Align equations within one column
Unless you need a caption, you can obtain the desired layout without a table. Only alignedat, and a shorter code with the spreadlines environment from mathtools:
\documentclass{article}
\usepackage{mathtools}
\usepackage{booktabs}
\begin{document}
\begin{spreadlines}{0.5cm}
\[%
\begin{alignedat}{2}
\toprule
\enspace & \text{Conversion} & &\phantom{ = }\hspace{1.5em}\text{Formula} \\
\midrule
& \text{RR to OR} & \hskip 4.8cm\mbox{OR} & = \cfrac{1-\mathrm{p}_{\textit{non-exposed }}}{1-\mathrm{p}_{\textit{exposed}}}\enspace \\
&\text{d to OR} & \mbox{OR} & = \exp\biggl(\mathrm{d} \cfrac{\pi}{\sqrt{3}}\biggr) \\
& \text{r to d} & \mbox{d} & = \cfrac{2\mathrm{r}}{\sqrt{1-\mathrm{r}^2}} \\
& \text{g to d} & \mbox{d} & = \cfrac{1}{\mathrm{J \left(df \right)}} \times \mathrm{g} \\
\bottomrule
\end{alignedat}
\]%
\end{spreadlines}
\end{document}
Well, one possibility is to change second column c to use three columns rcl and divide your formula into three parts: left part of formula, =, right part of formula.
Please see the following mwe
\documentclass{article}
\usepackage{amsmath}
\usepackage{booktabs}
\begin{document}
\begin{table}
\begin{tabular}{l@{\hskip 4.8cm} rcl} % <===============================
\toprule
\multicolumn{1}{l}{Conversion} & \multicolumn{3}{c}{Formula} \\ % <=====
\midrule
RR to OR & $\mbox{OR}$ & = & $\cfrac{1-\mbox{p}_{\mbox{\textit{non-exposed}}}}{1-\mbox{p}_{\mbox{\textit{exposed}}}}$ \\ \addlinespace[0.5cm] % <================================
d to OR & $\mbox{OR}$ & = & $\exp(\mbox{d} \cfrac{\pi}{\sqrt{3}})$ \\ \addlinespace[0.5cm]
r to d & $\mbox{d}$ & = & $\cfrac{2\mbox{r}}{\sqrt{1-\mbox{r}^2}} $ \\ \addlinespace[0.5cm]
g to d & $\mbox{d}$ & = & $\cfrac{1}{\mbox{J} \left( \mbox{df} \right)} \times \mbox{g} $ \\
% ^^^^^^^^^^ <=======================================
\bottomrule
\end{tabular}
\end{table}
\end{document}
and its result:
