A Comparison of Matching and Weighting Methods for Causal Inference Based on Routine Health Insurance Data, or: What to do If an RCT is Impossible

Abstract

Due to a multitude of reasons Randomized Control Trials on the basis of so-called “routine data” provided by insurance companies cannot be conducted. Therefore the estimation of “causal effects” for any kind of treatment is hampered since systematic bias due to specific selection processes must be suspected. The basic problem of counterfactual, which is to evaluate the difference between two potential outcomes for the same unit, is discussed. The focus lies on the comparison of the performance of different approaches to control for systematic differences between treatment and control group. These strategies are all based on propensity scores, namely matching or pruning, IPTW (inverse probability treatment weighting) and entropy balancing. Methods to evaluate these strategies are presented. A logit model is employed with 87 predictors to estimate the propensity score or to estimate the entropy balancing weights. All analyses are restricted to estimate the ATT (Average Treatment Effect for the Treated) Exemplary data come from a prospective controlled intervention-study with two measurement occasions. Data contain 35 857 chronically ill insurants with diabetes, congestive heart failure, arteriosclerosis, coronary heart disease or hypertension of one German sickness fund. The intervention group was offered an individual telephone coaching to improve health behavior and slow down disease progression while the control group received treatment as usual. Randomization took place before the insurants’ consent to participate was obtained so assumptions of an RCT are violated. A weighted mixture model (difference-in-difference) as the causal model of interest is employed to estimate treatment effects in terms of costs distinguishing the categories outpatient costs, medication costs, and total costs. It is shown that entropy balancing performs best with respect to balancing treatment and control group at baseline for the first three moments of all 87 predictors. This will result in least biased estimates of the treatment effect.

Zusammenfassung

Aus verschiedensten Gründen kann auf der Basis sogenannter „Routine-Daten“ von Versicherungsgesellschaften ein RCT nicht durchgeführt werden. Daher ist die Schätzung „kausaler“ Effekte unmöglich, da mit systematischer Verzerrung durch spezifische Selektionsprozesse gerechnet werden muss. Die grundlegenden Probleme des „Kontrafaktischen“, also die Beurteilung der Differenz zwischen zwei potentiellen Ergebnissen an derselben Beobachtungseinheit, werden abgehandelt. Der Fokus dieser Studie liegt im Vergleich von methodischen Zugängen die Differenzen zwischen Versuchs- und Kontrollgruppe zu kontrollieren. Alle Methoden basieren auf dem Propensity score, nämlich „Matchig“ bzw. „Pruning“, „Inverse Probability Weighting“ und „Entropy Balancing“. Methoden der Evaluation dieser Strategien werden dargestellt. Zur Balanzierung und/oder Schätzung des Propensity Scores dient ein Logit Modell mit 87 Prädiktoren. Alle Analysen beschränken sich auf die Schätzung des ATT (Average Treatment Effect for the Treated) Als Beispiel dienen Daten aus einer prospektiv kontrollierten Intervention-Studie mit 2 Messzeitpunkten. Die Daten beinhalten 35 857 chronisch kranke Versicherte mit Diabetes, Herzinsuffizienz, Arteriosklerose, Koronarer Herzkrankheit und Hypertonie. Der Interventionsgruppe wurde ein individuelles Telephoncoaching zur Verbesserung des Gesundheitsverhaltens und zur Verlangsamung des Krankheitsfortschrittes angeboten, wohingegen die Kontrollgruppe konventionelle Therapien bekam. Die Randomisierung wurde vor dem Einholen der Teilnahmezustimmung durchgeführt, wodurch die Vorrausetzungen eines RCT verletzt sind. Zur Schätzung des Behandlungseffektes mit Rücksicht auf Kosten wurde ein gewichtetes Mixture Modell (Differenz-in-Differenz) eingesetzt. Dabei wurde zwischen ambulanten Kosten, Medikationskosten und Gesamtkosten differenziert. Es kann gezeigt werden, dass das Verfahren des „Entropy Balancing“ die Verteilung der Prädiktoren zur baseline mit Rücksicht auf die ersten drei Momente am besten balanziert und damit die wohl am wenigsten verzerrten Behandlungseffekte liefert.

Key words

matching - weighting - Routine data - RCT - entropy balancing

Schlüsselwörter

propensity score - gewichtung - routine daten - RCT - entropy balancing

¹ In the original text D instead of T and P instead of ρ – changed here to achieve notational consistency

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