Chances are that N = 10 cases is too few to yield either much precision in any parameter estimates or sufficient statistical power for hypothesis tests.
As you mention the possibility of multiple IVs ("...predictors..."), the opportunity for overfitting a model to your data which then fails to generalize to other samples becomes more of a concern.
If you could specify the number and types of variables involved (both IV/s and DV/s), and the intended analytic method (e.g., as cases are censored by death, which possibly might not be due to the condition of interest, perhaps proportional hazards model), then I'm sure you'd get more focused advice as to how confidently you could continue with the proposed sample size.
In a small sample size of 10 patients, it is important to consider the limitations and potential challenges associated with statistical analysis. With such a small sample, it may be difficult to draw robust and generalizable conclusions. Nevertheless, if you still wish to explore the relationship between predictors and disease progression in this limited dataset, you can consider using a simple linear regression model or descriptive statistical analysis.
Descriptive Statistical Analysis: Start by examining summary statistics, such as means, standard deviations, and correlations between variables. This approach can provide initial insights into the relationship between predictors and disease progression. However, it does not account for confounding factors or allow for predictive modeling.
Simple Linear Regression: You can perform a simple linear regression if you have one predictor variable. This model will assess the linear relationship between the predictor and disease progression outcome. Keep in mind that with a sample size of only 10 patients, the results should be interpreted with caution due to limited statistical power and potential overfitting.
It is important to acknowledge that the small sample size greatly limits the reliability and generalizability of any findings. Larger sample sizes are preferred for robust statistical analysis and to account for potential confounding factors.
In this situation, it may be more appropriate to focus on descriptive statistics, case studies, or qualitative analysis to better understand the disease progression in your small sample of patients. Additionally, you could consider combining your data with existing literature or seeking expert opinions to provide context and support your findings.
craft your model with extra care. In particular getting the response distribution right is important. Never use tests for that (e.g. K-S test), but follow the principles in this chapter: https://schmettow.github.io/New_Stats/glm.html
use exact estimation methods, such as MCMC sampling, rather than asymptotic methods, such as max likelihood estimation.