19  Reporting

19.1 Analysis Information

Many reporting guideline already exists about what to report in a propensity score analysis. Most of the reporting guideline should be applicable in the hdPS context as well. On top of those, we also need to consider reporting the following information about hdPS for transparency.

(Karim et al. 2022; Simoneau et al. 2022)

19.2 Information about hdPS

Information	Description	Our example
Proxy data dimensions	The number of data dimensions (p) used.	p = 1 as only one proxy data dimension (dx) was available from medication usage
What was done to remove proxies that are problematic	Usually proxies of outcome, exposure as well as those identified as IV or mediator or collider are discarded.	obesity and diabetes related codes removed
Proxy feature parameters	The parameters used to select proxy features, including granularity [g], prevalence filter [n], and the minimum number of patients [m]	g = 3, n = 200, m = 20. This resulted in 126 empirical covariates.
Recurrence parameters	How many recurrence variables per code [r] and the covariate assessment period [CAP]	r = 3, CAP = 30 days. This resulted in 143 distinct recurrence covariates.
Prioritization process	The process used to prioritize proxy features, such as machine learning (ML), Bross, or hybrid methods	We used all of these, but used Bross formula for hdPS to calculate absolute log of the multiplicative bias, and then ranked based on magnitude to select / prioritize recurrence covariates.
Selected proxies	The number of proxies selected (k) for the model	k = 100 for the hdPS
Software	The software used to perform the analysis	R: autoCovariateSelection package

(Rassen et al. 2023; Tazare et al. 2022)

19.3 Diagnostics

Information	Description	Our example
Diagnostics used to assess the model	Standardized mean differences (SMD)	Within 0.1 in hdPS analysis
	Weight (IPW) summary assessment	Somewhat reasonable (maximum approximately 54) within hdPS analysis
	Comparison of propensity score distributions between each exposure group	Overlapping (common support) does not seem to be an issue.
	Assess distribution of absolute log bias	Most bias multiplier values are close to null (0), only a few values seem to deviate from null.
	Comparison with regular propensity score	Estimates slightly towards null

19.4 Sensitivity analysis

Information	Description	Our example
Sensitivity analysis	Varying the number of selected proxies [k].	OR estimates stabilizes around 1.5, shows variability below k = 50 and above 110
Sensitivity analysis	Varying the prevalence filter [n].	OR estimates stabilizes around 1.5 for above n = 60.

Karim, Mohammad Ehsanul, Fabio Pellegrini, Robert W Platt, Gabrielle Simoneau, Julie Rouette, and Carl de Moor. 2022. “The Use and Quality of Reporting of Propensity Score Methods in Multiple Sclerosis Literature: A Review.” Multiple Sclerosis Journal 28 (9): 1317–23.

Rassen, Jeremy A, Patrick Blin, Sebastian Kloss, Romain S Neugebauer, Robert W Platt, Anton Pottegård, Sebastian Schneeweiss, and Sengwee Toh. 2023. “High-Dimensional Propensity Scores for Empirical Covariate Selection in Secondary Database Studies: Planning, Implementation, and Reporting.” Pharmacoepidemiology and Drug Safety 32 (2): 93–106.

Simoneau, Gabrielle, Fabio Pellegrini, Thomas PA Debray, Julie Rouette, Johanna Muñoz, Robert W Platt, John Petkau, et al. 2022. “Recommendations for the Use of Propensity Score Methods in Multiple Sclerosis Research.” Multiple Sclerosis Journal 28 (9): 1467–80.

Tazare, John, Richard Wyss, Jessica M Franklin, Liam Smeeth, Stephen JW Evans, Shirley V Wang, Sebastian Schneeweiss, Ian J Douglas, Joshua J Gagne, and Elizabeth J Williamson. 2022. “Transparency of High-Dimensional Propensity Score Analyses: Guidance for Diagnostics and Reporting.” Pharmacoepidemiology and Drug Safety 31 (4): 411–23.