"based on careful consideration" is correct and is commonly used in written English.
You can use it to express the idea that something was decided after thoughtful consideration of all the available evidence or factors. For example, "The board of directors decided to invest in the new project based on careful consideration of the risks and rewards."
When I was young and naïve, I believed that important people took positions based on careful consideration of the options.
These estimates are based on careful consideration of high volume manufacturing processes.
Decisions regarding the graphical display and design are made based on careful consideration of user needs.
The Crown's position is based on careful consideration of all the relevant factors.
The decision to use a tapered schedule is based on careful consideration of science, adherence, and expense.
It is a deliberative processing model that implies individuals make behavioural decisions based on careful consideration of available information [ 29].
The above-mentioned promising measures for reducing building energy demands are thus recommended for use, and an appropriate U-value should be applied to the opaque parts based on careful considerations.
Different levels of evidence have been recognized, and based on careful compiling and consideration of the available evidence, health care or treatment protocols and directives have been established to promote evidence-based practice.
Given that the 2013 ACC/AHA and the 2014 NICE/UK guidelines lowered the threshold for primary prevention with statins based on careful risk-benefit and cost-effectiveness considerations, 3 4 33 the appropriateness of the much lower sensitivity of the SCORE-based treatment threshold recommended for use in many high-income European countries 1 deserves to be reconsidered.
So if Nan has just paid $5m for Audrey Niffenegger's second novel after the astonishing success of The Time Traveler's Wife, I'd be willing to bet it will be a finely calculated gamble, and one based on a careful consideration of the manuscript.
We chose a final set of 12 biomarkers based on careful integration of univariate and multivariate performance, and analytical considerations, including minimally a three-fold dynamic signal intensity range across tumour samples for all antibodies.
