# Response Surface Methodology Using Observational Data: A Systematic Literature Review
## 5 Synthesis and Discussion
On the other hand, observational data violate common assumptions in designed experiment data, such as treatment randomization and interfactor orthogonality, as the researcher cannot fully control each factor's level (see an editorial by [38]). Therefore, this section evaluated each reference paper to capture how they explain the condition of data before treating them as the input for RSM modeling based on different approaches in adopting data, i.e., using all observations or obtaining their subsets (Figure 9). Table 5 shows that more than 70% of papers did not mention specific raw-data conditions. Therefore, they adopted observational data directly as the input for this RSM-OD. The mathematical model and optimization technique were previously determined without evaluating data conditions because they forced the data to fit the model, whether linear or nonlinear, even ignoring the absence of randomization within data. Meanwhile, 5.19% of the papers followed the data condition as it was, which means that the RSM-OD model and optimization techniques were adjusted to adapt to the data condition, and a linear or nonlinear model was selected to give the best fit to the data. A total of 23.38% of the papers explicitly mentioned other conditions, such as factor independencies, ensuring orthogonality, and outlier removal, and considered assumptions as if they were a DoE \begin{table}
\begin{tabular}{l l} \hline \hline
**Rationales from Papers** & **Percentage** \\ \hline potential information from observational data & 33.33\% \\ flexible factor level or design space (using the data as provided) & 30.77\% \\ difficult to control process parameters & 21.79\% \\ historical data contain DoE & 5.13\% \\ conducting experiments can be highly expensive & 3.85\% \\ additional experiment points to standard DoE experiments & 2.56\% \\ avoid disruption to the production process & 2.56\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rationales for selecting RSM-OD. experiment. Some papers used orthogonality criteria for evaluating data conditions, such as variance inflation factors (for example, a paper by [43] and a data matrix subsetting used to achieve orthogonality in [3]). LRQ3: How historical data are adopted to RSM? As shown in Figure 1, the three stages of RSM form the integrated procedures for DoE-based optimization. Ideally, the RSM-OD with similar optimization purposes should also adopt these stages. The answers to LRQ2 explain how standard RSM stages with modifications adapt to observational data. Especially at the designed-experiment stage, several approaches show how the RSM-OD treats data as the input to the RSM analysis. At the DoE stage (Figure 10), two approaches were used to adopt observational data: the first type used all observations (80.52%), and the second type selected a subset (19.48%), with some required conditions. Those that used all provided observations mostly did not need to adopt a DoE. All observations were treated as an input for the RSM model, and the optimum was found based on this input. A few of these papers filtered data to remove unusual observations before RSM modeling. As for the other types, some observations were selected as the subset data for RSM modeling based on specific criteria. Mainly, the requirement of orthogonality between factors was one of the reasons for selecting observations into a subset; these criteria are required in standard RSM analysis and fulfilled by the DoE. Thus, a certain DoE-like adaptation is needed in the RSM-OD analysis, including common assumptions, such as treatment randomization and interfactor independence (orthogonality). Figure 10 shows that standard DoEs, such as factorial, optimal, and Taguchi designs, were used as references in selecting the observation subset. Figure 9: Data conditions based on the number of data involved in RSM-OD.