# Improving RNN Performance by Modelling Informative Missingness with Combined Indicators
## 1 Introduction  
Survey data from mobile applications can quickly generate large datasets suitable for deep learning. Recent literature demonstrates its potential in medical fields, in what is now referred to as'mobile health' [1; 2; 3; 4; 5]. A relevant example is the emergence of just-in-time adaptive interventions (JITAIs). These are mobile applications designed to provide users with personalized treatment, generally aimed at improving lifestyle, through surveys and sensors. JITAIs have been developed for, among others: gestational weight management [6], insomnia [7], anxiety in children [8], sedentary behavior in the elderly [9], diabetes self-management [10], and smoking cessation [11]. When surveys are included in the models that drive these applications, missing data are a persistent problem due to unanswered questions, or even entire missing surveys (Figure 1) [12; 13]. Developers could choose to make each question mandatory to avoid unanswered questions, but this would bias the results towards a group that is inclined to answer every question, or increase the number of entirely missing surveys. Furthermore, the missingness generating process must be taken into account (Table 1). This raises the question of how to deal with missing data in longitudinal surveys. A common solution to missing data in deep learning is to use indicators for missingness of the original variables [15], such that the model can learn to associate each variables' missingness with the outcome. However, this still leaves the question of how to impute the missing values in the original data. Moreover, including an indicator for each original variable doubles the input size, which may be problematic for data sets with a low number of observations relative to the number of features. Hence we propose a simple alternative for when the increase in variables is too high given the number of observations by Z-scoring, summing the missingness indicators, including the last recorded outcome in the input, and simplifying the padding of missing surveys. The golden standard in handling missing data that are MCAR or MAR is through full conditional specification (FCS), which repeatedly imputes missing values of one variable, given the others [16; 17]. Each imputation then trains a separate model, and the resulting models are pooled for inference or prediction. By drawing multiple imputations from the posterior, FCS can reflect the variance of the original variables. Furthermore, pre-existing relationships between variables can be preserved through passive imputation, resulting in greater precision [18; 19]. A downside to FCS is that it cannot impute data that are MNAR without introducing bias. Moreover, the computational cost is greatly increased by drawing the imputations and separately training models on each of them. Recent literature suggests the required number of imputations depends on the amount of missingness and can even exceed 100, which would increase the computational cost by a hundred-fold from training the individual models alone [20]. [PERSON] and [PERSON] (2017) [21] proposed training a denoising autoencoder on corrupted copies of a complete subset of the training data, minimizing the reconstruction error on the non-corrupt, non-missing subset. For purely predictive purposes, their method requires considerably less domain knowledge to use correctly compared to FCS, since the model automatically learns relationships \begin{table}
\begin{tabular}{c l l l} \hline \hline  & **MCAR** & **MAR** & **MNAR** \\ \hline Meaning & Missingness is not correlated with the outcome. & Missingness could be correlated with other variables. & Missingness is correlated with the outcome. \\ \hline Example & Question could be overlooked, survey forgotten. & Older individuals could be less inclined to state their weight. & Depressed individuals are less inclined to fill in depression survey. \\ \hline \hline \end{tabular}
\end{table}