simulation (DES) or Time-to-Event Models within the decision tree format. DES and Time node types facilitate a time-based approach to models.
While Markov models use fixed cycle lengths and probabilities for events, DES models rely on times associated with competing events. The times are drawn from distributions and the shortest time event drives patient flow through the model. Values (cost, effectiveness) are accumulated based on the time to the next event as well as fixed values associated with specific events.
DES models are analyzed via Microsimulation (individual-patient simulation) and use existing report and graphical outputs.