* Futures down: Dow 28 pts, S&P 4 pts, Nasdaq 7.75 pts
By Yashaswini Swamynathan
Oct 6 (Reuters) - U.S. stock index futures were lower on Thursday as improving economic data and comments from Federal Reserve officials suggested monetary policy could be tightened by the end of the year.
* The dollar index rose 0.2 percent as investors await the September jobs report on Friday that will help determine the future path of interest rates.
* A growing number of Fed officials have expressed the need for higher rates as the labor market remains robust and inflation inches towards the central bank's 2 percent target.
* Richmond Fed President Jeffrey Lacker on Wednesday said a strong employment report would bolster the case of a hike sooner than later.
* Wall Street rose on Wednesday, driven by financial and energy stocks.
* A report on weekly jobless claims is due at 8:30 a.m. ET (1230 GMT).
* The Fed is most likely to pull the trigger on rates in December as its November meeting falls days ahead of the U.S. presidential election.
* Traders have priced in a 15.5 percent chance of a change in rates next month, while the odds jump to 60 percent for December, according to the CME Group's FedWatch tool.
* Twitter shares plunged 16 percent to $21 in heavy premarket trading, after technology news website Recode said Disney and Alphabet were not bidding for the company.
* Alnylam dropped 42.2 percent after it abandoned testing its experimental drug for heart failure as trial data showed patients who took the treatment were more likely to die than those who got a placebo.
* Tesla fell 2.1 percent to $204.10 after Goldman Sachs downgraded its stock to "neutral" from "buy".
Futures snapshot at 6:59 a.m. ET:
* Dow e-minis were down 28 points, or 0.15 percent, with 15,698 contracts changing hands.
* S&P 500 e-minis were down 4 points, or 0.19 percent, with 101,010 contracts traded.
* Nasdaq 100 e-minis were down 7.75 points, or 0.16 percent, on volume of 14,534 contracts. (Reporting by Yashaswini Swamynathan in Bengaluru)