If one understands the nature of God and the Fallen World, one understands why Epicurus' words are non sequitur.
First, God cannot, and will not, abbrogate free agency. If evil, poverty, disease, famine exists, it exists for a reason. In some cases it exists because of the wickedness of the people suffering these things. The Gospel of Jesus Christ is meant to lead people out of sin and the effects of sin. In some cases, such as extreme poverty and famine throughout Africa, it is because of the wickedness of the leaders and political systems. When food, medical and other relief from the United States and other countries go to such regions, corrupt political despots rip off the U.S. information and sell it on the black market. God is omnipotent, but this doesn't mean unlimited power, but rather, all powerful. But this isn't the first earth He's created nor is it the first to have fallen. To bring to pass the immortality and eternal life of man, God works under certain restrictions which, if not complied with, would not bring about His desired purposes. In certain cases such as turning to God and prayer, and through repentance and living God's laws, God is able to negate evil and bring about good. If He sends people prophets and they reject them, kill them, stone them or ignore them, God allows them to suffer the consequences. If He destroys the despots and circumvents His own law, eternal justice is denied and God would be unable to retain the respect of His Creation and He becomes captricious, arbitrary and unpredictable. After all, He sends no one to this earth against his or her will. That, too, would be arbitrary and caprcious.
Every man, every animal and everything intelligent existed before this earth was created. The reasons are many and varied, but in some cases extreme suffering and evil is necessary to bring about perfection and eternal life and God's end purposes. When men submit to God, they prosper, but when they submit to Satan, they suffer. I can't explain this in one message, but it's the closest I can come.
Finally, God does not see the ending of human life with our perspective. When innocent victims pass on from this world, they are freed from all pain, all disease and all evil and they are healed and are made to understand their suffering (as we all do) in the context of the Gospel. If men are wicked and cause such suffering, they pass through an excruciating torment in which they are caused to suffer that which they inflicted. This is not done for retribution, but to put things into their proper context so they arrive at an understanding of their own wickedness and evil. But they are their own tormentors, something most don't understand. This isn't to say there's no eternal consequences for being wicked. There are. But we all have to pass through the fire to become fully tempered. In studying Roman history, I became familiar with the suffering that the Romans inflicted on the people of Carthage, Rome's trading competitors. Rome was good at that and they made the Carthaginians suffer their full and sustained wrath. But later I discovered how the Carthaginians murdered their own infants in the fires of Molech and engaged in other dispicable practices. It was thus little surprise to me that their cities were leveled and their fields sowed with salt; also, that the men were put to the sword and their women and children sold into slavery.
The people in Africa who are ravaged by hunger and withering disease have also lived in gross wickedness in many cases. I've spoken to people who have returned to the U.S. from the Peace Corps, and have heard some incredible stories of how these people beat their families, kill their enemies (many times neighbors) and take from others. Their lives won't change until they do. We won't escape, either, as long as we continue in our own iniquities...such as abortions, which is one of the crowning evils of our age.
So with all due respect to Epicurus, he just wasn't plugged into the system, nor did he have any idea what he was talking about.