Quantify build-vs-buy training decision

Your organization is preparing to launch a new employee training initiative and must decide among three options: (1) an external vendor's standard package, which is quickest to roll out but cannot be customized and keeps training data in the vendor's database; (2) an external vendor's premium package, which allows customization and offers stronger data security controls but takes longer to implement; (3) an in-house build, which is fully tailored but requires the longest implementation time. Develop a quantitative decision framework that: a) identifies the core KPIs (such as completion rate and performance uplift) and explains how you would estimate the causal incremental effect of training relative to a baseline, including an experiment or quasi-experiment with success metrics and power considerations; b) builds a risk-adjusted NPV model over a horizon $H$ with variables for implementation time $T$, upfront cost $C_0$, annual run cost $C_t$, annual benefit $V_t$, breach probability $p$ and loss $L$, and a discount rate $r$. Provide the exact decision rule or inequality for selecting among the three options, explicitly accounting for value lost during implementation; c) lays out a sensitivity analysis covering which parameters, what ranges, and what stopping rules, plus a pilot plan for updating priors on $V_t$ and $p$; d) using only the ordinal facts that Standard $<$ Premium $<$ Internal on customization and Standard is fastest, justify which option you would choose and identify the observable threshold that would make you switch.

Overview: The question tests skill in quantitative decision analysis, causal inference for experiments, KPI definition, and risk-adjusted financial modeling in the Analytics & Experimentation area, measuring abilities relevant to a Data Scientist making operational trade-offs.