In September of this year, JMP products were updated to the latest version, version 19.
This update adds a new platform called "Causal Treatment Effects" to JMP Pro and JMP Student Edition, allowing you to perform analyses using propensity score matching .
In this article, we will use an example to explain how to perform propensity score matching using this "causal treatment effect" platform.
Propensity Score Matching Example
To investigate the effectiveness of a medical treatment, data was collected from 181 patients. Each patient was classified as either "received the medical treatment" or "not received the medical treatment," and the outcome (effective or ineffective) was assessed.
Patient characteristics that may be related to treatment and outcomes will be used as covariates, including gender, age, smoking history, BMI, and severity score .
Outcome (result) : "Y: Outcome" (1: Effective, 0: Ineffective)
Treatment : "T: Treatment" (1: Treatment (treatment group), 0: No treatment (control group))
Total variables : "X1: Sex", "X2: Age", "X3: Smoking", "X4: BMI", "X5: Severity Score"
This data (JMP format) can be downloaded from this blog (PM_example.jmp).
Launching the Causal Treatment Effect Platform
For the above data, do the following:
- Select Analyze > Fit Model and change the method in the upper right corner of the Model Specification window to Causal Treatment Effects .
- As shown in the figure below, specify the columns corresponding to [Y] and [Treatment]. Also, open the "Treatment Model" tab and specify covariates (X1 to X5) using the "Add" button.
- Click Run.
Note : If you specify a nominal (or ordinal) scale column for Y, the number of categories must be two. Also, the treatment variable must be a nominal (ordinal) scale column with two categories. (Three or more categories cannot be used.)
In the "Fit Causal Treatment Effects" report that appears, expand "Other Propensity Score Methods" and select Nearest Neighbor from "Propensity Score Matching Method."
You can then specify various options for the propensity score method, as follows:
The meaning of the options is described below.
Number of matches per observation : Specify how many control subjects should be matched to one treatment subject.
The default "1" means one-to-one matching, "2" means one-to-two matching.
Minimum and maximum propensity score : Set the minimum and maximum values of the propensity score to be used for matching. Since the propensity score ranges from 0 to 1, the default setting is to use all observations for matching.
Caliper : Indicates the "maximum allowable difference in propensity scores" between observations to be matched. In practice, the tolerance is calculated by multiplying the specified caliper value by the "pooled estimate of the common standard deviation of the matched statistics." For example, if the estimated standard deviation is 0.1 and the caliper value is specified as 0.2, 0.02 (= 0.2 × 0.1) is used as the tolerance. Observations outside the tolerance are excluded from matching.
Matching statistics : You can specify either "Logit of propensity score" (default) or "Propensity score". If you specify "Logit of propensity score", matching will be performed using the logit-transformed value of the propensity score, rather than the propensity score itself.
Matching with replacement : If checked, the same observations from the control group can be reused for multiple treatment observations. If unchecked, observations from the control group that have been used once will not be reused. Generally, sampling with replacement increases the number of samples that can be matched.
For now, leave the default settings and click Run on the left.
Matching results
View the report "Propensity Score Matching Summary."
"Matching parameters" displays the values of the options you just specified.
"Propensity Score Distribution by Treatment" displays the logit distribution of the propensity score for each treatment group (=1) and control group (=0). Blue dots indicate matched observations, while red dots indicate unmatched (excluded) observations that fell outside the caliper.
At the same time, a new data table summarizing the matching results will be output. This table shows the status of the matched samples.The matched pairs are shown as "Match ID." In this example, 68 pairs were created for the treatment and control groups.
Note : If you select "Save causal effect columns to table" in the model report, columns showing the estimated causal effects, including the propensity score, the logit of the propensity score, and whether the row was matched, will be saved to the original data table.
Matching data analysis
The final report, "Analysis of Matched Data," provides information about the model fitted to the matched data.
The model used here is a logistic model with outcome Y, treatment as a fixed effect, and match ID as a random effect. In propensity score matching, treatment and control groups with similar scores are paired, so observations within ID cannot be considered independent, and this situation is addressed by treating them as random effects.
Looking at the "Parameter estimates for fixed effects," the parameter estimate for the term Treatment[0-1] is -1.663. The [0-1] displayed in the term indicates the "effect of the control group (=0) on the treatment group (=1)," indicating that the logit (probability of an effect) for the control group is 1.663 lower than that of the treatment group.
The 95% confidence interval for the estimated value (-1.663) is [-2.554, -0.772], which does not cross 0, and the p-value is small at 0.003, so there is a significant difference.
In other words, causal inference can be drawn that performing a medical procedure significantly increases the probability of achieving a positive outcome .
The predicted probability of "effective" for each group can be obtained by selecting [Marginal Predictor Plot] > [Profile] from the red triangle button to the left of the "Binomial" report. The predicted probability for the control group is 0.117, and the predicted probability for the treatment group is 0.411, indicating that the treatment can be expected to have an effect of approximately 30%.
If we invert the sign of the treatment estimate (= -1.663) and place that value on the shoulder of the exponent, we get
exp(1.663) = 5.28
This shows the odds ratio of the treatment group to the control group when the treatment is considered effective. In other words, receiving the treatment increases the odds of effectiveness by approximately 5.3 times compared to the control group.
Even if Y is a continuous variable
In the examples up to this point, Y has been a binary nominal variable, but propensity score matching can be performed using similar operations when Y is a continuous variable.
The JMP sample data "Blood Pressure Treatment.jmp" is an example of using a continuous variable, "post-administration systolic blood pressure," as Y.
In this case, a linear mixed model assuming a normal distribution for Y is fitted to the matched data.
by Naohiro Masukawa (JMP Japan)
Naohiro Masukawa - JMP User Community
