Get Started
Dr. Simon Müller
2023-04-29
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library(CaseBasedReasoning)
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Motivation
This section demonstrates how to apply Cox Proportional Hazards (CPH)
regression for Case-Based Reasoning (CBR). CPH regression is a popular
survival analysis technique that models the relationship between the
hazard rate and the predictor variables while accounting for the
time-to-event data. Linear and logistic regression models can be
employed similarly for CBR by initializing the models as follows:
Data Preparation: Begin by preparing the
dataset, ensuring that it includes the relevant features and the
time-to-event data. For CPH regression, you’ll need to include a column
indicating the event status (e.g., 1 for the event occurring and 0 for
censored observations). For linear and logistic regression models,
prepare the dependent and independent variables accordingly.
Feature Selection: Identify the most relevant
features or predictor variables for the regression models. Techniques
like correlation analysis, mutual information, or machine learning
algorithms can be used to select the most important features for the CBR
process.
Model Initialization: Initialize the appropriate
regression model for the analysis:
cph_model <- CoxModel$new(Surv(futime, fustat) ~ age + resid.ds + rx + ecog.ps, ovarian)
# linear_model <- LinearBetaModel$new(y ~ x1 + x2 + x3)
# logistic_model <- LogisticBetaModel$new(y ~ x1 + x2 + x3)
- Model Training: Fit the initialized regression
model to the training data.
Model Evaluation: Evaluate the performance of
the fitted regression models using appropriate evaluation metrics, such
as concordance index for CPH regression, R-squared for linear
regression, or accuracy and AUC-ROC for logistic regression.
Similarity Assessment: Use the trained
regression models to assess the similarity between cases by comparing
the predicted outcomes or coefficients of the predictor variables.
Techniques such as distance metrics or clustering algorithms can be
employed to group similar cases.
Retrieve, Reuse, Revise, and Retain: After
identifying the most similar cases using the trained regression models,
follow the traditional CBR process. Adapt the retrieved cases to fit the
new problem, evaluate the revised solution, and add the new case and
solution to the database for future reference.
By integrating regression models like CPH, linear, and logistic
regression into the CBR process, it becomes possible to capture the
relationships between variables more effectively, leading to more
accurate identification of similar cases and improved problem-solving
capabilities.
Cox Proportional Hazard
Model
In the first example, we demonstrate the application of the Cox
Proportional Hazards (CPH) model using the ovarian dataset from the
survival package. To begin, we initialize the R6 data object, which is
essential for managing and organizing the dataset. This step sets the
foundation for further analysis, enabling efficient implementation of
the CPH model in the Case-Based Reasoning process.
ovarian$resid.ds <- factor(ovarian$resid.ds)
ovarian$rx <- factor(ovarian$rx)
ovarian$ecog.ps <- factor(ovarian$ecog.ps)
# initialize R6 object
cph_model <- CoxModel$new(Surv(futime, fustat) ~ age + resid.ds + rx + ecog.ps, ovarian)
In the preprocessing stage, all cases with missing values in the
learning and endpoint variables are removed using the
na.omit function, and the cleaned dataset
is stored internally. A text output is provided, indicating the number
of cases that were dropped due to missing values. Additionally, any
character variables present in the data are converted to factor
variables to ensure compatibility with subsequent statistical
analyses.
Available Models
In the context of Case-Based Reasoning (CBR), linear regression,
logistic regression, and Cox proportional hazards regression can be used
for estimating the similarity between cases. Each of these regression
methods has its own advantages and disadvantages, which are outlined
below.
Linear
Regression
Advantages:
Simplicity: Linear regression models are easy to understand and
interpret, which makes it straightforward to explain the model’s
behavior to stakeholders.
Speed: Linear regression models are computationally efficient,
requiring less processing power and time to fit compared to more complex
models.
Disadvantages:
- Limited to continuous dependent variables: Linear regression models
can only be applied to problems with continuous dependent variables,
which limits their applicability in CBR scenarios.
Logistic
Regression
Advantages:
Binary classification: Logistic regression is suitable for binary
classification problems, making it more applicable in CBR scenarios
where the outcome is binary (e.g., success or failure).
Interpretability: Logistic regression models provide insights
into the relationship between variables through coefficients, allowing
for easier interpretation of feature importance.
Disadvantages:
- Limited to linear relationships: Logistic regression models assume a
linear relationship between the independent variables and the logit
transformation of the dependent variable, which may not always hold true
in real-world situations.
Cox
Proportional Hazards Regression
Advantages:
Time-to-event data: Cox proportional hazards regression is
specifically designed for time-to-event data, making it highly
applicable in CBR scenarios where the outcome is a survival or failure
event occurring over time.
Deals with censoring: Cox proportional hazards regression can
handle right-censored data, which is common in survival analysis
scenarios.
Disadvantages:
Proportional hazards assumption: Cox proportional hazards
regression assumes that the hazard ratios are constant over time, which
may not always hold true in real-world situations.
More complex: Cox proportional hazards regression is more complex
compared to linear and logistic regression models, which can make
explaining the model’s behavior to stakeholders more
challenging.
In conclusion, the choice between linear regression, logistic
regression, and Cox proportional hazards regression for CBR depends on
the specific problem and dataset at hand. Factors such as the type of
dependent variable (continuous, binary, or time-to-event), the presence
of censoring, and the need for interpretability should all be considered
when selecting the most appropriate method.
Random
Forests
Advantages:
Non-linear relationships: Random forests can capture complex,
non-linear relationships between variables, making them suitable for a
wider range of problems.
Robustness to outliers: Random forests are less susceptible to
outliers compared to linear regression models, leading to more stable
predictions.
Feature interactions: Random forests can capture interactions
between features, which can be particularly useful in CBR when there are
complex relationships between variables.
Reduced overfitting: Random forests employ an ensemble of
decision trees, which generally results in reduced overfitting compared
to single models, such as linear regression.
Disadvantages:
Complexity: Random forests are more complex and harder to
interpret compared to linear regression models, which can make
explaining the model’s behavior to stakeholders more
challenging.
Computationally expensive: Random forests require more processing
power and time to fit compared to linear regression models, particularly
with large datasets and a high number of trees.
Less interpretable feature importance: Although random forests
can provide feature importance scores, interpreting these scores can be
more challenging compared to the coefficients of a linear regression
model.
In conclusion, the choice between linear regression models and random
forests for CBR depends on the specific problem and dataset at hand.
Factors such as the complexity of relationships between variables, the
presence of outliers, computational resources, and the need for
interpretability should all be considered when selecting the most
appropriate method.
Case Based
Reasoning
Search for Similar
Cases
Once the initialization is complete, the goal is to identify the most
similar case from the training data for each case in the query dataset.
This process involves comparing the features of the query cases with
those of the training cases, using similarity measures or statistical
models, to retrieve the most closely matched cases, thereby facilitating
the Case-Based Reasoning process.
n <- nrow(ovarian)
trainID <- sample(1:n, floor(0.8 * n), F)
testID <- (1:n)[-trainID]
cph_model <- CoxModel$new(Surv(futime, fustat) ~ age + resid.ds + rx + ecog.ps, ovarian[trainID, ])
# fit model
cph_model$fit()
# get similar cases
matched_data_tbl = cph_model$get_similar_cases(query = ovarian[testID, ], k = 3)
knitr::kable(head(matched_data_tbl))
| 22 |
268 |
1 |
74.5041 |
2 |
1 |
2 |
0.3198076 |
1 |
| 1 |
59 |
1 |
72.3315 |
2 |
1 |
1 |
0.4332524 |
2 |
| 3 |
156 |
1 |
66.4658 |
2 |
1 |
2 |
1.9264911 |
3 |
| 19 |
1129 |
0 |
53.9068 |
1 |
2 |
1 |
0.2204346 |
1 |
| 5 |
431 |
1 |
50.3397 |
2 |
1 |
1 |
0.6154656 |
2 |
| 12 |
744 |
0 |
50.1096 |
1 |
2 |
1 |
0.7640594 |
3 |
After identifying the similar cases, you can extract them along with
the verum data and compile them together. However, keep in mind the
following notes:
Note 1: During the initialization step, we removed
all cases with missing values in the data and endPoint variables.
Therefore, it is crucial to perform a missing value analysis before
proceeding.
Note 2: The data.frame returned from
cph_model$get_similar_cases includes four
additional columns:
caseId: This column allows you to map the similar cases
to cases in the data. For example, if you had chosen k=3, the first
three elements in the caseId column will be 1 (followed by three 2’s,
and so on). These three cases are the three most similar cases to case 0
in the verum data.scDist: The calculated distance between the cases.scCaseId: Grouping number of the query case with its
matched data.group: Grouping indicator for matched or query
data.
These additional columns aid in organizing and interpreting the
results, ensuring a clear understanding of the most similar cases and
their corresponding query cases.
Check Proportional
Hazard Assumption
Lastly, it is important to check the Cox proportional hazard
assumption to ensure the validity of the model. This assumption states
that the hazard ratios between different groups remain constant over
time. By verifying this assumption, you can confirm that the
relationships captured by the model are accurate and reliable for the
given dataset, ultimately enhancing the effectiveness of the Case-Based
Reasoning process.
Distance Matrix
Calculation
Alternatively, you might be interested in examining the distance
matrix to better understand the relationships between cases:
distance_matrix = cph_model$calc_distance_matrix()
heatmap(distance_matrix)
cph_model$calc_distance_matrix()
computes the distance matrix between the train and test data. If test
data is omitted, the function calculates the distances between
observations in the train data. In the resulting matrix, rows represent
observations in the train data, and columns represent observations in
the test data. The distance matrix is stored internally in the
CoxModel object as
cph_model$distMat.
Visualizing the distance matrix as a heatmap can provide insights
into the relationships between cases, assisting in the identification of
similar cases and improving the Case-Based Reasoning process.