Synthetic Health-related
Longitudinal Data with Mixed-type Variables
Generated using Diffusion Models

GANs consist of two sub-networks – a generator and a discriminator²²2WGAN (Arjovsky et al., 2017) replaces the discriminator with a critic to rate the realisticness of all inputs.. These sub-networks participate in a two-player minimax game where the goal is to find a Nash equilibrium (Goodfellow et al., 2014). The generator creates synthetic data from a random latent prior, while the discriminator aims to determine the authenticity of the generated data by comparing it to real data. Ideally, when the discriminator has optimised and the difference between real and generated data is minimized, the generator has learned to model the underlying probability distribution of the real data.

The training of GANs interleaves the updates of the two sub-networks. This interplay can result in instability in the training process (Kodali et al., 2017; Mescheder et al., 2018), which causes fluctuations in the loss over time (Thanh-Tung et al., 2019), as well as mode collapse (Goodfellow, 2016), where the generator outputs the same sample repeatedly, reducing diversity in the generated data. To mitigate these challenges, prior studies have proposed several implementations to improve the stability and convergence of GAN training, including modifications to the network architecture (Radford et al., 2015), learning objectives (Arjovsky et al., 2017; Gulrajani et al., 2017), and auxiliary experimental setups (Salimans et al., 2016; Sønderby et al., 2016). Additionally, researchers have proposed techniques to mitigate mode collapse by measuring the diversity of the generated data through features learned within the GAN sub-networks. This has been achieved through methods such as minibatch discrimination (Salimans et al., 2016) and moment matching (Li et al., 2017).

There are also many theoretical work on GANs that emphasises the optimality on the minima (Nagarajan & Kolter, 2017; Mescheder et al., 2017; 2018) as well as the convexity of the learning objectives (Kodali et al., 2017). One approach enforces Lipschitz constraints on the discriminator network (Gulrajani et al., 2017; Liu et al., 2019); and another line of research has focused on improving the design of the discriminator or using multiple discriminators (Srivastava et al., 2017; Mordido et al., 2020; Thanh-Tung & Tran, 2020) to reduce the risk of catastrophic forgetting (McCloskey & Cohen, 1989; Kuo et al., 2021) – the abrupt lost of learnt knowledge by repetitive incremental update – in the discriminator to mitigate mode collapse.

While GANs have made significant advancements over the years, they still face certain limitations in the medical domain. Despite extensive research, GANs have primarily been limited to synthesising one type of data. For example, Choi et al. (2017) (i.e., MedGAN), Xie et al. (2018), and Camino et al. (2018) only support the generation of discrete variables; while Beaulieu-Jones et al. (2019) only support numeric variable simulations. Despite recent progress, GAN-generated datasets are largely static in nature (Park et al., 2018; Lu et al., 2019; Yoon et al., 2020; Walia et al., 2020) and may only be suitable for developing predictive algorithms. There is a scarcity of literature on GAN-generated datasets suitable for RL agents (Li et al., 2021; Kuo et al., 2022b), and hence there remains a need for further research in this area to address these limitations.

MedGAN (Choi et al., 2017) has gained popularity in clinical research and is frequently used as a baseline model (Baowaly et al., 2019a; b; Torfi & Fox, 2020). Despite its popularity, a study by Goncalves et al. (2020) found that MedGAN failed to accurately represent multivariate categorical medical data as it performed unfavourably on the log-cluster (Woo et al., 2009) metric.

Similarly, the Health Gym GAN (Kuo et al., 2022b), capable of generating mixed-type time-series clinical data, was found to be susceptible to mode collapse. In an extended study by the same panel of authors (Kuo et al., 2022a), they found that mode collapse negatively impacted the utility of the synthetic dataset because patients of minority ethnicity could be neglected during the synthesis procedure. To mitigate this issue, the authors stored features from the real data in an external buffer during training and replay them to the generator during synthesis. Marchesi et al. (2022) also found that by using a conditional architecture, the Health Gym GAN could synthesise data that captured a higher level of detail in the real data feature space.

In conclusion, applications of GANs in the medical domain are limited by mode collapse and training instability. Moreover, Kuo et al. (2022a) reported that previous solutions for preventing mode collapse in computer vision (Larsen et al., 2016; Salimans et al., 2016; Li et al., 2017; Mangalam & Garg, 2021) prove ineffective for mixed-type time-series clinical data. As an alternative, DPMs may circumvent these limitations, as they are not known for mode collapse and training instability.

The forward diffusion process adds Gaussian noise to a sample from $q(x)$ in $T$ time-steps,

where the magnitude of the noise is controlled by a pre-defined variance schedule $\{\beta_{t}\in(0,1)\}_{t=1}^{T}$. This results in a gradual loss of distinguishable features in the sample as $t$ increases. Furthermore, using properties of the Gaussian distribution, we can rewrite

where $\alpha_{t}=1-\beta_{t}$ and $\bar{\alpha}_{t}=\prod_{s=1}^{t}\alpha_{s}$.

Then, a reverse diffusion process removes noises to synthesise a data as if it were sampled from the real data distribution $q(x)$. A model $p_{\theta}$ with weights $\theta$ is learned to approximate the conditional probabilities (via mean $\mu$ and covariance $\Sigma$) between $q(x)$ and the Gaussian noise input $x_{T}$

The forward process is tractable when conditioned on $x_{0}$:

and Ho et al. (2020) showed a DPM should learn to configure

to predict the added noise $\epsilon$ in $x_{t}$ at time $t$ in Equation (1) via approximating $\epsilon_{\theta}(x_{t},t)$.

The perturbed inputs from Equation (2) can be rewritten as

Combined with the $\epsilon_{\theta}(x_{t},t)$ in Equation (6), Ho et al. (2020) further showed that optimising

is equivalent³³3 The equivalent loss is actually $\mathbb{E}_{x_{0},\epsilon}\left[\frac{\beta_{t}^{2}}{2\sigma_{t}^{2}\alpha(1-\bar{\alpha}_{t})}\lVert\epsilon-\epsilon_{\theta}\left(\sqrt{\bar{\alpha}_{t}}x_{0}+\sqrt{1-\bar{\alpha}_{t}}\epsilon,t\right)\lVert^{2}\right]$ with the additional coefficients. However Ho et al. (2020) noted that it was beneficial to train without the additional coefficients. to optimising the negative log-likelihood using the variational lower bound.

To create novel data, we followed Song & Ermon (2019)’s score-based generative method using Langevin dynamics with modifications on Equation (6), sampling $\mathbf{z}\sim\mathcal{N}(\mathbf{0},\mathbf{I})$ where $\sigma^{2}_{t}=\beta_{t}$ and

We provide supporting pseudo-codes that outline the structure of our proposed method in Algorithms 1 and 2. Details within the pseudo-codes will be further discussed in subsequent sections.

For each iteration, we draw ground truth data $\xi_{0}$ from the set of clinical datasets (see Section 4), and reformulate it to $x_{0}$ (to be addressed below). We also select a noise level $t$ and its corresponding strength of perturbation $\beta_{t}$ to introduce corruption to $x_{0}$ following Equation (2) to acquire the noisy inputs $x_{t}$. To estimate the manually injected noise $\epsilon$ of Equation (7), we feed $x_{t}$ into a tailored implementation of U-Net (Ronneberger et al., 2015), which serves as our backbone network for the denoising operations. The output of the U-Net network $\epsilon_{\theta}$ is the predicted estimation for $\epsilon$.

Our datasets encompass numeric, binary, and categorical variables. Hence, we elaborate on the data formulation prior to presenting it to the model. The ground truth data is partitioned as
$\hbox{\pagecolor{blue!25}$\xi_{0}$}=\hbox{\pagecolor{blue!10}$\xi_{0,\text{[num]}}$}\oplus\hbox{\pagecolor{blue!10}$\xi_{0,\text{[alt]}}$}$, with the numeric subset $\xi_{0,\text{[num]}}$ and the non-numeric subset $\xi_{0,\text{[alt]}}$. We transform each numeric feature in $\xi_{0,\text{[num]}}$ to the range $\in[0,1]$ and derive $x_{0,\text{[num]}}$. Each non-numeric variable $\xi_{0,\text{[alt]}}^{(i)}$ is converted into a list of one-hot vectors where the observed class is assigned a value of 1 and the others a value of 0. Here are some examples:

• •

  For the binary variable Gender = Female, we have
  $\texttt{Gender}=\begin{bmatrix}\texttt{Female}\\ \texttt{Male}\end{bmatrix}=\begin{bmatrix}1\\ 0\end{bmatrix}$, and

• •

  for the categorical variable Ethnicity = African, we have
  $\texttt{Ethnicity}=\begin{bmatrix}\texttt{Asian}\\ \texttt{African}\\ \texttt{Caucasian}\\ \texttt{Other}\end{bmatrix}=\begin{bmatrix}0\\ 1\\ 0\\ 0\end{bmatrix}$.

We denote the aggregate of all one-hot vectors as $\hbox{\pagecolor{purple!10}$x_{0,\text{[alt]}}$}=\bigcup_{i}\text{OneHot}\left(\hbox{\pagecolor{blue!10}$\xi_{0,\text{[alt]}}^{(i)}$}\right)$; and that
$\hbox{\pagecolor{purple!25}$x_{0}$}=\hbox{\pagecolor{purple!10}$x_{0,\text{[num]}}$}\oplus\hbox{\pagecolor{purple!10}$x_{0,\text{[alt]}}$}$. Embeddings (Landauer et al., 1998; Mikolov et al., 2013; Mottini et al., 2018) are not necessary in our framework. The forward diffusion process of the DPM (refer to Equation (7)) directly applies noise to the one-hot vectors.

At test time, we randomly sample a noisy input $x_{T}$ from a Gaussian distribution. Then, we iteratively estimate the corruption $\epsilon_{\theta}(x_{t},t)$ at step $t$ using our U-Net backbone to generate a less noisy $x_{t-1}$ as per Equation (9). Once⁴⁴4Similar to Ho et al. (2020), we used $x_{0}$ and $\xi_{0}$ for both the clean inputs and the denoised, reconstructed output; the terms should thus be used in context of before and after the reverse diffusion process. we reach the allegedly clean and novel data $x_{0}$, we compartmentalise it into $x_{0,\text{[num]}}$ and $x_{0,\text{[alt]}}$ to reverse the transformation in $x_{0,\text{[num]}}$, resulting in $\xi_{0,\text{[num]}}$. Next, we employ softmax to recover the non-numeric variables such that $\hbox{\pagecolor{blue!10}$\xi_{0,\text{[alt]}}$}=\bigcup_{i}\text{Softmax}\left(\hbox{\pagecolor{purple!10}$x_{0,\text{[alt]}}^{(i)}$}\right)$.

The dimensionality of the noisy input is $x_{t}\in\mathbb{R}^{\mathfrak{B}\times 1\times\mathfrak{L}\times\mathfrak{N}}$, where $\mathfrak{B}$ corresponds to the batch size, $\mathfrak{L}$ denotes the length of the time-series, and that there is 1 feature channel for all the $\mathfrak{N}$ variables. In Section 4, it was mentioned that all acute hypotension data possess a fixed sequence with a length of 48 units, hence $\mathfrak{L}_{\text{hypotension}}=48$. On the other hand, the HIV data has variable lengths and we utilise zero-padding to bring all the data to a pre-defined maximal length of $\mathfrak{L}_{\text{HIV}}=100$. This setup hence obviates the need for curriculum learning (Bengio et al., 2009) to enable training.

Moreover, inferring the size $\mathfrak{N}$ is a straightforward task, as it solely involves concatenating the numeric and one-hot representations of the binary and categorical variables in $x_{t}$. To illustrate, consider the ART for HIV dataset, whose variable specifications are provided in Table 3. By summing up the corresponding levels of every variable (with 1 for numeric variables), we obtain that
     $\mathfrak{N}_{\text{HIV}}=\text{sum}(\{1,1,1,2,4,6,4,4,6,2,2,2,2\})=37$.
Likewise, we deduce that $\mathfrak{N}_{\text{hypotension}}=54$ as per its respective specifications in Table 2.

U-Net (Ronneberger et al., 2015) is a convolutional neural network (CNN) architecture originally developed for medical image segmentation. As shown in Figure 2, the architecture has many details. The down-sampling (Zeiler & Fergus, 2014) compartment extracts high-level features from noisy data, while skip connections (Venables & Ripley, 2013) maintain fine-grained details and spatial information. The up-sampling compartment estimates noise for reconstructing clean data, leveraging localised features via the skip connections. U-Net is especially useful in denoising spatially correlated noise of varying intensities; and has been employed in various DPM applications (Saharia et al., 2022; Ho et al., 2022; Li et al., 2022).

Capturing both individual variable fidelity and correlations is crucial for realistic synthetic EHR. Previous studies in GANs used auxiliary loss functions, such as separate encoders and matching loss (Li et al., 2021), or assessed real data correlation before training (Kuo et al., 2022b). However, these approaches synthesise data per iteration, making them computationally costly. Including such losses in DPM is prohibitively expensive due to DPM’s slow sampling nature (Xiao et al., 2022).

To circumvent the iterative denoising in Equation (9), we estimate a one-step reconstruction loss

We utilise the predicted noise $\epsilon_{\theta}$ from the U-Net to replace the actual noise $\epsilon$, and apply a one-step reverse process to approximate the clean data $x_{0}$ using $\hat{x}_{0}$. This is analogous to taking a large step on the vector field (Song & Ermon, 2019; Song et al., 2021b), and may result in overshooting during the reconstruction dynamics. Hence, the use of $\hat{x}_{0}$ is restricted solely to our auxiliary loss.

We introduce a second auxiliary loss function to our model, defined as

At each iteration, we construct two random matrices $\mathcal{U}_{1}$ and $\mathcal{U}_{2}$ that do not require training. These matrices are used to project the clean data $x_{0}$ and its reconstructed counterpart $\hat{x}_{0}$ to a latent space, and the difference between them is minimised. This approach is inspired by Salimans et al. (2016)’s mini-batch discrimination technique and aims to minimise the variability of the variable combinations in a randomly projected feature space.

Hyper-parameters for the U-Net
Following Section 5.2.1-d), we choose to linearly project the $\mathfrak{N}$ variables in the input to a latent space of dimensionality 256. After this preliminary step, we employ our U-Net for denoising.

As detailed in Section 5.2.1-b), we adopt 3 distinct resolution levels. More specifically, resolution level 1 maintains the initial length of the noisy sequence for all time-series data, whereas the succeeding resolution levels condense the sequences while augmenting feature dimensions. In resolution level 2, all time-series have feature size 10, and in resolution level 3, all time-series possess feature size 20, regardless of the underlying dataset. However, the alteration in the length of the time-series depended on the dataset. For acute hypotension, resolution level 1 sequences span 48 time steps, which are subsequently reduced to 12 and 3 in resolution levels 2 and 3, respectively. Likewise in ART for HIV, they change from length 100 to 10 and then 3.

Following the previous descriptions, the 1-D CNNs employed in the blocks of Section 5.2.1-c) possess feature dimensions of 10 and 20 at resolution levels 1 and 2 respectively. Whereas the features in the bottleneck of resolution level 3 reduces from 20 to 10, subsequently reverting to 20.

An example using acute hypotension
The input data $x_{t}\in\mathbb{R}^{\mathfrak{B}\times 1\times 48\times 37}$ comprises a sequence length $\mathfrak{L}$ of 48 and $\mathfrak{N}$ variables of 37 (see Section 5.1). We project and contruct the latent structure of the noisy data in $\mathbb{R}^{\mathfrak{B}\times 1\times 48\times 256}$. In the subsequent use of U-Net, the dimensionality transforms to $\mathbb{R}^{\mathfrak{B}\times 10\times 12\times 256}$ in resolution level 2 and then $\mathbb{R}^{\mathfrak{B}\times 20\times 3\times 256}$ in resolution level 3.

Hyper-parameters for the DPM & Optimisation
We set the maximum perturbation at $\beta_{0}=0.01$ and the minimum at $\beta_{T}=1\times 10^{-4}$ (see Equation (1)) across both datasets. However, we use $T=1000$ for acute hypotension and $T=500$ for ART for HIV. The intermediate perturbations $\beta_{t}$ are distributed uniformly across the $T$ levels. As previously stated in Section 5.2.1-a), the denoising procedure of our DPM is informed by the noise level $t$. This information is conveyed to the U-Net architecture as a Transformer sinusoidal position embedding, featuring an embedding dimensionality of $100$.

Our DPMs are updated using the Adam optimiser (Kingma & Ba, 2014) with learning rate $1\times 10^{-3}$. We employ a batch size of $128$ for the acute hypotension and ART for HIV. The DPMs are trained for $5000$ epochs for acute hypotension and $3000$ epochs for ART for HIV. In addition, the losses are weighted at a ratio of $1:20:10$ for $\mathcal{L}_{\text{noise}}$, $\mathcal{L}_{\text{Recon}_{1}}$, and $\mathcal{L}_{\text{Recon}_{2}}$ (see Section 5.3), respectively.

We put forth five desiderata:

• •

  Section 6.2.1: that all generated variables to exhibit individual realism;

• •

  Section 6.2.2: that the collective realism of all variables hold across time;

• •

  Section 6.2.3: that there exists a sufficiently high level of diversity in variables;

• •

  Section 6.2.4: that our synthetic datasets ensure patient privacy; and

• •

  Section 6.2.5: that our datasets can function as a substitute for a genuine dataset in
                    downstream model construction.

Actute Hypotension
The KDE plots⁶⁶6The kernel density estimation uses Gaussian kernels to estimate the probability density function of a continuous variable. Thus, the KDE function can potentially produce tails beyond the range of the data. and barplots for the individual variable comparisons are presented in Figure 4. The grey bars represent the real variables from $\mathfrak{D}_{\text{real}}$, while the respective pink and blue bars in subplots 4(a) and 4(b) depict the synthetic variables in $\mathfrak{D}_{\text{null}}$ and $\mathfrak{D}_{\text{alt}}$, generated using Kuo et al. (2022b)’s Health Gym GAN and our DPM. Overall, the distributions in both subplots are comparable to their real counterparts in $\mathfrak{D}_{\text{real}}$. We observed that DPM captured the multi-modal nature of clinical variables better than GAN (e.g., PaO₂ and Lactic Acid), but we also found that our DPM generated more instances of less common classes in FiO₂.

The synthetic variables in our DPM-generated hypotension dataset $\mathfrak{D}_{\text{alt}}$ are representative of their real counterparts in $\mathfrak{D}_{\text{real}}$. The statistics in Table 4 in Appendix B revealed that all variables passed the three sigma rule test and are reliable. Most variables passed the KS test and thus captured detailed information in the real distributions. The minority of variables that failed the KS test still passed the t-test and F-test, demonstrating that both the mean and the variance are captured and only missing the extreme details in the cumulative distribution function.

The KL divergences in Table 6 in Appendix B indicated that most variables simulated by the DPM are on-par with those generated using GAN. Only the KL divergence of FiO₂ was much larger in $\mathfrak{D}_{\text{alt}}$, consistent with the previous finding that our DPM simulated less common classes for FiO₂.

ART for HIV
Refer to all results in Appendix B. In Figure 8, we observed that the variable distributions in our DPM-generated $\mathfrak{D}_{\text{alt}}$ capture the features of the real variables more accurately than those in $\mathfrak{D}_{\text{null}}$ generated using GAN in Kuo et al. (2022b). The statistical tests reported in Table 5 indicated that while all DPM-simulated variables are reliable, only VL failed the KS test. However, VL still passed the three sigma rule test; and that the KL divergences in Table 7 revealed that the quality of DPM-simulated distributions are on-par or superior to those generated using GAN.

Acute Hypotension
The correlations for acute hypotension are depicted in Figure 5. All panels on the left correspond to the synthetic dataset $\mathfrak{D}_{\text{null}}$ generated by Kuo et al. (2022b)’s GAN; the middle panels represent our DPM-simulated dataset $\mathfrak{D}_{\text{alt}}$; and all panels on the right correspond to the ground truth dataset $\mathfrak{D}_{\text{real}}$. Furthermore, Figure 5(a) shows the static correlations, Figure 5(b) illustrates the dynamic correlations in trends, and Figure 5(c) presents the dynamic correlations in cycles.

Figure 5 indicates that the correlations in our DPM-simulated dataset (located in the middle panels) exhibit a stronger resemblance to their real counterparts (located in the right panels) than those generated by GAN (located in the left panels). This applied to all three types of correlations considered, including static correlations as well as two types of dynamic correlations.

ART for HIV
Refer to all results in Appendix B. The correlations are shown in Figure 9. Both Kuo et al. (2022b)’s $\mathfrak{D}_{\text{null}}$ and our DPM-simulated $\mathfrak{D}_{\text{alt}}$ capture the ground truth correlations. However, we noted that our dataset $\mathfrak{D}_{\text{alt}}$ exhibits a closer alignment with the real dataset $\mathfrak{D}_{\text{real}}$; while the correlations in $\mathfrak{D}_{\text{null}}$ tend to be exaggerated for both the static and dynamic correlations.

We calculated the log-cluster metric ($U$) and category coverage (CAT) to quantitatively assess the similarity between the latent structure of synthetic datasets and their real counterparts. The outcomes are summarised in Table 1. The CAT score showed that all combinations of binary and categorical variables are present in our DPM-simulated dataset $\mathfrak{D}_{\text{alt}}$; but such is not the case for not all combinations in the GAN-generated dataset $\mathfrak{D}_{\text{null}}$ produced by Kuo et al. (2022b). Moreover, the $U$ scores indicated that the latent structure embedded in our $\mathfrak{D}_{\text{alt}}$ is more realistic than that in $\mathfrak{D}_{\text{null}}$.

The metrics in Table 1 can be more effectively contextualised through the qualitative analyses presented in Figure 6. For the patient demographics in the ART for HIV, we combined patient Gender and Ethnicity. The colours grey, pink, and blue correspond to the ground truth dataset $\mathfrak{D}_{\text{real}}$, Kuo et al. (2022b)’s $\mathfrak{D}_{\text{null}}$, and our $\mathfrak{D}_{\text{alt}}$, respectively. Note, we conducted this analysis only for ART for HIV because the acute hypotension dataset does not include variables relating patient demographics.

We found that our $\mathfrak{D}_{\text{alt}}$ covers all combinations of demographic features present in the real dataset; whereas this is not the case for Kuo et al. (2022b)’s $\mathfrak{D}_{\text{null}}$. This discrepancy suggests that mode collapse (as discussed in Section 2) may be occurring in GANs and that while they can capture information relating distribution and correlation, synthetic data diversity is low and it remains challenging for GANs to accurately represent the complex, multi-faceted nature of clinical EHR data.

Acute Hypotension
The variables in the hypotension dataset (see Table 2 in Appendix A) are all related to the patient’s bio-physiological states and do not contain any sensitive information that may reveal individuals’ identities. Consequently, we only tested Euclidean distances and did not assess the disclosure risk. We found that records in our DPM-simulated synthetic dataset $\mathfrak{D}_{\text{alt}}$ matched none of those in the real hypotension dataset $\mathfrak{D}_{\text{real}}$. The minimum Euclidean distance between any synthetic record and any real record was 2.79 ($>0$), indicating that no data was leaked into the synthetic dataset.

ART for HIV
Likewise, the minimum Euclidean distance between any real and synthetic HIV record was 0.09 ($>0$), thus no real records was leaked into our synthetic dataset $\mathfrak{D}_{\text{alt}}$. The HIV variables (see Table 3 in Appendix A) contain the quasi-identifiers of Gender and Ethnicity. We combined these two variables to form distinct equivalence classes (e.g., male Asians and female Caucasians). The risk of a successful synthetic-to-real attack was estimated to be 0.076%. This risk is also much lower than the standard threshold of 9% (see Section 6.2.4), signifying that our synthetic HIV dataset $\mathfrak{D}_{\text{alt}}$ can be released with minimal risk of sensitive information disclosure.

Acute Hypotension
After training RL agents to suggest clinical treatments, we used heatmaps to visualize their action patterns. Each tile on the heatmap represents a unique action and its associated number indicates the frequency of that action as a proportion of all actions taken.

We depicted the action patterns of the RL agents for acute hypotension in Figure 7. The action space is spanned by Vasopressor and Fluid Boluses. Subplot (a) exhibits the actions taken by an RL agent trained on the real dataset $\mathfrak{D}_{\text{real}}$; subplots (b) and (c) respectively display the actions taken by RL agents trained on Kuo et al. (2022b)’s synthetic dataset $\mathfrak{D}_{\text{null}}$ and our DPM-simulated $\mathfrak{D}_{\text{alt}}$. The heatmap in subplot (c) shows a better alignment with its counterpart in subplot (a), indicating that the RL agent trained on our $\mathfrak{D}_{\text{alt}}$ suggested actions that were more similar to those suggested by the RL agent trained on $\mathfrak{D}_{\text{real}}$.

ART for HIV
Refer to all results in Appendix B. For ART for HIV, we also found that our DPM-simulated dataset for $\mathfrak{D}_{\text{alt}}$ has a higher utility than the GAN-generated $\mathfrak{D}_{\text{null}}$ by Kuo et al. (2022b). Figure 10 shows that when the action space is spanned by Comp. NNRTI and Base Drug Combo, the RL agent trained on $\mathfrak{D}_{\text{null}}$ suggested the treatment of (NVP, DRV + FTC + TDF) for 48.97% of all actions. This suggests that the GAN model used to generate $\mathfrak{D}_{\text{null}}$ experienced mode collapse, thus creating an excessive number of synthetic records with similar attributes in $\mathfrak{D}_{\text{null}}$. Conversely, we attribute the higher utility in the DPM-simulated $\mathfrak{D}_{\text{alt}}$ to the higher robustness of DPM against mode collapse.