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## Assess the therapeutic effect for non-randomized studies using propensity score matching

A randomized controlled therapy study is considered the gold standard in medicine for checking a therapeutic effect. This is because the randomized assignment of the patients to a treatment group enables the patient characteristics to be evenly distributed among the treatment groups. Causal statements about the therapeutic effect are only possible if the groups are comparable with regard to the patients. However, randomization is not always suitable, necessary or feasible. Randomization may not be possible, for example, in the case of rare diseases, small samples or for ethical reasons. However, propensity score matching offers a way of evaluating non-randomized therapy studies. Because with this procedure one can ensure the same prerequisites for the therapy groups to be compared. Propensity Score Matching is used to adjust the evaluations with regard to the measured disturbance variables. In the following we give a short introduction to Propensity Score Matching and explain the Propensity Score Matching procedure step by step.

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• What is a propensity score?
• What is Propensity Score Matching?
• How does the Propensity Score Matching procedure work step by step?
• How is Propensity Score Matching done?

### What is a propensity score?

A propensity score is the probability that a patient will receive the target therapy. In a 1: 1 randomized study with two treatment groups, the propensity score is 0.5 for each individual study participant: Each patient has the probability of being assigned 0.5 to the therapy group.

In non-randomized studies, however, the propensity score of each patient is mostly unknown. The score must therefore first be estimated using the study data. The propensity score matching can therefore only take place after the complete data collection before the actual evaluation.

A logistic regression model is used to estimate the propensity score in two therapy or treatment groups. The therapy group represents the target variable. In principle, all patient characteristics measured at the start of the study (risk factors, confounders) can be taken into account as influencing variables, provided the size of the study (sample size) allows this. In particular, variables that could influence the success of the therapy should be included here. However, if more than two therapy groups are compared, a different regression model must be used.

The propensity score can then be specified using the regression model from the estimated probabilities for group membership.

### What is Propensity Score Matching?

Once the propensity scores of each patient have been estimated using suitable models, the analysis is then carried out with regard to the therapeutic effect.

In the propensity score matching procedure, each patient in the treatment group is assigned a patient from the comparison group or groups (1: 1 matching). As in case-control studies, there is also the option of 1:n Matching, being a treated patient n Partner in each peer group. A matching partner is assigned based on the propensity score: Study participants from different treatment groups with identical or only minimally deviating propensity scores are considered to be matching partners.

The study participants paired via the propensity score ultimately result in the collective that is used for further analyzes to assess the therapeutic effect. The evaluation is then carried out in analogy to case-control studies.

Patients without a matching partner are excluded from further evaluation.

### Propensity Score Matching procedure step by step

The evaluation of non-randomized studies with propensity score matching takes place in several steps. The following steps are carried out one after the other:

1. Collecting and processing the data
2. Estimation of the propensity score
3. Propensity Score Matching: Matching study participants from different treatment groups using the propensity score
4. Evaluation of the covariates and ensuring balanced groups
5. Evaluation of the therapeutic effect with procedures from case-control studies

### Advantages of Propensity Score Matching

• The descriptive description of all collectives is possible: All study participants, matched and unmatched study participants, treated and untreated
• The Propensity Score Matching approach is best suited to compensate for imbalances between treatment groups.
• The method is robust against extreme observations.
• The propensity score is not included in the analysis for assessing the therapeutic effect.
• Significantly better performance in the presence of rare events.
• Non-matched patients are also analyzed. Thus it can be clearly specified for which group the statements regarding the therapeutic effect apply.

### Disadvantages of Propensity Score Matching

• The true propensity score is always unknown in observational studies. It cannot be verified whether the calculated propensity score is correct.
• The exclusion of unmatched patients is accompanied by a loss of statistical power (test strength).
• Patients with the same propensity score may not have the same characteristics.
• Unknown or not ascertained confounders cannot be taken into account.

### Question

As an application, the Propensity Score Matching procedure will be demonstrated using a simple example. In a small, non-randomized study, 28 patients were treated with a newly developed preparation. 22 patients received a placebo for this. The primary outcome was the reduction in systolic blood pressure. Blood pressure measurements were taken before the start of the study and after the end of the treatment phase. Age and gender were recorded as population parameters.

#### Characteristic values ​​without matching

 Control group n = 22 Treatment group n = 28 Age in years 62,09 +/- 6,57 61,00 +/- 6,54 Syst. Blood pressure in mmHg at the start of the study 97,13 +/- 3,56 99,22 +/- 6,05 Number of women 11 15

### Propensity Score Matching procedure

In order to balance the groups with regard to the initial values, a propensity score matching was carried out. In the first step, the propensity score was calculated for each study participant using a logistic regression. Age, gender and systolic blood pressure at the start of the study were taken into account as influencing variables. The study participants were then matched on the basis of the predicted probabilities calculated in this way. For this purpose, a range of +/- 0.05 was taken into account as the matching interval.

After matching, 21 pairs could be formed. One study participant from the control group and 7 patients from the treatment group did not have a suitable matching partner. The following parameters result for the 21 pairs:

#### Characteristic values ​​of matched patients

 Control group n = 21 Treatment group n = 21 Age in years 61,48 +/- 6,05 61,90 +/- 5,25 Syst. Blood pressure in mmHg at the start of the study 97,48 +/- 3,24 96,83 +/- 3,92 Number of women 11 12

The excluded patients from the treatment group had very high propensity scores above 0.67. The characteristic values ​​of the excluded patients can be found in the table below.

#### Characteristic values ​​of excluded patients

 Control group n = 1 Treatment group n = 7 Age in years 75 58,28 +/- 9,43 Syst. Blood pressure in mmHg at the start of the study 89,8 106,39 +/- 5,81 Number of women 0 3

The excluded patients in the treatment group differ primarily with regard to systolic blood pressure at the start of the study. The mean value of the excluded patients is significantly higher than the mean value of the matched patients.

### Assessment of the therapeutic effect

The therapeutic effect is assessed on the basis of the change (difference) in systolic blood pressure before and after the study.

#### Therapy effect with and without matching

 Control group Treatment group T df p-value Without matching -4,95 +/- 2,25 -13,44 +/- 5,73 7,17 36,8 <0,001 With propensity score matching -5,16 +/- 2,07 -11,67 +/- 4,26 6,26 20 <0,001

### Summary

Propensity Score Matching is a powerful tool for evaluating non-randomized studies. Using the propensity score matching procedure, treatment groups can be adjusted with regard to known and measured patient characteristics. A selection bias can be counteracted in many cases. We would be happy to show you individually and tailor-made which methods can be used sensibly with your data. We are happy to support you with our advice in all phases of your study: From sample size planning to reporting. We look forward to your question. Feel free to contact us! We're glad!

### Further sources:

Rosenbaum, P. & Rubin, D. (1983). The central role of the prop. score in observational studies for causal effects.

Diamond, A. & Sekhon, J. (2013). Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies.

Propensity Score - an alternative method for analyzing the effects of therapy

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Keywords: Propensity Score Matching, Propensity Score Matching Procedure, Therapy Effect