Population health studies increasingly collect longitudinal, patient-reported symptom data via mobile devices, offering unique insights into experiences outside clinical settings, such as pain, fatigue or mood. However, such data present challenges due to ordinal measurement scales, irregular sampling and temporal autocorrelation.

This paper introduces two novel summary measures for analysing ordinal outcomes: (1) the mean absolute deviation from the median (Madm) for cross-sectional analyses and (2) the mean absolute deviation from expectation (Made) for longitudinal data. The latter is based on a latent cumulative model with penalized splines, enabling smooth transitions between irregular time points while accounting for the ordinal nature of the data. Unlike black-box machine learning approaches, this method is interpretable, computationally efficient and easy to implement in standard statistical software.

Through simulations, we demonstrate that the proposed measures outperform standard methods when the assumptions of normality or stationarity are violated. Application to real-world data from a national smartphone study, Cloudy with a Chance of Pain, highlights the utility of these measures in characterising symptom variability and trends over time.

The methods developed here provide intuitive tools for analysing patient-reported outcomes in longitudinal studies, with potential applications in prediction modelling, causal discovery and evaluation of interventions.

WGD has received consultancy fees from Bayer Pharmaceuticals and Google, unrelated to this study. The authors have no other relevant financial or non-financial interests to disclose.

This study was supported by the Centre for Epidemiology Versus Arthritis (grant reference 21744). 'Cloudy with a Chance of Pain' was funded by Versus Arthritis (grant reference 21225).

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

Yes

The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

Ethical approval was obtained from the University of Manchester Research Ethics Committee (ref: ethics/15522) and from the NHS IRAS (ref: 23/NW/0716). Participants were required to provide electronic consent for study inclusion.

I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.

Yes

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

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I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.

Yes

Data produced in the present study are available upon reasonable request.