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Objectives: To develop and validate a prognostic model to predict deterioration in health-related quality of life (dHRQoL) in older general practice patients with at least one chronic condition and one chronic prescription. Study Design and Setting: We used individual participant data from five cluster-randomized trials conducted in the Netherlands and Germany to predict dHRQoL, defined as a decrease in EQ-5D-3 L index score of ≥5% after 6-month follow-up in logistic regression models with stratified intercepts to account for between-study heterogeneity. The model was validated internally and by using internal–external cross-validation (IECV). Results: In 3,582 patients with complete data, of whom 1,046 (29.2%) showed deterioration in HRQoL, and 12/87 variables were selected that were related to single (chronic) conditions, inappropriate medication, medication underuse, functional status, well-being, and HRQoL. Bootstrap internal validation showed a C-statistic of 0.71 (0.69 to 0.72) and a calibration slope of 0.88 (0.78 to 0.98). In the IECV loop, the model provided a pooled C-statistic of 0.68 (0.65 to 0.70) and calibration-in-the-large of 0 (−0.13 to 0.13). HRQoL/functionality had the strongest prognostic value. Conclusion: The model performed well in terms of discrimination, calibration, and generalizability and might help clinicians identify older patients at high risk of dHRQoL.

Summary In this article, we first review the literature on dealing with missing values on a covariate in randomized studies and summarize what has been done and what is lacking to date. We then investigate the situation with a continuous outcome and a missing binary covariate in more details through simulations, comparing the performance of multiple imputation (MI) with various simple alternative methods. This is finally extended to the case of time‐to‐event outcome. The simulations consider five different missingness scenarios: missing completely at random (MCAR), at random (MAR) with missingness depending only on the treatment, and missing not at random (MNAR) with missingness depending on the covariate itself (MNAR1), missingness depending on both the treatment and covariate (MNAR2), and missingness depending on the treatment, covariate and their interaction (MNAR3). Here, we distinguish two different cases: (1) when the covariate is measured before randomization (best practice), where only MCAR and MNAR1 are plausible, and (2) when it is measured after randomization but before treatment (which sometimes occurs in nonpharmaceutical research), where the other three missingness mechanisms can also occur. The proposed methods are compared based on the treatment effect estimate and its standard error. The simulation results suggest that the patterns of results are very similar for all missingness scenarios in case (1) and also in case (2) except for MNAR3. Furthermore, in each scenario for continuous outcome, there is at least one simple method that performs at least as well as MI, while for time‐to‐event outcome MI is best.

SUMMARY Missing data are a common problem for both the construction and implementation of a prediction algorithm. Pattern submodels (PS)—a set of submodels for every missing data pattern that are fit using only data from that pattern—are a computationally efficient remedy for handling missing data at both stages. Here, we show that PS (i) retain their predictive accuracy even when the missing data mechanism is not missing at random (MAR) and (ii) yield an algorithm that is the most predictive among all standard missing data strategies. Specifically, we show that the expected loss of a forecasting algorithm is minimized when each pattern-specific loss is minimized. Simulations and a re-analysis of the SUPPORT study confirms that PS generally outperforms zero-imputation, mean-imputation, complete-case analysis, complete-case submodels, and even multiple imputation (MI). The degree of improvement is highly dependent on the missingness mechanism and the effect size of missing predictors. When the data are MAR, MI can yield comparable forecasting performance but generally requires a larger computational cost. We also show that predictions from the PS approach are equivalent to the limiting predictions for a MI procedure that is dependent on missingness indicators (the MIMI model). The focus of this article is on out-of-sample prediction; implications for model inference are only briefly explored.